From d5af6f12c187580be5953a0031f5b50b2c1fbcf8 Mon Sep 17 00:00:00 2001 From: mhjensen Date: Fri, 19 Oct 2018 06:43:54 +0200 Subject: [PATCH] deleting unnecessary material --- doc/pub/NeuralNet/html/._NeuralNet-bs000.html | 54 ++-- doc/pub/NeuralNet/html/._NeuralNet-bs001.html | 54 ++-- doc/pub/NeuralNet/html/._NeuralNet-bs002.html | 54 ++-- doc/pub/NeuralNet/html/._NeuralNet-bs003.html | 54 ++-- doc/pub/NeuralNet/html/._NeuralNet-bs004.html | 54 ++-- doc/pub/NeuralNet/html/._NeuralNet-bs005.html | 54 ++-- doc/pub/NeuralNet/html/._NeuralNet-bs006.html | 54 ++-- doc/pub/NeuralNet/html/._NeuralNet-bs007.html | 54 ++-- doc/pub/NeuralNet/html/._NeuralNet-bs008.html | 54 ++-- doc/pub/NeuralNet/html/._NeuralNet-bs009.html | 54 ++-- doc/pub/NeuralNet/html/._NeuralNet-bs010.html | 54 ++-- doc/pub/NeuralNet/html/._NeuralNet-bs011.html | 54 ++-- doc/pub/NeuralNet/html/._NeuralNet-bs012.html | 54 ++-- doc/pub/NeuralNet/html/._NeuralNet-bs013.html | 54 ++-- 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doc/pub/NeuralNet/html/._NeuralNet-bs101.html | 75 +++--- doc/pub/NeuralNet/html/._NeuralNet-bs102.html | 125 ++++----- doc/pub/NeuralNet/html/._NeuralNet-bs103.html | 117 ++++----- doc/pub/NeuralNet/html/._NeuralNet-bs104.html | 142 +++-------- doc/pub/NeuralNet/html/NeuralNet-bs.html | 54 ++-- doc/pub/NeuralNet/html/NeuralNet-reveal.html | 228 ++--------------- .../NeuralNet/html/NeuralNet-solarized.html | 238 +++--------------- doc/pub/NeuralNet/html/NeuralNet.html | 238 +++--------------- doc/pub/NeuralNet/ipynb/NeuralNet.ipynb | 232 ++--------------- .../ipynb/ipynb-NeuralNet-src.tar.gz | Bin 88051 -> 88051 bytes doc/pub/NeuralNet/pdf/NeuralNet-minted.pdf | Bin 664815 -> 626143 bytes doc/src/NeuralNet/NeuralNet.do.txt | 163 +----------- 113 files changed, 2879 insertions(+), 4700 deletions(-) diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs000.html b/doc/pub/NeuralNet/html/._NeuralNet-bs000.html index ddfcae71f..0c296c5a0 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs000.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs000.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -406,7 +398,7 @@ MathJax.Hub.Config({
  • 9
  • 10
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs001.html b/doc/pub/NeuralNet/html/._NeuralNet-bs001.html index de81d371e..3437f1a87 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs001.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs001.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -391,7 +383,7 @@ a weight variable.
  • 10
  • 11
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs002.html b/doc/pub/NeuralNet/html/._NeuralNet-bs002.html index e73bb72be..5a7d876bf 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs002.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs002.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
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  • Gradient Descent
    • +
  • More on GD and cost function
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  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -441,7 +433,7 @@ humanities to life science and medicine.
  • 11
  • 12
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs003.html b/doc/pub/NeuralNet/html/._NeuralNet-bs003.html index dcf0a0514..7433bc433 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs003.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs003.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -406,7 +398,7 @@ methods we discussed earlier.
  • 12
  • 13
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs004.html b/doc/pub/NeuralNet/html/._NeuralNet-bs004.html index 9c745763f..ebf6a3c7d 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs004.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs004.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
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  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
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  • Backpropagation
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  • Gradient Descent
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  • The final parts of the code
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  • Solving the ODE
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  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -398,7 +390,7 @@ to all nodes in the subsequent layer, making this a so-called
  • 13
  • 14
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs005.html b/doc/pub/NeuralNet/html/._NeuralNet-bs005.html index a0dfb186f..df80cc897 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs005.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs005.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -407,7 +399,7 @@ recognition.
  • 14
  • 15
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs006.html b/doc/pub/NeuralNet/html/._NeuralNet-bs006.html index 73eb8cfc7..1ea3e0bd1 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs006.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs006.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -399,7 +391,7 @@ especially well-suited for handwriting and speech recognition.
  • 15
  • 16
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs007.html b/doc/pub/NeuralNet/html/._NeuralNet-bs007.html index 9d5562fd5..9d8096052 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs007.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs007.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -400,7 +392,7 @@ type of NN due the unusual activation functions.
  • 16
  • 17
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs008.html b/doc/pub/NeuralNet/html/._NeuralNet-bs008.html index 1b186864d..77faa1342 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs008.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs008.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -398,7 +390,7 @@ Such networks are often called multilayer perceptrons (MLPs).
  • 17
  • 18
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs009.html b/doc/pub/NeuralNet/html/._NeuralNet-bs009.html index 3ea03c32f..508e66518 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs009.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs009.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -403,7 +395,7 @@ as to not restrict the range of output values.
  • 18
  • 19
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs010.html b/doc/pub/NeuralNet/html/._NeuralNet-bs010.html index 7cdbec57d..8a4eda371 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs010.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs010.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -404,7 +396,7 @@ of the outputs of all neurons in the previous layer.
  • 19
  • 20
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs011.html b/doc/pub/NeuralNet/html/._NeuralNet-bs011.html index 16d32e3f4..be98b9ac7 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs011.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs011.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -433,7 +425,7 @@ is obtained.
  • 20
  • 21
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs012.html b/doc/pub/NeuralNet/html/._NeuralNet-bs012.html index f26003662..5732e72e9 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs012.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs012.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -415,7 +407,7 @@ $$
  • 21
  • 22
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs013.html b/doc/pub/NeuralNet/html/._NeuralNet-bs013.html index b0b7038d1..5d37eacce 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs013.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs013.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -406,7 +398,7 @@ variables are the input values \( x_n \).
  • 22
  • 23
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs014.html b/doc/pub/NeuralNet/html/._NeuralNet-bs014.html index eb4f94e71..d405b7739 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs014.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs014.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -415,7 +407,7 @@ flexibility of a neural network.
  • 23
  • 24
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs015.html b/doc/pub/NeuralNet/html/._NeuralNet-bs015.html index 00c8edb01..55ee3dbf0 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs015.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs015.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -425,7 +417,7 @@ $$
  • 24
  • 25
  • ...
    • -
  • 109
    • +
  • 105
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs016.html b/doc/pub/NeuralNet/html/._NeuralNet-bs016.html index 11a02a8f9..bc3f4581d 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs016.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs016.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -409,7 +401,7 @@ used as input to the activation functions. For each operation
  • 25
  • 26
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs017.html b/doc/pub/NeuralNet/html/._NeuralNet-bs017.html index aef848854..df8aceedb 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs017.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs017.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -403,7 +395,7 @@ for a FFNN to fulfill the universal approximation theorem
  • 26
  • 27
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs018.html b/doc/pub/NeuralNet/html/._NeuralNet-bs018.html index dc8c5a10f..46287989f 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs018.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs018.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -411,7 +403,7 @@ $$
  • 27
  • 28
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs019.html b/doc/pub/NeuralNet/html/._NeuralNet-bs019.html index 10d9e9386..189c0d256 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs019.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs019.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -473,7 +465,7 @@ plt.show()
  • 28
  • 29
  • ...
    • -
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    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs020.html b/doc/pub/NeuralNet/html/._NeuralNet-bs020.html index 056ecf225..6bc393196 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs020.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs020.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -424,7 +416,7 @@ like logistic regression or linear regression and their modifications on the oth
  • 29
  • 30
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs021.html b/doc/pub/NeuralNet/html/._NeuralNet-bs021.html index ebd93e9a6..659318202 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs021.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs021.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
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  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -414,7 +406,7 @@ the potential of being universal approximators.
  • 30
  • 31
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs022.html b/doc/pub/NeuralNet/html/._NeuralNet-bs022.html index e676a8b6e..d666679a6 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs022.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs022.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
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  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
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  • The final parts of the code
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    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
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  • Wrapping it up
    • +
  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -420,7 +412,7 @@ classes.
  • 31
  • 32
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs023.html b/doc/pub/NeuralNet/html/._NeuralNet-bs023.html index 6b78ec10c..eea7ead41 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs023.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs023.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
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  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -424,7 +416,7 @@ $$
  • 32
  • 33
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs024.html b/doc/pub/NeuralNet/html/._NeuralNet-bs024.html index 53be8dcc2..b15b61ad6 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs024.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs024.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
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  • Setting up the code, feed forward part
    • -
  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
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  • Feed forward again
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  • The final parts of the code
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  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -408,7 +400,7 @@ $$
  • 33
  • 34
  • ...
    • -
  • 109
    • +
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  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs025.html b/doc/pub/NeuralNet/html/._NeuralNet-bs025.html index 29491da62..a8afb96d0 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs025.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs025.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
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  • Output
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  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
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  • The final parts of the code
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  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -411,7 +403,7 @@ $$
  • 34
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  • ...
    • -
  • 109
    • +
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  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs026.html b/doc/pub/NeuralNet/html/._NeuralNet-bs026.html index 6ae0ebf5e..08f610ded 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs026.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs026.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
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  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -436,7 +428,7 @@ $$
  • 35
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  • ...
    • -
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    • +
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  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs027.html b/doc/pub/NeuralNet/html/._NeuralNet-bs027.html index ef088d578..3d2cb8d3f 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs027.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs027.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
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  • Estimating errors
  • Creating a simple Deep Neural Net
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  • Feedforward
    • -
  • Result after weighting
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  • Output
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  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
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  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -403,7 +395,7 @@ That is, the error \( \delta_j^L \) is exactly equal to the rate of change of th
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs028.html b/doc/pub/NeuralNet/html/._NeuralNet-bs028.html index e40e694fe..531157c51 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs028.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs028.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
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  • Setting up the code, feed forward part
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  • Gradient Descent
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  • The final parts of the code
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    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
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    • +
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    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -448,7 +440,7 @@ one \( L-1 \) in terms of the errors in the final output layer.
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    • -
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    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs029.html b/doc/pub/NeuralNet/html/._NeuralNet-bs029.html index 39af94d22..52d2ecf9b 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs029.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs029.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
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  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
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  • Gradient Descent
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  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
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  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -418,7 +410,7 @@ We are now ready to set up the algorithm for back propagation and learning the w
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    • -
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    • +
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs030.html b/doc/pub/NeuralNet/html/._NeuralNet-bs030.html index 1c51545ef..81f845bbb 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs030.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs030.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
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  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -462,7 +454,7 @@ Here it is convenient to use stochastic gradient descent (see the examples below
  • 39
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    • -
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    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs031.html b/doc/pub/NeuralNet/html/._NeuralNet-bs031.html index 473fedee8..6cad37323 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs031.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs031.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
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    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -424,7 +416,7 @@ of our network.
  • 40
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  • ...
    • -
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    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs032.html b/doc/pub/NeuralNet/html/._NeuralNet-bs032.html index f28a6f4bc..bde55aac9 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs032.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs032.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -446,7 +438,7 @@ The back propagation equations need now only a small change, namely the definiti
  • 41
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    • -
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    • +
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs033.html b/doc/pub/NeuralNet/html/._NeuralNet-bs033.html index 64c11e975..ab60941fc 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs033.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs033.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -434,7 +426,7 @@ In case we use another activation function than the logistic one, we need to eva
  • 42
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    • -
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    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs034.html b/doc/pub/NeuralNet/html/._NeuralNet-bs034.html index b7eb14900..fcdc8f7b8 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs034.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs034.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
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  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -408,7 +400,7 @@ which in case of the simply binary model reduces to having \( i=j \).
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs035.html b/doc/pub/NeuralNet/html/._NeuralNet-bs035.html index 71e9befe1..2219f3dbd 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs035.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs035.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
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  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
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  • Feed forward again
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  • The final parts of the code
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    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
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  • Wrapping it up
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  • Backpropagation
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  • Gradient Descent
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  • An implementation of a Deep Neural Network
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  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -402,7 +394,7 @@ One can identify a set of key steps when using neural networks to solve supervis
  • 44
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    • -
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    • +
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs036.html b/doc/pub/NeuralNet/html/._NeuralNet-bs036.html index f33b5a40b..7972fa977 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs036.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs036.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
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  • The final parts of the code
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    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
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  • Wrapping it up
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    • +
  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -481,7 +473,7 @@ plt.show()
  • 45
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  • ...
    • -
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    • +
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs037.html b/doc/pub/NeuralNet/html/._NeuralNet-bs037.html index c7ab2aeaf..32aaefdca 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs037.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs037.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -435,7 +427,7 @@ X_train, X_test, Y_train, Y_test = train_tes
  • 46
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  • ...
    • -
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    • +
  • 105
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs038.html b/doc/pub/NeuralNet/html/._NeuralNet-bs038.html index f2d8151c6..5be78f07d 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs038.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs038.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
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  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -432,7 +424,7 @@ which is inspired by probability theory (see logistic regression) and was most c
  • 47
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  • ...
    • -
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    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs039.html b/doc/pub/NeuralNet/html/._NeuralNet-bs039.html index 38295173c..fbf7fde6d 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs039.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs039.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -431,7 +423,7 @@ weights to the output layer.
  • 48
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  • ...
    • -
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    • +
  • 105
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs040.html b/doc/pub/NeuralNet/html/._NeuralNet-bs040.html index 1de83339a..77566ed0f 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs040.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs040.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
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  • Setting up the code, feed forward part
    • -
  • Backpropagation
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  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
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  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -422,7 +414,7 @@ output_bias = np49
  • 50
  • ...
    • -
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    • +
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  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs041.html b/doc/pub/NeuralNet/html/._NeuralNet-bs041.html index b133d453e..dfec677f9 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs041.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs041.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -413,7 +405,7 @@ $$ a_{j}^{L} = \frac{\exp{(z_j^{L})}}
  • 50
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  • ...
    • -
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    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs042.html b/doc/pub/NeuralNet/html/._NeuralNet-bs042.html index c2a2f4587..fbadb1c4b 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs042.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs042.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
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  • Estimating errors
  • Creating a simple Deep Neural Net
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  • Feedforward
    • -
  • Result after weighting
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  • Output
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  • Setting up the code, feed forward part
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  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -461,7 +453,7 @@ predictions = predict(X_train)
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs043.html b/doc/pub/NeuralNet/html/._NeuralNet-bs043.html index b43f51687..29a5bcf7c 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs043.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs043.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -417,7 +409,7 @@ you got the correct label. The probability of category \( c \) is given by the s
  • 52
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  • ...
    • -
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    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs044.html b/doc/pub/NeuralNet/html/._NeuralNet-bs044.html index fa785a6c1..90fddebd1 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs044.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs044.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
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  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
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  • Wrapping it up
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  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
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  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -426,7 +418,7 @@ The various optmization methods, with codes and algorithms, are discussed in o
  • 53
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    • +
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs045.html b/doc/pub/NeuralNet/html/._NeuralNet-bs045.html index cb34f2101..5bd49f3e1 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs045.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs045.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
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  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -419,7 +411,7 @@ calculate the gradient efficently.
  • 54
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  • ...
    • -
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    • +
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  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs046.html b/doc/pub/NeuralNet/html/._NeuralNet-bs046.html index f7b6c6af9..e4a73380a 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs046.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs046.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -500,7 +492,7 @@ lmbd = 0.0155
  • 56
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    • -
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    • +
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs047.html b/doc/pub/NeuralNet/html/._NeuralNet-bs047.html index 353cd30f8..613a5dc46 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs047.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs047.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -406,7 +398,7 @@ Andrew Ng goes through some of these considerations in this 56
  • 57
  • ...
    • -
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    • +
  • 105
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs048.html b/doc/pub/NeuralNet/html/._NeuralNet-bs048.html index d66d4c2b3..79d59fd0b 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs048.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs048.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -499,7 +491,7 @@ being realizations of this object with different hyperparameters. An implementat
  • 57
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    • -
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    • +
  • 105
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs049.html b/doc/pub/NeuralNet/html/._NeuralNet-bs049.html index e32de07a8..f71738a7e 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs049.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs049.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
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  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
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  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -421,7 +413,7 @@ test_predict = dnn58
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs050.html b/doc/pub/NeuralNet/html/._NeuralNet-bs050.html index e1e9eaded..df2fbff1d 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs050.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs050.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -419,7 +411,7 @@ DNN_numpy = np.
  • 59
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    • -
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs051.html b/doc/pub/NeuralNet/html/._NeuralNet-bs051.html index 799cf8a88..11f161b54 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs051.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs051.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -428,7 +420,7 @@ plt.show()
  • 60
  • 61
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs052.html b/doc/pub/NeuralNet/html/._NeuralNet-bs052.html index bf2b566f0..02f6960cd 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs052.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs052.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -425,7 +417,7 @@ DNN_scikit = np
  • 61
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    • -
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    • +
  • 105
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs053.html b/doc/pub/NeuralNet/html/._NeuralNet-bs053.html index 0010c5a4f..d11d46492 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs053.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs053.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -428,7 +420,7 @@ plt.show()
  • 62
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  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs054.html b/doc/pub/NeuralNet/html/._NeuralNet-bs054.html index 7470337de..36a58f392 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs054.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs054.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -401,7 +393,7 @@ NumPy arrays.
  • 63
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    • -
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    • +
  • 105
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs055.html b/doc/pub/NeuralNet/html/._NeuralNet-bs055.html index 5c345ef38..7c91ede4e 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs055.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs055.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -431,7 +423,7 @@ and/or if you use anaconda, just write (or install from the graphical use
  • 64
  • 65
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs056.html b/doc/pub/NeuralNet/html/._NeuralNet-bs056.html index 2b57e12cd..3cb5d0094 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs056.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs056.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -452,7 +444,7 @@ X_train, X_test, Y_train, Y_test = train_tes
  • 65
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  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs057.html b/doc/pub/NeuralNet/html/._NeuralNet-bs057.html index 27f07c6ed..45127b18d 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs057.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs057.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -531,7 +523,7 @@ MathJax.Hub.Config({
  • 66
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  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs058.html b/doc/pub/NeuralNet/html/._NeuralNet-bs058.html index 0ea92c54e..af0a7130a 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs058.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs058.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -464,7 +456,7 @@ writer.add_graph(tf67
  • 68
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs059.html b/doc/pub/NeuralNet/html/._NeuralNet-bs059.html index f16661bde..6b3da62f1 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs059.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs059.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
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  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -485,7 +477,7 @@ plt.show()
  • 68
  • 69
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs060.html b/doc/pub/NeuralNet/html/._NeuralNet-bs060.html index 4d2c5638f..8eadb921c 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs060.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs060.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
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  • An implementation of a Deep Neural Network
    • -
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    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -415,7 +407,7 @@ learn at widely different speeds
  • 69
  • 70
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs061.html b/doc/pub/NeuralNet/html/._NeuralNet-bs061.html index e4c2f4f32..77bd15e0b 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs061.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs061.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
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  • Setting up the code, feed forward part
    • -
  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
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  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -416,7 +408,7 @@ better than the logistic function in deep networks).
  • 70
  • 71
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs062.html b/doc/pub/NeuralNet/html/._NeuralNet-bs062.html index fa2d57b53..01338cb55 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs062.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs062.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -422,7 +414,7 @@ fast to compute).
  • 71
  • 72
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs063.html b/doc/pub/NeuralNet/html/._NeuralNet-bs063.html index f8aefc426..a53731217 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs063.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs063.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
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  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -413,7 +405,7 @@ $$
  • 72
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  • ...
    • -
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    • +
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs064.html b/doc/pub/NeuralNet/html/._NeuralNet-bs064.html index d20879a62..e81c30225 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs064.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs064.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
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  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
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  • The final parts of the code
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  • And adding Back propagation
    • +
  • Solving the ODE
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  • Using neural network
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  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -406,7 +398,7 @@ bootstrap to evaluate other activation functions.
  • 73
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  • ...
    • -
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    • +
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs065.html b/doc/pub/NeuralNet/html/._NeuralNet-bs065.html index dfb40a9c2..ee9e11a31 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs065.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs065.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
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  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
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  • The final parts of the code
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  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
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  • Wrapping it up
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  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -428,7 +420,7 @@ supervised learning.
  • 74
  • 75
  • ...
    • -
  • 109
    • +
  • 105
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs066.html b/doc/pub/NeuralNet/html/._NeuralNet-bs066.html index 1e69e0d38..30575d9f4 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs066.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs066.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
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  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
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  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -412,7 +404,7 @@ Some of these remarks are particular to DNNs, others are shared by all supervise
  • 75
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  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs067.html b/doc/pub/NeuralNet/html/._NeuralNet-bs067.html index 3c7e90fa6..4ac465f8f 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs067.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs067.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
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  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
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  • The final parts of the code
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    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
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  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
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  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -416,7 +408,7 @@ and the slides of 76
  • 77
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs068.html b/doc/pub/NeuralNet/html/._NeuralNet-bs068.html index d7b435e61..3112352fd 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs068.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs068.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -414,7 +406,7 @@ would quickly lead to possible overfitting.
  • 77
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  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs069.html b/doc/pub/NeuralNet/html/._NeuralNet-bs069.html index c07eae397..a097400f2 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs069.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs069.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
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  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
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  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -426,7 +418,7 @@ dimension.
  • 78
  • 79
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs070.html b/doc/pub/NeuralNet/html/._NeuralNet-bs070.html index c97306768..8912ccbb0 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs070.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs070.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
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  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
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  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
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  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -409,7 +401,7 @@ A simple CNN for image classification could have the architecture:
  • 79
  • 80
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs071.html b/doc/pub/NeuralNet/html/._NeuralNet-bs071.html index 6f036636b..d3a258cb5 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs071.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs071.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
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  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -405,7 +397,7 @@ are consistent with the labels in the training set for each image.
  • 80
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  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs072.html b/doc/pub/NeuralNet/html/._NeuralNet-bs072.html index 2cc1fbb00..0d69841c7 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs072.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs072.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
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  • Estimating errors
  • Creating a simple Deep Neural Net
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  • Feedforward
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  • Result after weighting
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  • Output
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  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -407,7 +399,7 @@ and the slides of 81
  • 82
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs073.html b/doc/pub/NeuralNet/html/._NeuralNet-bs073.html index ffe6cc5c9..10eab5a52 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs073.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs073.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
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  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
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  • The final parts of the code
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  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
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  • Setting up the code, feed forward part
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  • An implementation of a Deep Neural Network
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  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -402,7 +394,7 @@ matrices, typically 1 for each color dimension (Red, Green, Blue).
  • 82
  • 83
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs074.html b/doc/pub/NeuralNet/html/._NeuralNet-bs074.html index b45367c01..3db00e542 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs074.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs074.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
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  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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    • -
  • Solving the ODE
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  • Using neural network
    • -
  • Using a deep neural network
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  • An implementation of a Deep Neural Network
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    • +
  • Solving the ODE
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  • Using neural network
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  • Using a deep neural network
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  • Wrapping it up
    • @@ -398,7 +390,7 @@ $$
  • 83
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  • ...
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs075.html b/doc/pub/NeuralNet/html/._NeuralNet-bs075.html index 72fda2090..5b41bdb34 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs075.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs075.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
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    • -
  • Solving the ODE
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  • Using neural network
    • -
  • Using a deep neural network
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  • An implementation of a Deep Neural Network
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    • +
  • Solving the ODE
    • +
  • Using neural network
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  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -404,7 +396,7 @@ single neuron in the first hidden layer.
  • 84
  • 85
  • ...
    • -
  • 109
    • +
  • 105
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs076.html b/doc/pub/NeuralNet/html/._NeuralNet-bs076.html index dc0bcc4b5..a6bacf9a6 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs076.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs076.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
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  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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    • -
  • Solving the ODE
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  • Using neural network
    • -
  • Using a deep neural network
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  • An implementation of a Deep Neural Network
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  • The final parts of the code
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    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -402,7 +394,7 @@ fixed, and known as a 85
  • 86
  • ...
    • -
  • 109
    • +
  • 105
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs077.html b/doc/pub/NeuralNet/html/._NeuralNet-bs077.html index b1edc81d0..09bebf34e 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs077.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs077.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
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  • Setting up the code, feed forward part
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  • Backpropagation
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
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  • The final parts of the code
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  • And adding Back propagation
    • -
  • Solving the ODE
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  • Using neural network
    • -
  • Using a deep neural network
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  • Wrapping it up
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  • Setting up the code, feed forward part
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
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    • +
  • Solving the ODE
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  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -408,7 +400,7 @@ layer.
  • 86
  • 87
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs078.html b/doc/pub/NeuralNet/html/._NeuralNet-bs078.html index f455a85a1..c13d902d5 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs078.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs078.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
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  • Feedforward
    • -
  • Result after weighting
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  • Output
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  • Setting up the code, feed forward part
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  • Gradient Descent
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  • More on GD and cost function
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    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
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  • Wrapping it up
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
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  • The final parts of the code
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  • And adding Back propagation
    • +
  • Solving the ODE
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  • Using neural network
    • +
  • Using a deep neural network
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  • Wrapping it up
    • @@ -401,7 +393,7 @@ classification.
  • 87
  • 88
  • ...
    • -
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    • +
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  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs079.html b/doc/pub/NeuralNet/html/._NeuralNet-bs079.html index cc3e2fe20..2caa7d852 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs079.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs079.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
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  • Feedforward
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  • Result after weighting
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  • Output
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  • Setting up the code, feed forward part
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  • Gradient Descent
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  • More on GD and cost function
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  • An implementation of a Deep Neural Network
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    • -
  • Solving the ODE
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  • Using neural network
    • -
  • Using a deep neural network
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  • Wrapping it up
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  • Solving the ODE
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  • Using neural network
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  • Using a deep neural network
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  • Wrapping it up
    • @@ -434,7 +426,7 @@ plt.show()
  • 88
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    • -
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    • +
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs080.html b/doc/pub/NeuralNet/html/._NeuralNet-bs080.html index 813ed2ac9..a0ed1ac3e 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs080.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs080.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -406,7 +398,7 @@ X_train, X_test, Y_train, Y_test = train_tes
  • 89
  • 90
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs081.html b/doc/pub/NeuralNet/html/._NeuralNet-bs081.html index 2fe02e70a..790bf815a 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs081.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs081.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -535,7 +527,7 @@ class ConvolutionalNeuralNetworkTensorflow:
  • 90
  • 91
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs082.html b/doc/pub/NeuralNet/html/._NeuralNet-bs082.html index 7566455ed..b2adef723 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs082.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs082.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -421,7 +413,7 @@ CNN_tf = np.91
  • 92
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs083.html b/doc/pub/NeuralNet/html/._NeuralNet-bs083.html index 1241709bb..f848e5ade 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs083.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs083.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -425,7 +417,7 @@ plt.show()
  • 92
  • 93
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs084.html b/doc/pub/NeuralNet/html/._NeuralNet-bs084.html index a9b4a6283..eea852e9c 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs084.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs084.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -429,7 +421,7 @@ lmbd_vals = np.
  • 93
  • 94
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs085.html b/doc/pub/NeuralNet/html/._NeuralNet-bs085.html index 56c43a35d..4b235b1f1 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs085.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs085.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -411,7 +403,7 @@ MathJax.Hub.Config({
  • 94
  • 95
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs086.html b/doc/pub/NeuralNet/html/._NeuralNet-bs086.html index f4e3e342e..422a5bffa 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs086.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs086.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -425,7 +417,7 @@ plt.show()
  • 95
  • 96
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs087.html b/doc/pub/NeuralNet/html/._NeuralNet-bs087.html index 233a4f3e7..a0b7e5007 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs087.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs087.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -395,7 +387,7 @@ MathJax.Hub.Config({
  • 96
  • 97
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs088.html b/doc/pub/NeuralNet/html/._NeuralNet-bs088.html index 908b5922f..733e3b52e 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs088.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs088.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -414,7 +406,7 @@ them and see how the neural network performs.
  • 97
  • 98
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs089.html b/doc/pub/NeuralNet/html/._NeuralNet-bs089.html index c2e377031..f78f8ee6c 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs089.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs089.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -421,7 +413,7 @@ represents the weights to each neuron.
  • 98
  • 99
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs090.html b/doc/pub/NeuralNet/html/._NeuralNet-bs090.html index 10131f1e9..9dfbca8d1 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs090.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs090.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -407,7 +399,7 @@ $$
  • 99
  • 100
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs091.html b/doc/pub/NeuralNet/html/._NeuralNet-bs091.html index affb277af..4216aec1e 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs091.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs091.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -416,7 +408,7 @@ is fulfilled as best as possible.
  • 100
  • 101
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs092.html b/doc/pub/NeuralNet/html/._NeuralNet-bs092.html index 39d3ae459..b499e91b6 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs092.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs092.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -437,7 +429,7 @@ $$
  • 101
  • 102
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs093.html b/doc/pub/NeuralNet/html/._NeuralNet-bs093.html index c54af6cb3..daa78f4be 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs093.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs093.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -383,6 +375,8 @@ painless. For simplicity, we assume that the input is an array \( \hat{x}= (x_1, \dots, x_N) \) with \( N \) elements. It is at these points the neural network should find \( P \) such that it fulfills (19). +All the ingredients discussed earlier, from the activation function, hidden layers and their weights, biases etc +are included below.

    @@ -410,7 +404,7 @@ network should find \( P \) such that it fulfills 102

  • 103
  • ...
    • -
  • 109
    • +
  • 105
  • »
    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs094.html b/doc/pub/NeuralNet/html/._NeuralNet-bs094.html index 99244eaac..2afa599f6 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs094.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs094.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -363,35 +355,54 @@ MathJax.Hub.Config({ -

    Feedforward

    - +

    Setting up the code, feed forward part

    -First, a feedforward of the inputs must be done. This means that \( \hat{x} \) -must be passed through an input layer, a hidden layer and a output - layer. The input layer in this case, does not need to process the - data any further. The input layer will consist of \( N_{\mathrm{input} } \) - neurons, passing its element to each neuron in the hidden layer. The - number of neurons in the hidden layer will be \( N_{\mathrm{hidden} } \). -

    -For the \( i \)-th in the hidden layer with weight \( w_i^{\mathrm{hidden} } \) -and bias \( b_i^{\mathrm{hidden} } \), the weighting from the \( j \)-th neuron -at the input layer is: + +

    # Note that we use the  numpy wrapper for Autograd (see the gradient descent  slides)
+import autograd.numpy as np
+from autograd import grad, elementwise_grad
+import autograd.numpy.random as npr
+from matplotlib import pyplot as plt
 
-$$
-\begin{aligned}
-z_{i,j}^{\mathrm{hidden}} &= b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}}x_j \\
-&= 
-\begin{pmatrix}
-b_i^{\mathrm{hidden}} & w_i^{\mathrm{hidden}}
-\end{pmatrix}
-\begin{pmatrix}
-1 \\
-x_j
-\end{pmatrix} 
-\end{aligned}
-$$
+def sigmoid(z):
+    return 1/(1 + np.exp(-z))
 
+def neural_network(params, x):
+    
+    # Find the weights (including and biases) for the hidden and output layer.
+    # Assume that params is a list of parameters for each layer. 
+    # The biases are the first element for each array in params, 
+    # and the weights are the remaning elements in each array in params.   
+    
+    w_hidden = params[0]
+    w_output = params[1]
+
+    # Assumes input x being an one-dimensional array
+    num_values = np.size(x)
+    x = x.reshape(-1, num_values)
+    
+    # Assume that the input layer does nothing to the input x
+    x_input = x
+
+    ## Hidden layer:
+    
+    # Add a row of ones to include bias
+    x_input = np.concatenate((np.ones((1,num_values)), x_input ), axis = 0)
+    
+    z_hidden = np.matmul(w_hidden, x_input)
+    x_hidden = sigmoid(z_hidden)
+
+    ## Output layer:
+    
+    # Include bias:
+    x_hidden = np.concatenate((np.ones((1,num_values)), x_hidden ), axis = 0)
+
+    z_output = np.matmul(w_output, x_hidden)
+    x_output = z_output
+
+    return x_output
+

    @@ -418,7 +429,7 @@ $$

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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs095.html b/doc/pub/NeuralNet/html/._NeuralNet-bs095.html index 7a2b19125..e69a3c7b9 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs095.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs095.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -361,41 +353,62 @@ MathJax.Hub.Config({

     

     

     

    - + -

    Result after weighting

    +

    Backpropagation

    -The result after weighting the input at the \( i \)-th hidden neuron can be written as a vector: +Now that the feedforward can be done, the next step is to decide how the +parameters should change such that they minimize the cost function. + +

    +Recall that the chosen cost function for this problem is + $$ -\begin{aligned} -\hat{z}_{i}^{\mathrm{hidden}} &= \Big( b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}}x_1 , \ b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}} x_2, \ \dots \, , \ b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}} x_N\Big) \\ -&= -\begin{pmatrix} - b_i^{\mathrm{hidden}} & w_i^{\mathrm{hidden}} -\end{pmatrix} -\begin{pmatrix} -1 & 1 & \dots & 1 \\ -x_1 & x_2 & \dots & x_N -\end{pmatrix} \\ -&= \hat{p}_{i, \mathrm{hidden}}^T X -\end{aligned} +c(x, P) = \sum_i \big(g_t'(x_i, P) - ( -\gamma g_t(x_i, P) \big)^2 $$

    -It is the vector \( \hat{p}_{i, \mathrm{hidden}}^T \) that defines each row -in \( P_{\mathrm{hidden} } \), which contains the weights for the neural -network to minimize according to (19). +In order to minimize it, an optimalization method must be chosen.

    -After having found \( \hat{z}_{i}^{\mathrm{hidden}} \) for every neuron \( i \) -in the hidden layer, the vector will be sent to an activation function -\( a_i(\hat{z}) \). In this example, the sigmoid function has been used: +Here, gradient descent with a constant step size has been chosen. -$$ -f(z) = \frac{1}{1 + \exp{(-z)}}. -$$ +

    +Before looking at the gradient descent method, let us set up the cost +function along with the right ride of the ODE and trial solution. +

    + + +

    # The trial solution using the deep neural network:
+def g_trial(x,params, g0 = 10):
+    return g0 + x*neural_network(params,x)
+
+# The right side of the ODE:
+def g(x, g_trial, gamma = 2):
+    return -gamma*g_trial
+
+# The cost function:
+def cost_function(P, x):
+    
+    # Evaluate the trial function with the current parameters P
+    g_t = g_trial(x,P)
+    
+    # Find the derivative w.r.t x of the neural network
+    d_net_out = elementwise_grad(neural_network,1)(P,x) 
+    
+    # Find the derivative w.r.t x of the trial function
+    d_g_t = elementwise_grad(g_trial,0)(x,P)  
+    
+    # The right side of the ODE 
+    func = g(x, g_t)
+
+    err_sqr = (d_g_t - func)**2
+    cost_sum = np.sum(err_sqr)
+    
+    return cost_sum
+

    @@ -421,8 +434,6 @@ $$

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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs096.html b/doc/pub/NeuralNet/html/._NeuralNet-bs096.html index 81744050f..4458d483f 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs096.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs096.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -363,63 +355,31 @@ MathJax.Hub.Config({ -

    Output

    +

    Gradient Descent

    -The output $\hat{x}_i^{\mathrm{hidden}}$from each \( i \)-th hidden neuron is: +The idea of the gradient descent algorithm is to update parameters in +direction where the cost function decreases goes to a minimum. + +

    +In general, the update of some parameters \( \hat{\omega} \) given a cost +function defined by some weights \( \hat{\omega} \), \( c(x, \hat{\omega}) \), +goes as follows: $$ -\hat{x}_i^{\mathrm{hidden} } = f\big( \hat{z}_{i}^{\mathrm{hidden}} \big). +\hat{\omega}_{\mathrm{new} } = \hat{\omega} - \lambda \nabla_{\hat{\omega}} c(x, \hat{\omega}), $$

    -The outputs \( \hat{x}_i^{\mathrm{hidden} } \) are then sent to the output layer. +for a number of iterations or until \( \big|\big| \hat{\omega}_{\mathrm{new} } - \hat{\omega} \big|\big| \) +is smaller than some +given tolerance.

    -The output layer consist of one neuron in this case, and combines the -output from each of the neurons in the hidden layers. The output layer -combines the results from the hidden layer using some weights \( -w_i^{\mathrm{output}} \) and biases \( b_i^{\mathrm{output}} \). In this case, -it is assumes that the number of neurons in the output layer is one. - -

    -The procedure of weigthing the output neuron \( j \) in the hidden layer -to the \( i \)-th neuron in the output layer is similar as for the hidden -layer described previously. - -$$ -\begin{aligned} -z_{1,j}^{\mathrm{output}} & = -\begin{pmatrix} -b_1^{\mathrm{output}} & \hat{w}_1^{\mathrm{output}} -\end{pmatrix} -\begin{pmatrix} -1 \\ -\hat{x}_j^{\mathrm{hidden}} -\end{pmatrix} -\end{aligned} -$$ - -

    -Expressing \( z_{1,j}^{\mathrm{output}} \) as a vector gives the following procedure of weighting the inputs from the hidden layer: - -$$ -\hat{z}_{1}^{\mathrm{output}} = -\begin{pmatrix} -b_1^{\mathrm{output}} & \hat{w}_1^{\mathrm{output}} -\end{pmatrix} -\begin{pmatrix} -1 & 1 & \dots & 1 \\ -\hat{x}_1^{\mathrm{hidden}} & \hat{x}_2^{\mathrm{hidden}} & \dots & \hat{x}_N^{\mathrm{hidden}} -\end{pmatrix} -$$ - -

    -In this case we seek a continous range of values since we are -approximating a function. This means that after computing -\( \hat{z}_{1}^{\mathrm{output}} \) the neural network has finished its -feedforward step, and \( \hat{z}_{1}^{\mathrm{output}} \) is the final -output of the network. +The value of \( \lambda \) decides how large steps the algorithm must take +in the direction of $ \nabla_{\hat{\omega}} c(x, \hat{\omega})$. The +notatation \( \nabla_{\hat{\omega}} \) denotes the gradient with respect to +the elements in \( \hat{\omega} \).

    @@ -445,9 +405,6 @@ output of the network.

  • 103
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs097.html b/doc/pub/NeuralNet/html/._NeuralNet-bs097.html index df1409bf4..e406304cc 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs097.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs097.html @@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source ('Reformulating the problem', 2, None, '___sec90'), ('Estimating errors', 2, None, '___sec91'), ('Creating a simple Deep Neural Net', 2, None, '___sec92'), - ('Feedforward', 2, None, '___sec93'), - ('Result after weighting', 2, None, '___sec94'), - ('Output', 2, None, '___sec95'), - ('Setting up the code, feed forward part', 2, None, '___sec96'), - ('Backpropagation', 2, None, '___sec97'), - ('Gradient Descent', 2, None, '___sec98'), - ('More on GD and cost function', 2, None, '___sec99'), + ('Setting up the code, feed forward part', 2, None, '___sec93'), + ('Backpropagation', 2, None, '___sec94'), + ('Gradient Descent', 2, None, '___sec95'), + ('More on GD and cost function', 2, None, '___sec96'), ('An implementation of a Deep Neural Network', 2, None, - '___sec100'), - ('Feed forward again', 2, None, '___sec101'), - ('The final parts of the code', 2, None, '___sec102'), - ('And adding Back propagation', 2, None, '___sec103'), - ('Solving the ODE', 2, None, '___sec104'), - ('Using neural network', 2, None, '___sec105'), - ('Using a deep neural network', 2, None, '___sec106'), - ('Wrapping it up', 2, None, '___sec107')]} + '___sec97'), + ('The final parts of the code', 2, None, '___sec98'), + ('And adding Back propagation', 2, None, '___sec99'), + ('Solving the ODE', 2, None, '___sec100'), + ('Using neural network', 2, None, '___sec101'), + ('Using a deep neural network', 2, None, '___sec102'), + ('Wrapping it up', 2, None, '___sec103')]} end of tocinfo --> @@ -333,21 +329,17 @@ MathJax.Hub.Config({
  • Reformulating the problem
  • Estimating errors
  • Creating a simple Deep Neural Net
    • -
  • Feedforward
    • -
  • Result after weighting
    • -
  • Output
    • -
  • Setting up the code, feed forward part
    • -
  • Backpropagation
    • -
  • Gradient Descent
    • -
  • More on GD and cost function
    • -
  • An implementation of a Deep Neural Network
    • -
  • Feed forward again
    • -
  • The final parts of the code
    • -
  • And adding Back propagation
    • -
  • Solving the ODE
    • -
  • Using neural network
    • -
  • Using a deep neural network
    • -
  • Wrapping it up
    • +
  • Setting up the code, feed forward part
    • +
  • Backpropagation
    • +
  • Gradient Descent
    • +
  • More on GD and cost function
    • +
  • An implementation of a Deep Neural Network
    • +
  • The final parts of the code
    • +
  • And adding Back propagation
    • +
  • Solving the ODE
    • +
  • Using neural network
    • +
  • Using a deep neural network
    • +
  • Wrapping it up
    • @@ -363,53 +355,67 @@ MathJax.Hub.Config({ -

    Setting up the code, feed forward part

    +

    More on GD and cost function

    + +

    +In our case, we have to minimize the cost function \( c(x, P) \) with +respect to the two sets of weights and bisases, that is for the hidden +layer \( P_{\mathrm{hidden} } \) and for the ouput layer \( P_{\mathrm{output} +} \) . + +

    +This means that \( P_{\mathrm{hidden} } \) and \( P_{\mathrm{output} } \) is +updated by + +$$ +\begin{align} +P_{\mathrm{hidden},\mathrm{new}} &= P_{\mathrm{hidden}} - \lambda \nabla_{P_{\mathrm{hidden}}} c(x, P) +\tag{20}\\ +P_{\mathrm{output},\mathrm{new}} &= P_{\mathrm{output}} - \lambda \nabla_{P_{\mathrm{output}}} c(x, P) +\tag{21} +\end{align} +$$ + +

    +This might look like a cumberstone to set up the correct expression +for finding the gradients. Luckily, Autograd comes to the rescue. +

    -

    # Note that we use the  numpy wrapper for Autograd (see the gradient descent  slides)
-import autograd.numpy as np
-from autograd import grad, elementwise_grad
-import autograd.numpy.random as npr
-from matplotlib import pyplot as plt
-
-def sigmoid(z):
-    return 1/(1 + np.exp(-z))
-
-def neural_network(params, x):
+
    def solve_ode_neural_network(x, num_neurons_hidden, num_iter, lmb):
+    ## Set up initial weigths and biases 
     
-    # Find the weights (including and biases) for the hidden and output layer.
-    # Assume that params is a list of parameters for each layer. 
-    # The biases are the first element for each array in params, 
-    # and the weights are the remaning elements in each array in params.   
-    
-    w_hidden = params[0]
-    w_output = params[1]
+    # For the hidden layer
+    p0 = npr.randn(num_neurons_hidden, 2 ) 
 
-    # Assumes input x being an one-dimensional array
-    num_values = np.size(x)
-    x = x.reshape(-1, num_values)
-    
-    # Assume that the input layer does nothing to the input x
-    x_input = x
+    # For the output layer
+    p1 = npr.randn(1, num_neurons_hidden + 1 ) # +1 since bias is included
 
-    ## Hidden layer:
-    
-    # Add a row of ones to include bias
-    x_input = np.concatenate((np.ones((1,num_values)), x_input ), axis = 0)
-    
-    z_hidden = np.matmul(w_hidden, x_input)
-    x_hidden = sigmoid(z_hidden)
+    P = [p0, p1]
 
-    ## Output layer:
+    print('Initial cost: %g'%cost_function(P, x))
     
-    # Include bias:
-    x_hidden = np.concatenate((np.ones((1,num_values)), x_hidden ), axis = 0)
+    ## Start finding the optimal weigths using gradient descent
+    
+    # Find the Python function that represents the gradient of the cost function
+    # w.r.t the 0-th input argument -- that is the weights and biases in the hidden and output layer
+    cost_function_grad = grad(cost_function,0)
+    
+    # Let the update be done num_iter times
+    for i in range(num_iter):
+        # Evaluate the gradient at the current weights and biases in P. 
+        # The cost_grad consist now of two arrays; 
+        # one for the gradient w.r.t P_hidden and 
+        # one for the gradient w.r.t P_output
+        cost_grad =  cost_function_grad(P, x)
+    
+        P[0] = P[0] - lmb * cost_grad[0]
+        P[1] = P[1] - lmb * cost_grad[1]
 
-    z_output = np.matmul(w_output, x_hidden)
-    x_output = z_output
-
-    return x_output
+    print('Final cost: %g'%cost_function(P, x))
+    
+    return P
 
    
 
    
 
    
@@ -434,10 +440,6 @@ MathJax.Hub.Config({
   
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    • 
   
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-  
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-  
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-  
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    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs098.html b/doc/pub/NeuralNet/html/._NeuralNet-bs098.html
index 9bdb40cbc..ef5e97c8e 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs098.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs098.html
@@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source
               ('Reformulating the problem', 2, None, '___sec90'),
               ('Estimating errors', 2, None, '___sec91'),
               ('Creating a simple Deep Neural Net', 2, None, '___sec92'),
-              ('Feedforward', 2, None, '___sec93'),
-              ('Result after weighting', 2, None, '___sec94'),
-              ('Output', 2, None, '___sec95'),
-              ('Setting up the code, feed forward part', 2, None, '___sec96'),
-              ('Backpropagation', 2, None, '___sec97'),
-              ('Gradient Descent', 2, None, '___sec98'),
-              ('More on GD and cost function', 2, None, '___sec99'),
+              ('Setting up the code, feed forward part', 2, None, '___sec93'),
+              ('Backpropagation', 2, None, '___sec94'),
+              ('Gradient Descent', 2, None, '___sec95'),
+              ('More on GD and cost function', 2, None, '___sec96'),
               ('An implementation of a Deep Neural Network',
                2,
                None,
-               '___sec100'),
-              ('Feed forward again', 2, None, '___sec101'),
-              ('The final parts of the code', 2, None, '___sec102'),
-              ('And adding Back propagation', 2, None, '___sec103'),
-              ('Solving the ODE', 2, None, '___sec104'),
-              ('Using neural network', 2, None, '___sec105'),
-              ('Using a deep neural network', 2, None, '___sec106'),
-              ('Wrapping it up', 2, None, '___sec107')]}
+               '___sec97'),
+              ('The final parts of the code', 2, None, '___sec98'),
+              ('And adding Back propagation', 2, None, '___sec99'),
+              ('Solving the ODE', 2, None, '___sec100'),
+              ('Using neural network', 2, None, '___sec101'),
+              ('Using a deep neural network', 2, None, '___sec102'),
+              ('Wrapping it up', 2, None, '___sec103')]}
 end of tocinfo -->
 
 
@@ -333,21 +329,17 @@ MathJax.Hub.Config({
       
  • Reformulating the problem
    • 
       
  • Estimating errors
    • 
       
  • Creating a simple Deep Neural Net
    • 
-      
  • Feedforward
    • 
-      
  • Result after weighting
    • 
-      
  • Output
    • 
-      
  • Setting up the code, feed forward part
    • 
-      
  • Backpropagation
    • 
-      
  • Gradient Descent
    • 
-      
  • More on GD and cost function
    • 
-      
  • An implementation of a Deep Neural Network
    • 
-      
  • Feed forward again
    • 
-      
  • The final parts of the code
    • 
-      
  • And adding Back propagation
    • 
-      
  • Solving the ODE
    • 
-      
  • Using neural network
    • 
-      
  • Using a deep neural network
    • 
-      
  • Wrapping it up
    • 
+      
  • Setting up the code, feed forward part
    • 
+      
  • Backpropagation
    • 
+      
  • Gradient Descent
    • 
+      
  • More on GD and cost function
    • 
+      
  • An implementation of a Deep Neural Network
    • 
+      
  • The final parts of the code
    • 
+      
  • And adding Back propagation
    • 
+      
  • Solving the ODE
    • 
+      
  • Using neural network
    • 
+      
  • Using a deep neural network
    • 
+      
  • Wrapping it up
    • 
 
         
       
@@ -363,60 +355,19 @@ MathJax.Hub.Config({
 
 
 
-
    Backpropagation 
    
+
    An implementation of a Deep Neural Network 
    
 
 
    
-Now that feedforward can be done, the next step is to decide how the
-parameters should change such that they minimize the cost function.
+As previously stated, a Deep Neural Network (DNN) follows the same
+concept of a neural network, but having more than one hidden
+layer. Suppose that the network has \( N_{\mathrm{hidden}} \) hidden layers
+where the \( l \)-th layer has \( N_{\mathrm{hidden}}^{(l)} \) neurons. The
+input is still assumed to be an array of size \( 1 \times N \). The
+network must now try to optimalize its output with respect to the
+collection of weigths and biases \( P = \big\{P_{\mathrm{input} }, \
+P_{\mathrm{hidden} }^{(1)}, \ P_{\mathrm{hidden} }^{(2)}, \ \dots , \
+P_{\mathrm{hidden} }^{(N_{\mathrm{hidden}})}, \ P_{\mathrm{output} }\big\} \).
 
-
    
-Recall that the chosen cost function for this problem is 
-
-$$
-c(x, P) = \sum_i  \big(g_t'(x_i, P) - ( -\gamma g_t(x_i, P) \big)^2
-$$
-
-
    
-In order to minimize it, an optimalization method must be chosen.
-
-
    
-Here, gradient descent with a constant step size has been chosen.
-
-
    
-Before looking at the gradient descent method, let us set up the cost
-function along with the right ride of the ODE and trial solution.
-
-
    
-
-
-
    # The trial solution using the deep neural network:
-def g_trial(x,params, g0 = 10):
-    return g0 + x*neural_network(params,x)
-
-# The right side of the ODE:
-def g(x, g_trial, gamma = 2):
-    return -gamma*g_trial
-
-# The cost function:
-def cost_function(P, x):
-    
-    # Evaluate the trial function with the current parameters P
-    g_t = g_trial(x,P)
-    
-    # Find the derivative w.r.t x of the neural network
-    d_net_out = elementwise_grad(neural_network,1)(P,x) 
-    
-    # Find the derivative w.r.t x of the trial function
-    d_g_t = elementwise_grad(g_trial,0)(x,P)  
-    
-    # The right side of the ODE 
-    func = g(x, g_t)
-
-    err_sqr = (d_g_t - func)**2
-    cost_sum = np.sum(err_sqr)
-    
-    return cost_sum
-
    
 
    
 
    
 
@@ -439,11 +390,6 @@ function along with the right ride of the ODE and trial solution.
   
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diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs099.html b/doc/pub/NeuralNet/html/._NeuralNet-bs099.html
index 6674d6455..69d592b71 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs099.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs099.html
@@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source
               ('Reformulating the problem', 2, None, '___sec90'),
               ('Estimating errors', 2, None, '___sec91'),
               ('Creating a simple Deep Neural Net', 2, None, '___sec92'),
-              ('Feedforward', 2, None, '___sec93'),
-              ('Result after weighting', 2, None, '___sec94'),
-              ('Output', 2, None, '___sec95'),
-              ('Setting up the code, feed forward part', 2, None, '___sec96'),
-              ('Backpropagation', 2, None, '___sec97'),
-              ('Gradient Descent', 2, None, '___sec98'),
-              ('More on GD and cost function', 2, None, '___sec99'),
+              ('Setting up the code, feed forward part', 2, None, '___sec93'),
+              ('Backpropagation', 2, None, '___sec94'),
+              ('Gradient Descent', 2, None, '___sec95'),
+              ('More on GD and cost function', 2, None, '___sec96'),
               ('An implementation of a Deep Neural Network',
                2,
                None,
-               '___sec100'),
-              ('Feed forward again', 2, None, '___sec101'),
-              ('The final parts of the code', 2, None, '___sec102'),
-              ('And adding Back propagation', 2, None, '___sec103'),
-              ('Solving the ODE', 2, None, '___sec104'),
-              ('Using neural network', 2, None, '___sec105'),
-              ('Using a deep neural network', 2, None, '___sec106'),
-              ('Wrapping it up', 2, None, '___sec107')]}
+               '___sec97'),
+              ('The final parts of the code', 2, None, '___sec98'),
+              ('And adding Back propagation', 2, None, '___sec99'),
+              ('Solving the ODE', 2, None, '___sec100'),
+              ('Using neural network', 2, None, '___sec101'),
+              ('Using a deep neural network', 2, None, '___sec102'),
+              ('Wrapping it up', 2, None, '___sec103')]}
 end of tocinfo -->
 
 
@@ -333,21 +329,17 @@ MathJax.Hub.Config({
       
  • Reformulating the problem
    • 
       
  • Estimating errors
    • 
       
  • Creating a simple Deep Neural Net
    • 
-      
  • Feedforward
    • 
-      
  • Result after weighting
    • 
-      
  • Output
    • 
-      
  • Setting up the code, feed forward part
    • 
-      
  • Backpropagation
    • 
-      
  • Gradient Descent
    • 
-      
  • More on GD and cost function
    • 
-      
  • An implementation of a Deep Neural Network
    • 
-      
  • Feed forward again
    • 
-      
  • The final parts of the code
    • 
-      
  • And adding Back propagation
    • 
-      
  • Solving the ODE
    • 
-      
  • Using neural network
    • 
-      
  • Using a deep neural network
    • 
-      
  • Wrapping it up
    • 
+      
  • Setting up the code, feed forward part
    • 
+      
  • Backpropagation
    • 
+      
  • Gradient Descent
    • 
+      
  • More on GD and cost function
    • 
+      
  • An implementation of a Deep Neural Network
    • 
+      
  • The final parts of the code
    • 
+      
  • And adding Back propagation
    • 
+      
  • Solving the ODE
    • 
+      
  • Using neural network
    • 
+      
  • Using a deep neural network
    • 
+      
  • Wrapping it up
    • 
 
         
       
@@ -363,32 +355,53 @@ MathJax.Hub.Config({
 
 
 
-
    Gradient Descent 
    
-
+
    The final parts of the code 
    
 
    
-The idea of the gradient descent algorithm is to update parameters in
-direction where the cost function decreases goes to a minimum.
 
-
    
-In general, the update of some parameters \( \hat{\omega} \) given a cost
-function defined by some weights \( \hat{\omega} \), \( c(x, \hat{\omega}) \),
-goes as follows:
+
+
    def deep_neural_network(deep_params, x):
+    # N_hidden is the number of hidden layers  
+    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer
+        
+    # Assumes input x being an one-dimensional array
+    num_values = np.size(x)
+    x = x.reshape(-1, num_values)
+    
+    # Assume that the input layer does nothing to the input x
+    x_input = x
+    
+    # Due to multiple hidden layers, define a variable referencing to the
+    # output of the previous layer:
+    x_prev = x_input 
+    
+    ## Hidden layers:
+    
+    for l in range(N_hidden):
+        # From the list of parameters P; find the correct weigths and bias for this layer
+        w_hidden = deep_params[l]
+        
+        # Add a row of ones to include bias
+        x_prev = np.concatenate((np.ones((1,num_values)), x_prev ), axis = 0)
 
-$$
-\hat{\omega}_{\mathrm{new} } = \hat{\omega} - \lambda \nabla_{\hat{\omega}} c(x, \hat{\omega}),
-$$
+        z_hidden = np.matmul(w_hidden, x_prev)
+        x_hidden = sigmoid(z_hidden)
 
-
    
-for a number of iterations or until \( \big|\big| \hat{\omega}_{\mathrm{new} } - \hat{\omega} \big|\big| \) 
-is smaller than some
-given tolerance.
+        # Update x_prev such that next layer can use the output from this layer
+        x_prev = x_hidden 
 
-
    
-The value of \( \lambda \) decides how large steps the algorithm must take
-in the direction of $ \nabla_{\hat{\omega}} c(x, \hat{\omega})$. The
-notatation \( \nabla_{\hat{\omega}} \) denotes the gradient with respect to
-the elements in \( \hat{\omega} \).
+    ## Output layer:
+    
+    # Get the weights and bias for this layer
+    w_output = deep_params[-1]
+    
+    # Include bias:
+    x_prev = np.concatenate((np.ones((1,num_values)), x_prev), axis = 0)
 
+    z_output = np.matmul(w_output, x_prev)
+    x_output = z_output
+
+    return x_output
+
    
 
    
 
    
 
@@ -410,10 +423,6 @@ the elements in \( \hat{\omega} \).
   
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diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs100.html b/doc/pub/NeuralNet/html/._NeuralNet-bs100.html
index 4d5df7946..676cf404a 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs100.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs100.html
@@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source
               ('Reformulating the problem', 2, None, '___sec90'),
               ('Estimating errors', 2, None, '___sec91'),
               ('Creating a simple Deep Neural Net', 2, None, '___sec92'),
-              ('Feedforward', 2, None, '___sec93'),
-              ('Result after weighting', 2, None, '___sec94'),
-              ('Output', 2, None, '___sec95'),
-              ('Setting up the code, feed forward part', 2, None, '___sec96'),
-              ('Backpropagation', 2, None, '___sec97'),
-              ('Gradient Descent', 2, None, '___sec98'),
-              ('More on GD and cost function', 2, None, '___sec99'),
+              ('Setting up the code, feed forward part', 2, None, '___sec93'),
+              ('Backpropagation', 2, None, '___sec94'),
+              ('Gradient Descent', 2, None, '___sec95'),
+              ('More on GD and cost function', 2, None, '___sec96'),
               ('An implementation of a Deep Neural Network',
                2,
                None,
-               '___sec100'),
-              ('Feed forward again', 2, None, '___sec101'),
-              ('The final parts of the code', 2, None, '___sec102'),
-              ('And adding Back propagation', 2, None, '___sec103'),
-              ('Solving the ODE', 2, None, '___sec104'),
-              ('Using neural network', 2, None, '___sec105'),
-              ('Using a deep neural network', 2, None, '___sec106'),
-              ('Wrapping it up', 2, None, '___sec107')]}
+               '___sec97'),
+              ('The final parts of the code', 2, None, '___sec98'),
+              ('And adding Back propagation', 2, None, '___sec99'),
+              ('Solving the ODE', 2, None, '___sec100'),
+              ('Using neural network', 2, None, '___sec101'),
+              ('Using a deep neural network', 2, None, '___sec102'),
+              ('Wrapping it up', 2, None, '___sec103')]}
 end of tocinfo -->
 
 
@@ -333,21 +329,17 @@ MathJax.Hub.Config({
       
  • Reformulating the problem
    • 
       
  • Estimating errors
    • 
       
  • Creating a simple Deep Neural Net
    • 
-      
  • Feedforward
    • 
-      
  • Result after weighting
    • 
-      
  • Output
    • 
-      
  • Setting up the code, feed forward part
    • 
-      
  • Backpropagation
    • 
-      
  • Gradient Descent
    • 
-      
  • More on GD and cost function
    • 
-      
  • An implementation of a Deep Neural Network
    • 
-      
  • Feed forward again
    • 
-      
  • The final parts of the code
    • 
-      
  • And adding Back propagation
    • 
-      
  • Solving the ODE
    • 
-      
  • Using neural network
    • 
-      
  • Using a deep neural network
    • 
-      
  • Wrapping it up
    • 
+      
  • Setting up the code, feed forward part
    • 
+      
  • Backpropagation
    • 
+      
  • Gradient Descent
    • 
+      
  • More on GD and cost function
    • 
+      
  • An implementation of a Deep Neural Network
    • 
+      
  • The final parts of the code
    • 
+      
  • And adding Back propagation
    • 
+      
  • Solving the ODE
    • 
+      
  • Using neural network
    • 
+      
  • Using a deep neural network
    • 
+      
  • Wrapping it up
    • 
 
         
       
@@ -363,63 +355,78 @@ MathJax.Hub.Config({
 
 
 
-
    More on GD and cost function 
    
+
    And adding Back propagation 
    
 
 
    
-In our case, we have to minimize the cost function \( c(x, P) \) with
-respect to the two sets of weights and bisases, that is for the hidden
-layer \( P_{\mathrm{hidden} } \) and for the ouput layer \( P_{\mathrm{output}
-} \) .
-
-
    
-This means that \( P_{\mathrm{hidden} } \) and \( P_{\mathrm{output} } \) is
-updated by
-
-$$
-\begin{aligned}
-P_{\mathrm{hidden},\mathrm{new}} &= P_{\mathrm{hidden}} - \lambda \nabla_{P_{\mathrm{hidden}}} c(x, P)  \\
-P_{\mathrm{output},\mathrm{new}} &= P_{\mathrm{output}} - \lambda \nabla_{P_{\mathrm{output}}} c(x, P)  
-\end{aligned}
-$$
-
-
    
-This might look like a cumberstone to set up the correct expression
-for finding the gradients. Luckily, Autograd comes to the rescue.
+This step is very similar for the neural network. The idea in this
+step is the same as for the neural network, but with more parameters
+to update for. Again there is no need for computing the gradients
+analytically since Autograd does the work for us.
 
 
    
 
 
-
    def solve_ode_neural_network(x, num_neurons_hidden, num_iter, lmb):
+
    # The trial solution using the deep neural network:
+def g_trial_deep(x,params, g0 = 10):
+    return g0 + x*deep_neural_network(params,x)
+
+# The same cost function as for the neural network, but calls deep_neural_network instead.
+def cost_function_deep(P, x):
+    
+    # Evaluate the trial function with the current parameters P
+    g_t = g_trial_deep(x,P)
+    
+    # Find the derivative w.r.t x of the neural network
+    d_net_out = elementwise_grad(deep_neural_network,1)(P,x) 
+    
+    # Find the derivative w.r.t x of the trial function
+    d_g_t = elementwise_grad(g_trial_deep,0)(x,P)  
+    
+    # The right side of the ODE 
+    func = g(x, g_t)
+
+    err_sqr = (d_g_t - func)**2
+    cost_sum = np.sum(err_sqr)
+    
+    return cost_sum
+
+def solve_ode_deep_neural_network(x, num_neurons, num_iter, lmb):
+    # num_hidden_neurons is now a list of number of neurons within each hidden layer
+
+    # Find the number of hidden layers:
+    N_hidden = np.size(num_neurons)
+    
     ## Set up initial weigths and biases 
     
-    # For the hidden layer
-    p0 = npr.randn(num_neurons_hidden, 2 ) 
+    # Initialize the list of parameters:
+    P = [None]*(N_hidden + 1) # + 1 to include the output layer
 
+    P[0] = npr.randn(num_neurons[0], 2 ) 
+    for l in range(1,N_hidden):
+        P[l] = npr.randn(num_neurons[l], num_neurons[l-1] + 1) # +1 to include bias 
+    
     # For the output layer
-    p1 = npr.randn(1, num_neurons_hidden + 1 ) # +1 since bias is included
+    P[-1] = npr.randn(1, num_neurons[-1] + 1 ) # +1 since bias is included
 
-    P = [p0, p1]
-
-    print('Initial cost: %g'%cost_function(P, x))
+    print('Initial cost: %g'%cost_function_deep(P, x))
     
     ## Start finding the optimal weigths using gradient descent
     
     # Find the Python function that represents the gradient of the cost function
     # w.r.t the 0-th input argument -- that is the weights and biases in the hidden and output layer
-    cost_function_grad = grad(cost_function,0)
+    cost_function_deep_grad = grad(cost_function_deep,0)
     
     # Let the update be done num_iter times
     for i in range(num_iter):
         # Evaluate the gradient at the current weights and biases in P. 
-        # The cost_grad consist now of two arrays; 
-        # one for the gradient w.r.t P_hidden and 
-        # one for the gradient w.r.t P_output
-        cost_grad =  cost_function_grad(P, x)
-    
-        P[0] = P[0] - lmb * cost_grad[0]
-        P[1] = P[1] - lmb * cost_grad[1]
+        # The cost_grad consist now of N_hidden + 1 arrays; the gradient w.r.t the weights and biases
+        # in the hidden layers and output layers evaluated at x.
+        cost_deep_grad =  cost_function_deep_grad(P, x)
+        
+        for l in range(N_hidden+1):
+            P[l] = P[l] - lmb * cost_deep_grad[l]
 
-    print('Final cost: %g'%cost_function(P, x))
+    print('Final cost: %g'%cost_function_deep(P, x))
     
     return P
 
    
@@ -443,10 +450,6 @@ for finding the gradients. Luckily, Autograd comes to the rescue.
   
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diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs101.html b/doc/pub/NeuralNet/html/._NeuralNet-bs101.html
index 39d3c2082..9e8e49b8d 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs101.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs101.html
@@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source
               ('Reformulating the problem', 2, None, '___sec90'),
               ('Estimating errors', 2, None, '___sec91'),
               ('Creating a simple Deep Neural Net', 2, None, '___sec92'),
-              ('Feedforward', 2, None, '___sec93'),
-              ('Result after weighting', 2, None, '___sec94'),
-              ('Output', 2, None, '___sec95'),
-              ('Setting up the code, feed forward part', 2, None, '___sec96'),
-              ('Backpropagation', 2, None, '___sec97'),
-              ('Gradient Descent', 2, None, '___sec98'),
-              ('More on GD and cost function', 2, None, '___sec99'),
+              ('Setting up the code, feed forward part', 2, None, '___sec93'),
+              ('Backpropagation', 2, None, '___sec94'),
+              ('Gradient Descent', 2, None, '___sec95'),
+              ('More on GD and cost function', 2, None, '___sec96'),
               ('An implementation of a Deep Neural Network',
                2,
                None,
-               '___sec100'),
-              ('Feed forward again', 2, None, '___sec101'),
-              ('The final parts of the code', 2, None, '___sec102'),
-              ('And adding Back propagation', 2, None, '___sec103'),
-              ('Solving the ODE', 2, None, '___sec104'),
-              ('Using neural network', 2, None, '___sec105'),
-              ('Using a deep neural network', 2, None, '___sec106'),
-              ('Wrapping it up', 2, None, '___sec107')]}
+               '___sec97'),
+              ('The final parts of the code', 2, None, '___sec98'),
+              ('And adding Back propagation', 2, None, '___sec99'),
+              ('Solving the ODE', 2, None, '___sec100'),
+              ('Using neural network', 2, None, '___sec101'),
+              ('Using a deep neural network', 2, None, '___sec102'),
+              ('Wrapping it up', 2, None, '___sec103')]}
 end of tocinfo -->
 
 
@@ -333,21 +329,17 @@ MathJax.Hub.Config({
       
  • Reformulating the problem
    • 
       
  • Estimating errors
    • 
       
  • Creating a simple Deep Neural Net
    • 
-      
  • Feedforward
    • 
-      
  • Result after weighting
    • 
-      
  • Output
    • 
-      
  • Setting up the code, feed forward part
    • 
-      
  • Backpropagation
    • 
-      
  • Gradient Descent
    • 
-      
  • More on GD and cost function
    • 
-      
  • An implementation of a Deep Neural Network
    • 
-      
  • Feed forward again
    • 
-      
  • The final parts of the code
    • 
-      
  • And adding Back propagation
    • 
-      
  • Solving the ODE
    • 
-      
  • Using neural network
    • 
-      
  • Using a deep neural network
    • 
-      
  • Wrapping it up
    • 
+      
  • Setting up the code, feed forward part
    • 
+      
  • Backpropagation
    • 
+      
  • Gradient Descent
    • 
+      
  • More on GD and cost function
    • 
+      
  • An implementation of a Deep Neural Network
    • 
+      
  • The final parts of the code
    • 
+      
  • And adding Back propagation
    • 
+      
  • Solving the ODE
    • 
+      
  • Using neural network
    • 
+      
  • Using a deep neural network
    • 
+      
  • Wrapping it up
    • 
 
         
       
@@ -363,19 +355,18 @@ MathJax.Hub.Config({
 
 
 
-
    An implementation of a Deep Neural Network 
    
+
    Solving the ODE  
    
 
 
    
-As previously stated, a Deep Neural Network (DNN) follows the same
-concept of a neural network, but having more than one hidden
-layer. Suppose that the network has \( N_{\mathrm{hidden}} \) hidden layers
-where the \( l \)-th layer has \( N_{\mathrm{hidden}}^{(l)} \) neurons. The
-input is still assumed to be an array of size \( 1 \times N \). The
-network must now try to optimalize its output with respect to the
-collection of weigths and biases \( P = \big\{P_{\mathrm{input} }, \
-P_{\mathrm{hidden} }^{(1)}, \ P_{\mathrm{hidden} }^{(2)}, \ \dots , \
-P_{\mathrm{hidden} }^{(N_{\mathrm{hidden}})}, \ P_{\mathrm{output} }\big\} \).
+Finally, having set up the networks we are ready to use them to solve the ODE problem. 
+We add the analytical solution
 
+
    
+
+
+
    def g_analytic(x, gamma = 2, g0 = 10):
+    return g0*np.exp(-gamma*x)
+
    
 
    
 
    
 
@@ -395,10 +386,6 @@ P_{\mathrm{hidden} }^{(N_{\mathrm{hidden}})}, \ P_{\mathrm{output} }\big\} \).
   
  • 103
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    • 
-  
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-  
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diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs102.html b/doc/pub/NeuralNet/html/._NeuralNet-bs102.html
index 9a6b42535..204ca01b7 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs102.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs102.html
@@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source
               ('Reformulating the problem', 2, None, '___sec90'),
               ('Estimating errors', 2, None, '___sec91'),
               ('Creating a simple Deep Neural Net', 2, None, '___sec92'),
-              ('Feedforward', 2, None, '___sec93'),
-              ('Result after weighting', 2, None, '___sec94'),
-              ('Output', 2, None, '___sec95'),
-              ('Setting up the code, feed forward part', 2, None, '___sec96'),
-              ('Backpropagation', 2, None, '___sec97'),
-              ('Gradient Descent', 2, None, '___sec98'),
-              ('More on GD and cost function', 2, None, '___sec99'),
+              ('Setting up the code, feed forward part', 2, None, '___sec93'),
+              ('Backpropagation', 2, None, '___sec94'),
+              ('Gradient Descent', 2, None, '___sec95'),
+              ('More on GD and cost function', 2, None, '___sec96'),
               ('An implementation of a Deep Neural Network',
                2,
                None,
-               '___sec100'),
-              ('Feed forward again', 2, None, '___sec101'),
-              ('The final parts of the code', 2, None, '___sec102'),
-              ('And adding Back propagation', 2, None, '___sec103'),
-              ('Solving the ODE', 2, None, '___sec104'),
-              ('Using neural network', 2, None, '___sec105'),
-              ('Using a deep neural network', 2, None, '___sec106'),
-              ('Wrapping it up', 2, None, '___sec107')]}
+               '___sec97'),
+              ('The final parts of the code', 2, None, '___sec98'),
+              ('And adding Back propagation', 2, None, '___sec99'),
+              ('Solving the ODE', 2, None, '___sec100'),
+              ('Using neural network', 2, None, '___sec101'),
+              ('Using a deep neural network', 2, None, '___sec102'),
+              ('Wrapping it up', 2, None, '___sec103')]}
 end of tocinfo -->
 
 
@@ -333,21 +329,17 @@ MathJax.Hub.Config({
       
  • Reformulating the problem
    • 
       
  • Estimating errors
    • 
       
  • Creating a simple Deep Neural Net
    • 
-      
  • Feedforward
    • 
-      
  • Result after weighting
    • 
-      
  • Output
    • 
-      
  • Setting up the code, feed forward part
    • 
-      
  • Backpropagation
    • 
-      
  • Gradient Descent
    • 
-      
  • More on GD and cost function
    • 
-      
  • An implementation of a Deep Neural Network
    • 
-      
  • Feed forward again
    • 
-      
  • The final parts of the code
    • 
-      
  • And adding Back propagation
    • 
-      
  • Solving the ODE
    • 
-      
  • Using neural network
    • 
-      
  • Using a deep neural network
    • 
-      
  • Wrapping it up
    • 
+      
  • Setting up the code, feed forward part
    • 
+      
  • Backpropagation
    • 
+      
  • Gradient Descent
    • 
+      
  • More on GD and cost function
    • 
+      
  • An implementation of a Deep Neural Network
    • 
+      
  • The final parts of the code
    • 
+      
  • And adding Back propagation
    • 
+      
  • Solving the ODE
    • 
+      
  • Using neural network
    • 
+      
  • Using a deep neural network
    • 
+      
  • Wrapping it up
    • 
 
         
       
@@ -363,50 +355,47 @@ MathJax.Hub.Config({
 
 
 
-
    Feed forward again 
    
+
    Using neural network 
    
 
 
    
-The feedforward step is similar to as for the neural netowork, but now considering more than one hidden layer.
+The code below solves the ODE using a neural network. The number of
+values for the input \( \vec x \) is 10, number of hidden neurons in the
+hidden layer being 10 and th step size used in gradien descent
+\( \lambda = 0.001 \). The program updates the weights and biases in the
+network for a given number of iterations. Finally, it plots the results from using the
+neural network along with the analytical solution.
 
 
    
-The \( i \)-th neuron at layer \( l \) recieves the result
-\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) from the \( j \)-th neuron at layer
-\( l-1 \). The \( i \)-th neuron at layer \( l \) weights all of the elements in
-\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( w_{i,j}^{(l), \ \mathrm{hidden}} \) with as many weigths as there are
-elements in$\hat{x}_j^{(l-1),\mathrm{hidden} }$, and adds a bias
-\( b_i^{(l), \ \mathrm{hidden} } \):
 
-$$
-\begin{aligned}
-z_{i,j}^{(l),\ \mathrm{hidden}} &= b_i^{(l), \ \mathrm{hidden}} + \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T\hat{x}_j^{(l-1),\mathrm{hidden} } \\
-&= 
-\begin{pmatrix}
-b_i^{(l), \ \mathrm{hidden}}  & \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T
-\end{pmatrix}
-\begin{pmatrix}
-1  \\
-\hat{x}_j^{(l-1),\mathrm{hidden} }
-\end{pmatrix} 
-\end{aligned}
-$$
+
+
    npr.seed(15)
 
-
    
-The output from the \( i \)-th neuron at the hidden layer \( l \) becomes a vector \( \hat{z}_{i}^{(l),\ \mathrm{hidden}} \):
+## Decide the vales of arguments to the function to solve
+N = 10
+x = np.linspace(0, 1, N)
 
-$$
-\begin{aligned}
-\hat{z}_{i}^{(l),\ \mathrm{hidden}} &= \Big(  b_i^{(l), \ \mathrm{hidden}} + \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T\hat{x}_1^{(l-1),\mathrm{hidden} }, \ \dots \ , \  b_i^{(l), \ \mathrm{hidden}} + \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T\hat{x}_{N_{hidden}^{(l-1)}}^{(l-1),\mathrm{hidden} } \Big) \\
-&= 
-\begin{pmatrix}
-b_i^{(l), \ \mathrm{hidden}} & \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T
-\end{pmatrix}
-\begin{pmatrix}
-1 & 1 & \dots & 1 \\
-\hat{x}_{1}^{(l-1),\mathrm{hidden} } & \hat{x}_{2}^{(l-1),\mathrm{hidden} } & \dots & \hat{x}_{N_{hidden}^{(l-1)}}^{(l-1),\mathrm{hidden} }
-\end{pmatrix}
-\end{aligned}
-$$
+## Set up the initial parameters
+num_hidden_neurons = 10
+num_iter = 10000
+lmb = 0.001
 
+P = solve_ode_neural_network(x, num_hidden_neurons, num_iter, lmb)
+
+res = g_trial(x,P) 
+res_analytical = g_analytic(x)
+
+print('Max absolute difference: %g'%np.max(np.abs(res - res_analytical)))
+
+plt.figure(figsize=(10,10))
+
+plt.title('Performance of neural network solving an ODE compared to the analytical solution')
+plt.plot(x, res_analytical)
+plt.plot(x, res[0,:])
+plt.legend(['analytical','nn'])
+plt.xlabel('x')
+plt.ylabel('g(x)')
+plt.show()
+
    
 
    
 
    
 
@@ -425,10 +414,6 @@ $$
   
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diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs103.html b/doc/pub/NeuralNet/html/._NeuralNet-bs103.html
index 4193a3e1a..82f95bb3f 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs103.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs103.html
@@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source
               ('Reformulating the problem', 2, None, '___sec90'),
               ('Estimating errors', 2, None, '___sec91'),
               ('Creating a simple Deep Neural Net', 2, None, '___sec92'),
-              ('Feedforward', 2, None, '___sec93'),
-              ('Result after weighting', 2, None, '___sec94'),
-              ('Output', 2, None, '___sec95'),
-              ('Setting up the code, feed forward part', 2, None, '___sec96'),
-              ('Backpropagation', 2, None, '___sec97'),
-              ('Gradient Descent', 2, None, '___sec98'),
-              ('More on GD and cost function', 2, None, '___sec99'),
+              ('Setting up the code, feed forward part', 2, None, '___sec93'),
+              ('Backpropagation', 2, None, '___sec94'),
+              ('Gradient Descent', 2, None, '___sec95'),
+              ('More on GD and cost function', 2, None, '___sec96'),
               ('An implementation of a Deep Neural Network',
                2,
                None,
-               '___sec100'),
-              ('Feed forward again', 2, None, '___sec101'),
-              ('The final parts of the code', 2, None, '___sec102'),
-              ('And adding Back propagation', 2, None, '___sec103'),
-              ('Solving the ODE', 2, None, '___sec104'),
-              ('Using neural network', 2, None, '___sec105'),
-              ('Using a deep neural network', 2, None, '___sec106'),
-              ('Wrapping it up', 2, None, '___sec107')]}
+               '___sec97'),
+              ('The final parts of the code', 2, None, '___sec98'),
+              ('And adding Back propagation', 2, None, '___sec99'),
+              ('Solving the ODE', 2, None, '___sec100'),
+              ('Using neural network', 2, None, '___sec101'),
+              ('Using a deep neural network', 2, None, '___sec102'),
+              ('Wrapping it up', 2, None, '___sec103')]}
 end of tocinfo -->
 
 
@@ -333,21 +329,17 @@ MathJax.Hub.Config({
       
  • Reformulating the problem
    • 
       
  • Estimating errors
    • 
       
  • Creating a simple Deep Neural Net
    • 
-      
  • Feedforward
    • 
-      
  • Result after weighting
    • 
-      
  • Output
    • 
-      
  • Setting up the code, feed forward part
    • 
-      
  • Backpropagation
    • 
-      
  • Gradient Descent
    • 
-      
  • More on GD and cost function
    • 
-      
  • An implementation of a Deep Neural Network
    • 
-      
  • Feed forward again
    • 
-      
  • The final parts of the code
    • 
-      
  • And adding Back propagation
    • 
-      
  • Solving the ODE
    • 
-      
  • Using neural network
    • 
-      
  • Using a deep neural network
    • 
-      
  • Wrapping it up
    • 
+      
  • Setting up the code, feed forward part
    • 
+      
  • Backpropagation
    • 
+      
  • Gradient Descent
    • 
+      
  • More on GD and cost function
    • 
+      
  • An implementation of a Deep Neural Network
    • 
+      
  • The final parts of the code
    • 
+      
  • And adding Back propagation
    • 
+      
  • Solving the ODE
    • 
+      
  • Using neural network
    • 
+      
  • Using a deep neural network
    • 
+      
  • Wrapping it up
    • 
 
         
       
@@ -361,54 +353,37 @@ MathJax.Hub.Config({
 
     
     
     
     
 
 
-
+
+
+
    Using a deep neural network 
    
 
-
    The final parts of the code 
    
 
    
 
 
-
    def deep_neural_network(deep_params, x):
-    # N_hidden is the number of hidden layers  
-    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer
-        
-    # Assumes input x being an one-dimensional array
-    num_values = np.size(x)
-    x = x.reshape(-1, num_values)
-    
-    # Assume that the input layer does nothing to the input x
-    x_input = x
-    
-    # Due to multiple hidden layers, define a variable referencing to the
-    # output of the previous layer:
-    x_prev = x_input 
-    
-    ## Hidden layers:
-    
-    for l in range(N_hidden):
-        # From the list of parameters P; find the correct weigths and bias for this layer
-        w_hidden = deep_params[l]
-        
-        # Add a row of ones to include bias
-        x_prev = np.concatenate((np.ones((1,num_values)), x_prev ), axis = 0)
+
    npr.seed(15)
 
-        z_hidden = np.matmul(w_hidden, x_prev)
-        x_hidden = sigmoid(z_hidden)
+## Decide the vales of arguments to the function to solve
+N = 10
+x = np.linspace(0, 1, N)
 
-        # Update x_prev such that next layer can use the output from this layer
-        x_prev = x_hidden 
+## Set up the initial parameters
+num_hidden_neurons = np.array([10,10])
+num_iter = 10000
+lmb = 0.001
 
-    ## Output layer:
-    
-    # Get the weights and bias for this layer
-    w_output = deep_params[-1]
-    
-    # Include bias:
-    x_prev = np.concatenate((np.ones((1,num_values)), x_prev), axis = 0)
+P = solve_ode_deep_neural_network(x, num_hidden_neurons, num_iter, lmb)
 
-    z_output = np.matmul(w_output, x_prev)
-    x_output = z_output
+res = g_trial_deep(x,P) 
+res_analytical = g_analytic(x)
 
-    return x_output
+plt.figure(figsize=(10,10))
+
+plt.title('Performance of a deep neural network solving an ODE compared to the analytical solution')
+plt.plot(x, res_analytical)
+plt.plot(x, res[0,:])
+plt.legend(['analytical','dnn'])
+plt.ylabel('g(x)')
+plt.show()
 
    
 
    
 
    
@@ -427,10 +402,6 @@ MathJax.Hub.Config({
   
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    • 
   
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    • 
   
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    • 
-  
  • 106
    • 
-  
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    • 
-  
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-  
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    • 
 
 
diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs104.html b/doc/pub/NeuralNet/html/._NeuralNet-bs104.html
index e8a1b8085..b9dbd8af4 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs104.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs104.html
@@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source
               ('Reformulating the problem', 2, None, '___sec90'),
               ('Estimating errors', 2, None, '___sec91'),
               ('Creating a simple Deep Neural Net', 2, None, '___sec92'),
-              ('Feedforward', 2, None, '___sec93'),
-              ('Result after weighting', 2, None, '___sec94'),
-              ('Output', 2, None, '___sec95'),
-              ('Setting up the code, feed forward part', 2, None, '___sec96'),
-              ('Backpropagation', 2, None, '___sec97'),
-              ('Gradient Descent', 2, None, '___sec98'),
-              ('More on GD and cost function', 2, None, '___sec99'),
+              ('Setting up the code, feed forward part', 2, None, '___sec93'),
+              ('Backpropagation', 2, None, '___sec94'),
+              ('Gradient Descent', 2, None, '___sec95'),
+              ('More on GD and cost function', 2, None, '___sec96'),
               ('An implementation of a Deep Neural Network',
                2,
                None,
-               '___sec100'),
-              ('Feed forward again', 2, None, '___sec101'),
-              ('The final parts of the code', 2, None, '___sec102'),
-              ('And adding Back propagation', 2, None, '___sec103'),
-              ('Solving the ODE', 2, None, '___sec104'),
-              ('Using neural network', 2, None, '___sec105'),
-              ('Using a deep neural network', 2, None, '___sec106'),
-              ('Wrapping it up', 2, None, '___sec107')]}
+               '___sec97'),
+              ('The final parts of the code', 2, None, '___sec98'),
+              ('And adding Back propagation', 2, None, '___sec99'),
+              ('Solving the ODE', 2, None, '___sec100'),
+              ('Using neural network', 2, None, '___sec101'),
+              ('Using a deep neural network', 2, None, '___sec102'),
+              ('Wrapping it up', 2, None, '___sec103')]}
 end of tocinfo -->
 
 
@@ -333,21 +329,17 @@ MathJax.Hub.Config({
       
  • Reformulating the problem
    • 
       
  • Estimating errors
    • 
       
  • Creating a simple Deep Neural Net
    • 
-      
  • Feedforward
    • 
-      
  • Result after weighting
    • 
-      
  • Output
    • 
-      
  • Setting up the code, feed forward part
    • 
-      
  • Backpropagation
    • 
-      
  • Gradient Descent
    • 
-      
  • More on GD and cost function
    • 
-      
  • An implementation of a Deep Neural Network
    • 
-      
  • Feed forward again
    • 
-      
  • The final parts of the code
    • 
-      
  • And adding Back propagation
    • 
-      
  • Solving the ODE
    • 
-      
  • Using neural network
    • 
-      
  • Using a deep neural network
    • 
-      
  • Wrapping it up
    • 
+      
  • Setting up the code, feed forward part
    • 
+      
  • Backpropagation
    • 
+      
  • Gradient Descent
    • 
+      
  • More on GD and cost function
    • 
+      
  • An implementation of a Deep Neural Network
    • 
+      
  • The final parts of the code
    • 
+      
  • And adding Back propagation
    • 
+      
  • Solving the ODE
    • 
+      
  • Using neural network
    • 
+      
  • Using a deep neural network
    • 
+      
  • Wrapping it up
    • 
 
         
       
@@ -363,82 +355,21 @@ MathJax.Hub.Config({
 
 
 
-
    And adding Back propagation 
    
+
    Wrapping it up 
    
 
 
    
-This step is very similar for the neural network. The idea in this
-step is the same as for the neural network, but with more parameters
-to update for. Again there is no need for computing the gradients
-analytically since Autograd does the work for us.
+By rewriting the ODE as a minimization problem, it was possible to
+solve equation using either a neural network (one hidden layer) or a
+deep neural network (more than one hidden layers). How well the
+network performed is measured by a specified cost function, which is
+the function the network tries to minimize. Using a trial solution
+which satisfies the additional condition and being defined by using
+the output from the network in some way, the minimization problem
+could be explicitly defined for out network to solve. The proposed
+solution from the network is then the trial solution with parameters,
+that is weights and biases within each layer in the network, such that
+the solution minimizes the cost function.
 
-
    
-
-
-
    # The trial solution using the deep neural network:
-def g_trial_deep(x,params, g0 = 10):
-    return g0 + x*deep_neural_network(params,x)
-
-# The same cost function as for the neural network, but calls deep_neural_network instead.
-def cost_function_deep(P, x):
-    
-    # Evaluate the trial function with the current parameters P
-    g_t = g_trial_deep(x,P)
-    
-    # Find the derivative w.r.t x of the neural network
-    d_net_out = elementwise_grad(deep_neural_network,1)(P,x) 
-    
-    # Find the derivative w.r.t x of the trial function
-    d_g_t = elementwise_grad(g_trial_deep,0)(x,P)  
-    
-    # The right side of the ODE 
-    func = g(x, g_t)
-
-    err_sqr = (d_g_t - func)**2
-    cost_sum = np.sum(err_sqr)
-    
-    return cost_sum
-
-def solve_ode_deep_neural_network(x, num_neurons, num_iter, lmb):
-    # num_hidden_neurons is now a list of number of neurons within each hidden layer
-
-    # Find the number of hidden layers:
-    N_hidden = np.size(num_neurons)
-    
-    ## Set up initial weigths and biases 
-    
-    # Initialize the list of parameters:
-    P = [None]*(N_hidden + 1) # + 1 to include the output layer
-
-    P[0] = npr.randn(num_neurons[0], 2 ) 
-    for l in range(1,N_hidden):
-        P[l] = npr.randn(num_neurons[l], num_neurons[l-1] + 1) # +1 to include bias 
-    
-    # For the output layer
-    P[-1] = npr.randn(1, num_neurons[-1] + 1 ) # +1 since bias is included
-
-    print('Initial cost: %g'%cost_function_deep(P, x))
-    
-    ## Start finding the optimal weigths using gradient descent
-    
-    # Find the Python function that represents the gradient of the cost function
-    # w.r.t the 0-th input argument -- that is the weights and biases in the hidden and output layer
-    cost_function_deep_grad = grad(cost_function_deep,0)
-    
-    # Let the update be done num_iter times
-    for i in range(num_iter):
-        # Evaluate the gradient at the current weights and biases in P. 
-        # The cost_grad consist now of N_hidden + 1 arrays; the gradient w.r.t the weights and biases
-        # in the hidden layers and output layers evaluated at x.
-        cost_deep_grad =  cost_function_deep_grad(P, x)
-        
-        for l in range(N_hidden+1):
-            P[l] = P[l] - lmb * cost_deep_grad[l]
-
-    print('Final cost: %g'%cost_function_deep(P, x))
-    
-    return P
-
    
-
    
 
    
 
 
    
 
 
diff --git a/doc/pub/NeuralNet/html/NeuralNet-bs.html b/doc/pub/NeuralNet/html/NeuralNet-bs.html
index ddfcae71f..0c296c5a0 100644
--- a/doc/pub/NeuralNet/html/NeuralNet-bs.html
+++ b/doc/pub/NeuralNet/html/NeuralNet-bs.html
@@ -185,24 +185,20 @@ Automatically generated HTML file from DocOnce source
               ('Reformulating the problem', 2, None, '___sec90'),
               ('Estimating errors', 2, None, '___sec91'),
               ('Creating a simple Deep Neural Net', 2, None, '___sec92'),
-              ('Feedforward', 2, None, '___sec93'),
-              ('Result after weighting', 2, None, '___sec94'),
-              ('Output', 2, None, '___sec95'),
-              ('Setting up the code, feed forward part', 2, None, '___sec96'),
-              ('Backpropagation', 2, None, '___sec97'),
-              ('Gradient Descent', 2, None, '___sec98'),
-              ('More on GD and cost function', 2, None, '___sec99'),
+              ('Setting up the code, feed forward part', 2, None, '___sec93'),
+              ('Backpropagation', 2, None, '___sec94'),
+              ('Gradient Descent', 2, None, '___sec95'),
+              ('More on GD and cost function', 2, None, '___sec96'),
               ('An implementation of a Deep Neural Network',
                2,
                None,
-               '___sec100'),
-              ('Feed forward again', 2, None, '___sec101'),
-              ('The final parts of the code', 2, None, '___sec102'),
-              ('And adding Back propagation', 2, None, '___sec103'),
-              ('Solving the ODE', 2, None, '___sec104'),
-              ('Using neural network', 2, None, '___sec105'),
-              ('Using a deep neural network', 2, None, '___sec106'),
-              ('Wrapping it up', 2, None, '___sec107')]}
+               '___sec97'),
+              ('The final parts of the code', 2, None, '___sec98'),
+              ('And adding Back propagation', 2, None, '___sec99'),
+              ('Solving the ODE', 2, None, '___sec100'),
+              ('Using neural network', 2, None, '___sec101'),
+              ('Using a deep neural network', 2, None, '___sec102'),
+              ('Wrapping it up', 2, None, '___sec103')]}
 end of tocinfo -->
 
 
@@ -333,21 +329,17 @@ MathJax.Hub.Config({
       
  • Reformulating the problem
    • 
       
  • Estimating errors
    • 
       
  • Creating a simple Deep Neural Net
    • 
-      
  • Feedforward
    • 
-      
  • Result after weighting
    • 
-      
  • Output
    • 
-      
  • Setting up the code, feed forward part
    • 
-      
  • Backpropagation
    • 
-      
  • Gradient Descent
    • 
-      
  • More on GD and cost function
    • 
-      
  • An implementation of a Deep Neural Network
    • 
-      
  • Feed forward again
    • 
-      
  • The final parts of the code
    • 
-      
  • And adding Back propagation
    • 
-      
  • Solving the ODE
    • 
-      
  • Using neural network
    • 
-      
  • Using a deep neural network
    • 
-      
  • Wrapping it up
    • 
+      
  • Setting up the code, feed forward part
    • 
+      
  • Backpropagation
    • 
+      
  • Gradient Descent
    • 
+      
  • More on GD and cost function
    • 
+      
  • An implementation of a Deep Neural Network
    • 
+      
  • The final parts of the code
    • 
+      
  • And adding Back propagation
    • 
+      
  • Solving the ODE
    • 
+      
  • Using neural network
    • 
+      
  • Using a deep neural network
    • 
+      
  • Wrapping it up
    • 
 
         
       
@@ -406,7 +398,7 @@ MathJax.Hub.Config({
   
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    • 
   
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    • 
   
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    • 
-  
  • 109
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+  
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diff --git a/doc/pub/NeuralNet/html/NeuralNet-reveal.html b/doc/pub/NeuralNet/html/NeuralNet-reveal.html
index 26dec382d..9ec93ee5b 100644
--- a/doc/pub/NeuralNet/html/NeuralNet-reveal.html
+++ b/doc/pub/NeuralNet/html/NeuralNet-reveal.html
@@ -3974,152 +3974,13 @@ painless.
 For simplicity, we assume that the input is an array 
 \( \hat{x}= (x_1, \dots, x_N) \) with \( N \) elements. It is at these points the neural
 network should find \( P \) such that it fulfills (19).
+All the ingredients discussed earlier, from the activation function, hidden layers and their weights, biases etc
+are included below.
 
 
 
 
    
-
    Feedforward 
    
-
-
    
-First, a feedforward of the inputs must be done. This means that \( \hat{x} \) 
-must be passed through an input layer, a hidden layer and a output
- layer. The input layer in this case, does not need to process the
- data any further. The input layer will consist of \( N_{\mathrm{input} } \)
- neurons, passing its element to each neuron in the hidden layer.  The
- number of neurons in the hidden layer will be \( N_{\mathrm{hidden} } \).
-
-
    
-For the \( i \)-th in the hidden layer with weight \( w_i^{\mathrm{hidden} } \)
-and bias \( b_i^{\mathrm{hidden} } \), the weighting from the \( j \)-th neuron
-at the input layer is:
-
-
     
    
-$$
-\begin{aligned}
-z_{i,j}^{\mathrm{hidden}} &= b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}}x_j \\
-&= 
-\begin{pmatrix}
-b_i^{\mathrm{hidden}} & w_i^{\mathrm{hidden}}
-\end{pmatrix}
-\begin{pmatrix}
-1 \\
-x_j
-\end{pmatrix} 
-\end{aligned}
-$$
-
     
    
-
    
-
-
-
    
-
    Result after weighting 
    
-
-
    
-The result after weighting the input at the \( i \)-th hidden neuron can be written as a vector:
-
     
    
-$$
-\begin{aligned}
-\hat{z}_{i}^{\mathrm{hidden}} &= \Big( b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}}x_1 , \ b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}} x_2, \ \dots \, , \ b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}} x_N\Big)  \\
-&= 
-\begin{pmatrix}
- b_i^{\mathrm{hidden}}  & w_i^{\mathrm{hidden}}
-\end{pmatrix}
-\begin{pmatrix}
-1  & 1 & \dots & 1 \\
-x_1 & x_2 & \dots & x_N
-\end{pmatrix} \\
-&= \hat{p}_{i, \mathrm{hidden}}^T X
-\end{aligned}
-$$
-
     
    
-
-
    
-It is the vector \( \hat{p}_{i, \mathrm{hidden}}^T \) that defines each row
-in \( P_{\mathrm{hidden} } \), which contains the weights for the neural
-network to minimize according to (19).
-
-
    
-After having found \( \hat{z}_{i}^{\mathrm{hidden}}  \) for every neuron \( i \)
-in the hidden layer, the vector will be sent to an activation function
-\( a_i(\hat{z}) \).  In this example, the sigmoid function has been used:
-
-
     
    
-$$
-f(z) = \frac{1}{1 + \exp{(-z)}}.
-$$
-
     
    
-
    
-
-
-
    
-
    Output 
    
-
-
    
-The output $\hat{x}_i^{\mathrm{hidden}}$from each \( i \)-th hidden neuron is:
-
-
     
    
-$$
-\hat{x}_i^{\mathrm{hidden} } = f\big(  \hat{z}_{i}^{\mathrm{hidden}} \big).
-$$
-
     
    
-
-
    
-The outputs \( \hat{x}_i^{\mathrm{hidden} }  \) are then sent to the output layer.
-
-
    
-The output layer consist of one neuron in this case, and combines the
-output from each of the neurons in the hidden layers. The output layer
-combines the results from the hidden layer using some weights \( 
-w_i^{\mathrm{output}} \) and biases \( b_i^{\mathrm{output}} \). In this case,
-it is assumes that the number of neurons in the output layer is one.
-
-
    
-The procedure of weigthing the output neuron \( j \) in the hidden layer
-to the \( i \)-th neuron in the output layer is similar as for the hidden
-layer described previously.
-
-
     
    
-$$
-\begin{aligned}
-z_{1,j}^{\mathrm{output}} & = 
-\begin{pmatrix}
-b_1^{\mathrm{output}} & \hat{w}_1^{\mathrm{output}}
-\end{pmatrix}
-\begin{pmatrix}
-1 \\
-\hat{x}_j^{\mathrm{hidden}}
-\end{pmatrix}
-\end{aligned}
-$$
-
     
    
-
-
    
-Expressing \( z_{1,j}^{\mathrm{output}} \) as a vector gives the following procedure of weighting the inputs from the hidden layer:
-
-
     
    
-$$
-\hat{z}_{1}^{\mathrm{output}} = 
-\begin{pmatrix}
-b_1^{\mathrm{output}} & \hat{w}_1^{\mathrm{output}}
-\end{pmatrix}
-\begin{pmatrix}
-1 & 1 & \dots & 1 \\
-\hat{x}_1^{\mathrm{hidden}} & \hat{x}_2^{\mathrm{hidden}} & \dots & \hat{x}_N^{\mathrm{hidden}}
-\end{pmatrix}
-$$
-
     
    
-
-
    
-In this case we seek a continous range of values since we are
-approximating a function. This means that after computing
-\( \hat{z}_{1}^{\mathrm{output}} \) the neural network has finished its
-feedforward step, and \( \hat{z}_{1}^{\mathrm{output}} \) is the final
-output of the network.
-
    
-
-
-
    
-
    Setting up the code, feed forward part 
    
+
    Setting up the code, feed forward part 
    
 
    
 
 
@@ -4171,10 +4032,10 @@ output of the network.
 
 
 
    
-
    Backpropagation 
    
+
    Backpropagation 
    
 
 
    
-Now that feedforward can be done, the next step is to decide how the
+Now that the feedforward can be done, the next step is to decide how the
 parameters should change such that they minimize the cost function.
 
 
    
@@ -4231,7 +4092,7 @@ function along with the right ride of the ODE and trial solution.
 
 
 
    
-
    Gradient Descent 
    
+
    Gradient Descent 
    
 
 
    
 The idea of the gradient descent algorithm is to update parameters in
@@ -4262,7 +4123,7 @@ the elements in \( \hat{\omega} \).
 
 
 
    
-
    More on GD and cost function 
    
+
    More on GD and cost function 
    
 
 
    
 In our case, we have to minimize the cost function \( c(x, P) \) with
@@ -4276,10 +4137,12 @@ updated by
 
 
     
    
 $$
-\begin{aligned}
-P_{\mathrm{hidden},\mathrm{new}} &= P_{\mathrm{hidden}} - \lambda \nabla_{P_{\mathrm{hidden}}} c(x, P)  \\
+\begin{align}
+P_{\mathrm{hidden},\mathrm{new}} &= P_{\mathrm{hidden}} - \lambda \nabla_{P_{\mathrm{hidden}}} c(x, P)  
+\tag{20}\\
 P_{\mathrm{output},\mathrm{new}} &= P_{\mathrm{output}} - \lambda \nabla_{P_{\mathrm{output}}} c(x, P)  
-\end{aligned}
+\tag{21}
+\end{align}
 $$
 
     
    
 
@@ -4328,7 +4191,7 @@ for finding the gradients. Luckily, Autograd comes to the rescue.
 
 
 
    
-
    An implementation of a Deep Neural Network 
    
+
    An implementation of a Deep Neural Network 
    
 
 
    
 As previously stated, a Deep Neural Network (DNN) follows the same
@@ -4344,58 +4207,7 @@ P_{\mathrm{hidden} }^{(N_{\mathrm{hidden}})}, \ P_{\mathrm{output} }\big\} \).
 
 
 
    
-
    Feed forward again 
    
-
-
    
-The feedforward step is similar to as for the neural netowork, but now considering more than one hidden layer.
-
-
    
-The \( i \)-th neuron at layer \( l \) recieves the result
-\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) from the \( j \)-th neuron at layer
-\( l-1 \). The \( i \)-th neuron at layer \( l \) weights all of the elements in
-\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( w_{i,j}^{(l), \ \mathrm{hidden}} \) with as many weigths as there are
-elements in$\hat{x}_j^{(l-1),\mathrm{hidden} }$, and adds a bias
-\( b_i^{(l), \ \mathrm{hidden} } \):
-
-
     
    
-$$
-\begin{aligned}
-z_{i,j}^{(l),\ \mathrm{hidden}} &= b_i^{(l), \ \mathrm{hidden}} + \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T\hat{x}_j^{(l-1),\mathrm{hidden} } \\
-&= 
-\begin{pmatrix}
-b_i^{(l), \ \mathrm{hidden}}  & \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T
-\end{pmatrix}
-\begin{pmatrix}
-1  \\
-\hat{x}_j^{(l-1),\mathrm{hidden} }
-\end{pmatrix} 
-\end{aligned}
-$$
-
     
    
-
-
    
-The output from the \( i \)-th neuron at the hidden layer \( l \) becomes a vector \( \hat{z}_{i}^{(l),\ \mathrm{hidden}} \):
-
-
     
    
-$$
-\begin{aligned}
-\hat{z}_{i}^{(l),\ \mathrm{hidden}} &= \Big(  b_i^{(l), \ \mathrm{hidden}} + \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T\hat{x}_1^{(l-1),\mathrm{hidden} }, \ \dots \ , \  b_i^{(l), \ \mathrm{hidden}} + \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T\hat{x}_{N_{hidden}^{(l-1)}}^{(l-1),\mathrm{hidden} } \Big) \\
-&= 
-\begin{pmatrix}
-b_i^{(l), \ \mathrm{hidden}} & \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T
-\end{pmatrix}
-\begin{pmatrix}
-1 & 1 & \dots & 1 \\
-\hat{x}_{1}^{(l-1),\mathrm{hidden} } & \hat{x}_{2}^{(l-1),\mathrm{hidden} } & \dots & \hat{x}_{N_{hidden}^{(l-1)}}^{(l-1),\mathrm{hidden} }
-\end{pmatrix}
-\end{aligned}
-$$
-
     
    
-
    
-
-
-
    
-
    The final parts of the code 
    
+
    The final parts of the code 
    
 
    
 
 
@@ -4446,7 +4258,7 @@ $$
 
 
 
    
-
    And adding Back propagation 
    
+
    And adding Back propagation 
    
 
 
    
 This step is very similar for the neural network. The idea in this
@@ -4525,7 +4337,7 @@ analytically since Autograd does the work for us.
 
 
 
    
-
    Solving the ODE  
    
+
    Solving the ODE  
    
 
 
    
 Finally, having set up the networks we are ready to use them to solve the ODE problem. 
@@ -4541,14 +4353,14 @@ We add the analytical solution
 
 
 
    
-
    Using neural network 
    
+
    Using neural network 
    
 
 
    
 The code below solves the ODE using a neural network. The number of
 values for the input \( \vec x \) is 10, number of hidden neurons in the
 hidden layer being 10 and th step size used in gradien descent
 \( \lambda = 0.001 \). The program updates the weights and biases in the
-network num_iter times. Finally, it plots the results from using the
+network for a given number of iterations. Finally, it plots the results from using the
 neural network along with the analytical solution.
 
 
    
@@ -4586,7 +4398,7 @@ plt.show()
 
 
 
    
-
    Using a deep neural network 
    
+
    Using a deep neural network 
    
 
 
    
 
@@ -4620,7 +4432,7 @@ plt.show()
 
 
 
    
-
    Wrapping it up 
    
+
    Wrapping it up 
    
 
 
    
 By rewriting the ODE as a minimization problem, it was possible to
diff --git a/doc/pub/NeuralNet/html/NeuralNet-solarized.html b/doc/pub/NeuralNet/html/NeuralNet-solarized.html
index 419531dea..f5c9407fe 100644
--- a/doc/pub/NeuralNet/html/NeuralNet-solarized.html
+++ b/doc/pub/NeuralNet/html/NeuralNet-solarized.html
@@ -205,24 +205,20 @@ div { text-align: justify; text-justify: inter-word; }
               ('Reformulating the problem', 2, None, '___sec90'),
               ('Estimating errors', 2, None, '___sec91'),
               ('Creating a simple Deep Neural Net', 2, None, '___sec92'),
-              ('Feedforward', 2, None, '___sec93'),
-              ('Result after weighting', 2, None, '___sec94'),
-              ('Output', 2, None, '___sec95'),
-              ('Setting up the code, feed forward part', 2, None, '___sec96'),
-              ('Backpropagation', 2, None, '___sec97'),
-              ('Gradient Descent', 2, None, '___sec98'),
-              ('More on GD and cost function', 2, None, '___sec99'),
+              ('Setting up the code, feed forward part', 2, None, '___sec93'),
+              ('Backpropagation', 2, None, '___sec94'),
+              ('Gradient Descent', 2, None, '___sec95'),
+              ('More on GD and cost function', 2, None, '___sec96'),
               ('An implementation of a Deep Neural Network',
                2,
                None,
-               '___sec100'),
-              ('Feed forward again', 2, None, '___sec101'),
-              ('The final parts of the code', 2, None, '___sec102'),
-              ('And adding Back propagation', 2, None, '___sec103'),
-              ('Solving the ODE', 2, None, '___sec104'),
-              ('Using neural network', 2, None, '___sec105'),
-              ('Using a deep neural network', 2, None, '___sec106'),
-              ('Wrapping it up', 2, None, '___sec107')]}
+               '___sec97'),
+              ('The final parts of the code', 2, None, '___sec98'),
+              ('And adding Back propagation', 2, None, '___sec99'),
+              ('Solving the ODE', 2, None, '___sec100'),
+              ('Using neural network', 2, None, '___sec101'),
+              ('Using a deep neural network', 2, None, '___sec102'),
+              ('Wrapping it up', 2, None, '___sec103')]}
 end of tocinfo -->
 
 
@@ -3842,140 +3838,13 @@ painless.
 For simplicity, we assume that the input is an array 
 \( \hat{x}= (x_1, \dots, x_N) \) with \( N \) elements. It is at these points the neural
 network should find \( P \) such that it fulfills \eqref{eq:min}.
+All the ingredients discussed earlier, from the activation function, hidden layers and their weights, biases etc
+are included below.
 
 
    
 









    
 
-
    Feedforward 
    
-
-
    
-First, a feedforward of the inputs must be done. This means that \( \hat{x} \) 
-must be passed through an input layer, a hidden layer and a output
- layer. The input layer in this case, does not need to process the
- data any further. The input layer will consist of \( N_{\mathrm{input} } \)
- neurons, passing its element to each neuron in the hidden layer.  The
- number of neurons in the hidden layer will be \( N_{\mathrm{hidden} } \).
-
-
    
-For the \( i \)-th in the hidden layer with weight \( w_i^{\mathrm{hidden} } \)
-and bias \( b_i^{\mathrm{hidden} } \), the weighting from the \( j \)-th neuron
-at the input layer is:
-
-$$
-\begin{aligned}
-z_{i,j}^{\mathrm{hidden}} &= b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}}x_j \\
-&= 
-\begin{pmatrix}
-b_i^{\mathrm{hidden}} & w_i^{\mathrm{hidden}}
-\end{pmatrix}
-\begin{pmatrix}
-1 \\
-x_j
-\end{pmatrix} 
-\end{aligned}
-$$
-
-
    
-
-
-
    Result after weighting 
    
-
-
    
-The result after weighting the input at the \( i \)-th hidden neuron can be written as a vector:
-$$
-\begin{aligned}
-\hat{z}_{i}^{\mathrm{hidden}} &= \Big( b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}}x_1 , \ b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}} x_2, \ \dots \, , \ b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}} x_N\Big)  \\
-&= 
-\begin{pmatrix}
- b_i^{\mathrm{hidden}}  & w_i^{\mathrm{hidden}}
-\end{pmatrix}
-\begin{pmatrix}
-1  & 1 & \dots & 1 \\
-x_1 & x_2 & \dots & x_N
-\end{pmatrix} \\
-&= \hat{p}_{i, \mathrm{hidden}}^T X
-\end{aligned}
-$$
-
-
    
-It is the vector \( \hat{p}_{i, \mathrm{hidden}}^T \) that defines each row
-in \( P_{\mathrm{hidden} } \), which contains the weights for the neural
-network to minimize according to \eqref{eq:min}.
-
-
    
-After having found \( \hat{z}_{i}^{\mathrm{hidden}}  \) for every neuron \( i \)
-in the hidden layer, the vector will be sent to an activation function
-\( a_i(\hat{z}) \).  In this example, the sigmoid function has been used:
-
-$$
-f(z) = \frac{1}{1 + \exp{(-z)}}.
-$$
-
-
    
-









    
-
-
    Output 
    
-
-
    
-The output $\hat{x}_i^{\mathrm{hidden}}$from each \( i \)-th hidden neuron is:
-
-$$
-\hat{x}_i^{\mathrm{hidden} } = f\big(  \hat{z}_{i}^{\mathrm{hidden}} \big).
-$$
-
-
    
-The outputs \( \hat{x}_i^{\mathrm{hidden} }  \) are then sent to the output layer.
-
-
    
-The output layer consist of one neuron in this case, and combines the
-output from each of the neurons in the hidden layers. The output layer
-combines the results from the hidden layer using some weights \( 
-w_i^{\mathrm{output}} \) and biases \( b_i^{\mathrm{output}} \). In this case,
-it is assumes that the number of neurons in the output layer is one.
-
-
    
-The procedure of weigthing the output neuron \( j \) in the hidden layer
-to the \( i \)-th neuron in the output layer is similar as for the hidden
-layer described previously.
-
-$$
-\begin{aligned}
-z_{1,j}^{\mathrm{output}} & = 
-\begin{pmatrix}
-b_1^{\mathrm{output}} & \hat{w}_1^{\mathrm{output}}
-\end{pmatrix}
-\begin{pmatrix}
-1 \\
-\hat{x}_j^{\mathrm{hidden}}
-\end{pmatrix}
-\end{aligned}
-$$
-
-
    
-Expressing \( z_{1,j}^{\mathrm{output}} \) as a vector gives the following procedure of weighting the inputs from the hidden layer:
-
-$$
-\hat{z}_{1}^{\mathrm{output}} = 
-\begin{pmatrix}
-b_1^{\mathrm{output}} & \hat{w}_1^{\mathrm{output}}
-\end{pmatrix}
-\begin{pmatrix}
-1 & 1 & \dots & 1 \\
-\hat{x}_1^{\mathrm{hidden}} & \hat{x}_2^{\mathrm{hidden}} & \dots & \hat{x}_N^{\mathrm{hidden}}
-\end{pmatrix}
-$$
-
-
    
-In this case we seek a continous range of values since we are
-approximating a function. This means that after computing
-\( \hat{z}_{1}^{\mathrm{output}} \) the neural network has finished its
-feedforward step, and \( \hat{z}_{1}^{\mathrm{output}} \) is the final
-output of the network.
-
-
    
-









    
-
-
    Setting up the code, feed forward part 
    
+
    Setting up the code, feed forward part 
    
 
    
 
 
@@ -4026,10 +3895,10 @@ output of the network.
 
    
 









    
 
-
    Backpropagation 
    
+
    Backpropagation 
    
 
 
    
-Now that feedforward can be done, the next step is to decide how the
+Now that the feedforward can be done, the next step is to decide how the
 parameters should change such that they minimize the cost function.
 
 
    
@@ -4083,7 +3952,7 @@ function along with the right ride of the ODE and trial solution.
 
    
 









    
 
-
    Gradient Descent 
    
+
    Gradient Descent 
    
 
 
    
 The idea of the gradient descent algorithm is to update parameters in
@@ -4112,7 +3981,7 @@ the elements in \( \hat{\omega} \).
 
    
 









    
 
-
    More on GD and cost function 
    
+
    More on GD and cost function 
    
 
 
    
 In our case, we have to minimize the cost function \( c(x, P) \) with
@@ -4125,10 +3994,12 @@ This means that \( P_{\mathrm{hidden} } \) and \( P_{\mathrm{output} } \) is
 updated by
 
 $$
-\begin{aligned}
-P_{\mathrm{hidden},\mathrm{new}} &= P_{\mathrm{hidden}} - \lambda \nabla_{P_{\mathrm{hidden}}} c(x, P)  \\
+\begin{align}
+P_{\mathrm{hidden},\mathrm{new}} &= P_{\mathrm{hidden}} - \lambda \nabla_{P_{\mathrm{hidden}}} c(x, P)  
+\label{_auto13}\\
 P_{\mathrm{output},\mathrm{new}} &= P_{\mathrm{output}} - \lambda \nabla_{P_{\mathrm{output}}} c(x, P)  
-\end{aligned}
+\label{_auto14}
+\end{align}
 $$
 
 
    
@@ -4175,7 +4046,7 @@ for finding the gradients. Luckily, Autograd comes to the rescue.
 
    
 









    
 
-
    An implementation of a Deep Neural Network 
    
+
    An implementation of a Deep Neural Network 
    
 
 
    
 As previously stated, a Deep Neural Network (DNN) follows the same
@@ -4191,54 +4062,7 @@ P_{\mathrm{hidden} }^{(N_{\mathrm{hidden}})}, \ P_{\mathrm{output} }\big\} \).
 
    
 









    
 
-
    Feed forward again 
    
-
-
    
-The feedforward step is similar to as for the neural netowork, but now considering more than one hidden layer.
-
-
    
-The \( i \)-th neuron at layer \( l \) recieves the result
-\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) from the \( j \)-th neuron at layer
-\( l-1 \). The \( i \)-th neuron at layer \( l \) weights all of the elements in
-\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( w_{i,j}^{(l), \ \mathrm{hidden}} \) with as many weigths as there are
-elements in$\hat{x}_j^{(l-1),\mathrm{hidden} }$, and adds a bias
-\( b_i^{(l), \ \mathrm{hidden} } \):
-
-$$
-\begin{aligned}
-z_{i,j}^{(l),\ \mathrm{hidden}} &= b_i^{(l), \ \mathrm{hidden}} + \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T\hat{x}_j^{(l-1),\mathrm{hidden} } \\
-&= 
-\begin{pmatrix}
-b_i^{(l), \ \mathrm{hidden}}  & \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T
-\end{pmatrix}
-\begin{pmatrix}
-1  \\
-\hat{x}_j^{(l-1),\mathrm{hidden} }
-\end{pmatrix} 
-\end{aligned}
-$$
-
-
    
-The output from the \( i \)-th neuron at the hidden layer \( l \) becomes a vector \( \hat{z}_{i}^{(l),\ \mathrm{hidden}} \):
-
-$$
-\begin{aligned}
-\hat{z}_{i}^{(l),\ \mathrm{hidden}} &= \Big(  b_i^{(l), \ \mathrm{hidden}} + \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T\hat{x}_1^{(l-1),\mathrm{hidden} }, \ \dots \ , \  b_i^{(l), \ \mathrm{hidden}} + \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T\hat{x}_{N_{hidden}^{(l-1)}}^{(l-1),\mathrm{hidden} } \Big) \\
-&= 
-\begin{pmatrix}
-b_i^{(l), \ \mathrm{hidden}} & \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T
-\end{pmatrix}
-\begin{pmatrix}
-1 & 1 & \dots & 1 \\
-\hat{x}_{1}^{(l-1),\mathrm{hidden} } & \hat{x}_{2}^{(l-1),\mathrm{hidden} } & \dots & \hat{x}_{N_{hidden}^{(l-1)}}^{(l-1),\mathrm{hidden} }
-\end{pmatrix}
-\end{aligned}
-$$
-
-
    
-









    
-
-
    The final parts of the code 
    
+
    The final parts of the code 
    
 
    
 
 
@@ -4288,7 +4112,7 @@ $$
 
    
 









    
 
-
    And adding Back propagation 
    
+
    And adding Back propagation 
    
 
 
    
 This step is very similar for the neural network. The idea in this
@@ -4366,7 +4190,7 @@ analytically since Autograd does the work for us.
 
    
 









    
 
-
    Solving the ODE  
    
+
    Solving the ODE  
    
 
 
    
 Finally, having set up the networks we are ready to use them to solve the ODE problem. 
@@ -4381,14 +4205,14 @@ We add the analytical solution
 
    
 









    
 
-
    Using neural network 
    
+
    Using neural network 
    
 
 
    
 The code below solves the ODE using a neural network. The number of
 values for the input \( \vec x \) is 10, number of hidden neurons in the
 hidden layer being 10 and th step size used in gradien descent
 \( \lambda = 0.001 \). The program updates the weights and biases in the
-network num_iter times. Finally, it plots the results from using the
+network for a given number of iterations. Finally, it plots the results from using the
 neural network along with the analytical solution.
 
 
    
@@ -4425,7 +4249,7 @@ plt.show()
 
    
 
 
-
    Using a deep neural network 
    
+
    Using a deep neural network 
    
 
 
    
 
@@ -4458,7 +4282,7 @@ plt.show()
 
    
 









    
 
-
    Wrapping it up 
    
+
    Wrapping it up 
    
 
 
    
 By rewriting the ODE as a minimization problem, it was possible to
diff --git a/doc/pub/NeuralNet/html/NeuralNet.html b/doc/pub/NeuralNet/html/NeuralNet.html
index ff0d73330..67f62dbb7 100644
--- a/doc/pub/NeuralNet/html/NeuralNet.html
+++ b/doc/pub/NeuralNet/html/NeuralNet.html
@@ -210,24 +210,20 @@ div { text-align: justify; text-justify: inter-word; }
               ('Reformulating the problem', 2, None, '___sec90'),
               ('Estimating errors', 2, None, '___sec91'),
               ('Creating a simple Deep Neural Net', 2, None, '___sec92'),
-              ('Feedforward', 2, None, '___sec93'),
-              ('Result after weighting', 2, None, '___sec94'),
-              ('Output', 2, None, '___sec95'),
-              ('Setting up the code, feed forward part', 2, None, '___sec96'),
-              ('Backpropagation', 2, None, '___sec97'),
-              ('Gradient Descent', 2, None, '___sec98'),
-              ('More on GD and cost function', 2, None, '___sec99'),
+              ('Setting up the code, feed forward part', 2, None, '___sec93'),
+              ('Backpropagation', 2, None, '___sec94'),
+              ('Gradient Descent', 2, None, '___sec95'),
+              ('More on GD and cost function', 2, None, '___sec96'),
               ('An implementation of a Deep Neural Network',
                2,
                None,
-               '___sec100'),
-              ('Feed forward again', 2, None, '___sec101'),
-              ('The final parts of the code', 2, None, '___sec102'),
-              ('And adding Back propagation', 2, None, '___sec103'),
-              ('Solving the ODE', 2, None, '___sec104'),
-              ('Using neural network', 2, None, '___sec105'),
-              ('Using a deep neural network', 2, None, '___sec106'),
-              ('Wrapping it up', 2, None, '___sec107')]}
+               '___sec97'),
+              ('The final parts of the code', 2, None, '___sec98'),
+              ('And adding Back propagation', 2, None, '___sec99'),
+              ('Solving the ODE', 2, None, '___sec100'),
+              ('Using neural network', 2, None, '___sec101'),
+              ('Using a deep neural network', 2, None, '___sec102'),
+              ('Wrapping it up', 2, None, '___sec103')]}
 end of tocinfo -->
 
 
@@ -3847,140 +3843,13 @@ painless.
 For simplicity, we assume that the input is an array 
 \( \hat{x}= (x_1, \dots, x_N) \) with \( N \) elements. It is at these points the neural
 network should find \( P \) such that it fulfills \eqref{eq:min}.
+All the ingredients discussed earlier, from the activation function, hidden layers and their weights, biases etc
+are included below.
 
 
    
 









    
 
-
    Feedforward 
    
-
-
    
-First, a feedforward of the inputs must be done. This means that \( \hat{x} \) 
-must be passed through an input layer, a hidden layer and a output
- layer. The input layer in this case, does not need to process the
- data any further. The input layer will consist of \( N_{\mathrm{input} } \)
- neurons, passing its element to each neuron in the hidden layer.  The
- number of neurons in the hidden layer will be \( N_{\mathrm{hidden} } \).
-
-
    
-For the \( i \)-th in the hidden layer with weight \( w_i^{\mathrm{hidden} } \)
-and bias \( b_i^{\mathrm{hidden} } \), the weighting from the \( j \)-th neuron
-at the input layer is:
-
-$$
-\begin{aligned}
-z_{i,j}^{\mathrm{hidden}} &= b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}}x_j \\
-&= 
-\begin{pmatrix}
-b_i^{\mathrm{hidden}} & w_i^{\mathrm{hidden}}
-\end{pmatrix}
-\begin{pmatrix}
-1 \\
-x_j
-\end{pmatrix} 
-\end{aligned}
-$$
-
-
    
-
-
-
    Result after weighting 
    
-
-
    
-The result after weighting the input at the \( i \)-th hidden neuron can be written as a vector:
-$$
-\begin{aligned}
-\hat{z}_{i}^{\mathrm{hidden}} &= \Big( b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}}x_1 , \ b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}} x_2, \ \dots \, , \ b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}} x_N\Big)  \\
-&= 
-\begin{pmatrix}
- b_i^{\mathrm{hidden}}  & w_i^{\mathrm{hidden}}
-\end{pmatrix}
-\begin{pmatrix}
-1  & 1 & \dots & 1 \\
-x_1 & x_2 & \dots & x_N
-\end{pmatrix} \\
-&= \hat{p}_{i, \mathrm{hidden}}^T X
-\end{aligned}
-$$
-
-
    
-It is the vector \( \hat{p}_{i, \mathrm{hidden}}^T \) that defines each row
-in \( P_{\mathrm{hidden} } \), which contains the weights for the neural
-network to minimize according to \eqref{eq:min}.
-
-
    
-After having found \( \hat{z}_{i}^{\mathrm{hidden}}  \) for every neuron \( i \)
-in the hidden layer, the vector will be sent to an activation function
-\( a_i(\hat{z}) \).  In this example, the sigmoid function has been used:
-
-$$
-f(z) = \frac{1}{1 + \exp{(-z)}}.
-$$
-
-
    
-









    
-
-
    Output 
    
-
-
    
-The output $\hat{x}_i^{\mathrm{hidden}}$from each \( i \)-th hidden neuron is:
-
-$$
-\hat{x}_i^{\mathrm{hidden} } = f\big(  \hat{z}_{i}^{\mathrm{hidden}} \big).
-$$
-
-
    
-The outputs \( \hat{x}_i^{\mathrm{hidden} }  \) are then sent to the output layer.
-
-
    
-The output layer consist of one neuron in this case, and combines the
-output from each of the neurons in the hidden layers. The output layer
-combines the results from the hidden layer using some weights \( 
-w_i^{\mathrm{output}} \) and biases \( b_i^{\mathrm{output}} \). In this case,
-it is assumes that the number of neurons in the output layer is one.
-
-
    
-The procedure of weigthing the output neuron \( j \) in the hidden layer
-to the \( i \)-th neuron in the output layer is similar as for the hidden
-layer described previously.
-
-$$
-\begin{aligned}
-z_{1,j}^{\mathrm{output}} & = 
-\begin{pmatrix}
-b_1^{\mathrm{output}} & \hat{w}_1^{\mathrm{output}}
-\end{pmatrix}
-\begin{pmatrix}
-1 \\
-\hat{x}_j^{\mathrm{hidden}}
-\end{pmatrix}
-\end{aligned}
-$$
-
-
    
-Expressing \( z_{1,j}^{\mathrm{output}} \) as a vector gives the following procedure of weighting the inputs from the hidden layer:
-
-$$
-\hat{z}_{1}^{\mathrm{output}} = 
-\begin{pmatrix}
-b_1^{\mathrm{output}} & \hat{w}_1^{\mathrm{output}}
-\end{pmatrix}
-\begin{pmatrix}
-1 & 1 & \dots & 1 \\
-\hat{x}_1^{\mathrm{hidden}} & \hat{x}_2^{\mathrm{hidden}} & \dots & \hat{x}_N^{\mathrm{hidden}}
-\end{pmatrix}
-$$
-
-
    
-In this case we seek a continous range of values since we are
-approximating a function. This means that after computing
-\( \hat{z}_{1}^{\mathrm{output}} \) the neural network has finished its
-feedforward step, and \( \hat{z}_{1}^{\mathrm{output}} \) is the final
-output of the network.
-
-
    
-









    
-
-
    Setting up the code, feed forward part 
    
+
    Setting up the code, feed forward part 
    
 
    
 
 
@@ -4031,10 +3900,10 @@ output of the network.
 
    
 









    
 
-
    Backpropagation 
    
+
    Backpropagation 
    
 
 
    
-Now that feedforward can be done, the next step is to decide how the
+Now that the feedforward can be done, the next step is to decide how the
 parameters should change such that they minimize the cost function.
 
 
    
@@ -4088,7 +3957,7 @@ function along with the right ride of the ODE and trial solution.
 
    
 









    
 
-
    Gradient Descent 
    
+
    Gradient Descent 
    
 
 
    
 The idea of the gradient descent algorithm is to update parameters in
@@ -4117,7 +3986,7 @@ the elements in \( \hat{\omega} \).
 
    
 









    
 
-
    More on GD and cost function 
    
+
    More on GD and cost function 
    
 
 
    
 In our case, we have to minimize the cost function \( c(x, P) \) with
@@ -4130,10 +3999,12 @@ This means that \( P_{\mathrm{hidden} } \) and \( P_{\mathrm{output} } \) is
 updated by
 
 $$
-\begin{aligned}
-P_{\mathrm{hidden},\mathrm{new}} &= P_{\mathrm{hidden}} - \lambda \nabla_{P_{\mathrm{hidden}}} c(x, P)  \\
+\begin{align}
+P_{\mathrm{hidden},\mathrm{new}} &= P_{\mathrm{hidden}} - \lambda \nabla_{P_{\mathrm{hidden}}} c(x, P)  
+\label{_auto13}\\
 P_{\mathrm{output},\mathrm{new}} &= P_{\mathrm{output}} - \lambda \nabla_{P_{\mathrm{output}}} c(x, P)  
-\end{aligned}
+\label{_auto14}
+\end{align}
 $$
 
 
    
@@ -4180,7 +4051,7 @@ for finding the gradients. Luckily, Autograd comes to the rescue.
 
    
 









    
 
-
    An implementation of a Deep Neural Network 
    
+
    An implementation of a Deep Neural Network 
    
 
 
    
 As previously stated, a Deep Neural Network (DNN) follows the same
@@ -4196,54 +4067,7 @@ P_{\mathrm{hidden} }^{(N_{\mathrm{hidden}})}, \ P_{\mathrm{output} }\big\} \).
 
    
 









    
 
-
    Feed forward again 
    
-
-
    
-The feedforward step is similar to as for the neural netowork, but now considering more than one hidden layer.
-
-
    
-The \( i \)-th neuron at layer \( l \) recieves the result
-\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) from the \( j \)-th neuron at layer
-\( l-1 \). The \( i \)-th neuron at layer \( l \) weights all of the elements in
-\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( w_{i,j}^{(l), \ \mathrm{hidden}} \) with as many weigths as there are
-elements in$\hat{x}_j^{(l-1),\mathrm{hidden} }$, and adds a bias
-\( b_i^{(l), \ \mathrm{hidden} } \):
-
-$$
-\begin{aligned}
-z_{i,j}^{(l),\ \mathrm{hidden}} &= b_i^{(l), \ \mathrm{hidden}} + \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T\hat{x}_j^{(l-1),\mathrm{hidden} } \\
-&= 
-\begin{pmatrix}
-b_i^{(l), \ \mathrm{hidden}}  & \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T
-\end{pmatrix}
-\begin{pmatrix}
-1  \\
-\hat{x}_j^{(l-1),\mathrm{hidden} }
-\end{pmatrix} 
-\end{aligned}
-$$
-
-
    
-The output from the \( i \)-th neuron at the hidden layer \( l \) becomes a vector \( \hat{z}_{i}^{(l),\ \mathrm{hidden}} \):
-
-$$
-\begin{aligned}
-\hat{z}_{i}^{(l),\ \mathrm{hidden}} &= \Big(  b_i^{(l), \ \mathrm{hidden}} + \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T\hat{x}_1^{(l-1),\mathrm{hidden} }, \ \dots \ , \  b_i^{(l), \ \mathrm{hidden}} + \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T\hat{x}_{N_{hidden}^{(l-1)}}^{(l-1),\mathrm{hidden} } \Big) \\
-&= 
-\begin{pmatrix}
-b_i^{(l), \ \mathrm{hidden}} & \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T
-\end{pmatrix}
-\begin{pmatrix}
-1 & 1 & \dots & 1 \\
-\hat{x}_{1}^{(l-1),\mathrm{hidden} } & \hat{x}_{2}^{(l-1),\mathrm{hidden} } & \dots & \hat{x}_{N_{hidden}^{(l-1)}}^{(l-1),\mathrm{hidden} }
-\end{pmatrix}
-\end{aligned}
-$$
-
-
    
-









    
-
-
    The final parts of the code 
    
+
    The final parts of the code 
    
 
    
 
 
@@ -4293,7 +4117,7 @@ $$
 
    
 









    
 
-
    And adding Back propagation 
    
+
    And adding Back propagation 
    
 
 
    
 This step is very similar for the neural network. The idea in this
@@ -4371,7 +4195,7 @@ analytically since Autograd does the work for us.
 
    
 









    
 
-
    Solving the ODE  
    
+
    Solving the ODE  
    
 
 
    
 Finally, having set up the networks we are ready to use them to solve the ODE problem. 
@@ -4386,14 +4210,14 @@ We add the analytical solution
 
    
 









    
 
-
    Using neural network 
    
+
    Using neural network 
    
 
 
    
 The code below solves the ODE using a neural network. The number of
 values for the input \( \vec x \) is 10, number of hidden neurons in the
 hidden layer being 10 and th step size used in gradien descent
 \( \lambda = 0.001 \). The program updates the weights and biases in the
-network num_iter times. Finally, it plots the results from using the
+network for a given number of iterations. Finally, it plots the results from using the
 neural network along with the analytical solution.
 
 
    
@@ -4430,7 +4254,7 @@ plt.show()
 
    
 
 
-
    Using a deep neural network 
    
+
    Using a deep neural network 
    
 
 
    
 
@@ -4463,7 +4287,7 @@ plt.show()
 
    
 









    
 
-
    Wrapping it up 
    
+
    Wrapping it up 
    
 
 
    
 By rewriting the ODE as a minimization problem, it was possible to
diff --git a/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb b/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb
index dad165cbf..4a8251538 100644
--- a/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb
+++ b/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb
@@ -4266,148 +4266,9 @@
     "For simplicity, we assume that the input is an array \n",
     "$\\hat{x}= (x_1, \\dots, x_N)$ with $N$ elements. It is at these points the neural\n",
     "network should find $P$ such that it fulfills ([eq:min](#eq:min)).\n",
+    "All the ingredients discussed earlier, from the activation function, hidden layers and their weights, biases etc\n",
+    "are included below.\n",
     "\n",
-    "## Feedforward\n",
-    "\n",
-    "First, a feedforward of the inputs must be done. This means that $\\hat{x}$ \n",
-    "must be passed through an input layer, a hidden layer and a output\n",
-    " layer. The input layer in this case, does not need to process the\n",
-    " data any further. The input layer will consist of $N_{\\mathrm{input} }$\n",
-    " neurons, passing its element to each neuron in the hidden layer.  The\n",
-    " number of neurons in the hidden layer will be $N_{\\mathrm{hidden} }$.\n",
-    "\n",
-    "For the $i$-th in the hidden layer with weight $w_i^{\\mathrm{hidden} }$\n",
-    "and bias $b_i^{\\mathrm{hidden} }$, the weighting from the $j$-th neuron\n",
-    "at the input layer is:"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\begin{aligned}\n",
-    "z_{i,j}^{\\mathrm{hidden}} &= b_i^{\\mathrm{hidden}} + w_i^{\\mathrm{hidden}}x_j \\\\\n",
-    "&= \n",
-    "\\begin{pmatrix}\n",
-    "b_i^{\\mathrm{hidden}} & w_i^{\\mathrm{hidden}}\n",
-    "\\end{pmatrix}\n",
-    "\\begin{pmatrix}\n",
-    "1 \\\\\n",
-    "x_j\n",
-    "\\end{pmatrix} \n",
-    "\\end{aligned}\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "\n",
-    "## Result after weighting\n",
-    "\n",
-    "The result after weighting the input at the $i$-th hidden neuron can be written as a vector:"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\hat{z}_{i}^{\\mathrm{hidden}} &= \\Big( b_i^{\\mathrm{hidden}} + w_i^{\\mathrm{hidden}}x_1 , \\ b_i^{\\mathrm{hidden}} + w_i^{\\mathrm{hidden}} x_2, \\ \\dots \\, , \\ b_i^{\\mathrm{hidden}} + w_i^{\\mathrm{hidden}} x_N\\Big)  \\\\\n",
-    "&= \n",
-    "\\begin{pmatrix}\n",
-    " b_i^{\\mathrm{hidden}}  & w_i^{\\mathrm{hidden}}\n",
-    "\\end{pmatrix}\n",
-    "\\begin{pmatrix}\n",
-    "1  & 1 & \\dots & 1 \\\\\n",
-    "x_1 & x_2 & \\dots & x_N\n",
-    "\\end{pmatrix} \\\\\n",
-    "&= \\hat{p}_{i, \\mathrm{hidden}}^T X\n",
-    "\\end{aligned}\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "It is the vector $\\hat{p}_{i, \\mathrm{hidden}}^T$ that defines each row\n",
-    "in $P_{\\mathrm{hidden} }$, which contains the weights for the neural\n",
-    "network to minimize according to ([eq:min](#eq:min)).\n",
-    "\n",
-    "After having found $\\hat{z}_{i}^{\\mathrm{hidden}} $ for every neuron $i$\n",
-    "in the hidden layer, the vector will be sent to an activation function\n",
-    "$a_i(\\hat{z})$.  In this example, the sigmoid function has been used:\n",
-    "\n",
-    "$$\n",
-    "f(z) = \\frac{1}{1 + \\exp{(-z)}}.\n",
-    "$$\n",
-    "\n",
-    "\n",
-    "## Output\n",
-    "\n",
-    "The output $\\hat{x}_i^{\\mathrm{hidden}}$from each $i$-th hidden neuron is:\n",
-    "\n",
-    "$$\n",
-    "\\hat{x}_i^{\\mathrm{hidden} } = f\\big(  \\hat{z}_{i}^{\\mathrm{hidden}} \\big).\n",
-    "$$\n",
-    "\n",
-    "The outputs $\\hat{x}_i^{\\mathrm{hidden} } $ are then sent to the output layer. \n",
-    "\n",
-    "The output layer consist of one neuron in this case, and combines the\n",
-    "output from each of the neurons in the hidden layers. The output layer\n",
-    "combines the results from the hidden layer using some weights $\n",
-    "w_i^{\\mathrm{output}}$ and biases $b_i^{\\mathrm{output}}$. In this case,\n",
-    "it is assumes that the number of neurons in the output layer is one.\n",
-    "\n",
-    "The procedure of weigthing the output neuron $j$ in the hidden layer\n",
-    "to the $i$-th neuron in the output layer is similar as for the hidden\n",
-    "layer described previously."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\begin{aligned}\n",
-    "z_{1,j}^{\\mathrm{output}} & = \n",
-    "\\begin{pmatrix}\n",
-    "b_1^{\\mathrm{output}} & \\hat{w}_1^{\\mathrm{output}}\n",
-    "\\end{pmatrix}\n",
-    "\\begin{pmatrix}\n",
-    "1 \\\\\n",
-    "\\hat{x}_j^{\\mathrm{hidden}}\n",
-    "\\end{pmatrix}\n",
-    "\\end{aligned}\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Expressing $z_{1,j}^{\\mathrm{output}}$ as a vector gives the following procedure of weighting the inputs from the hidden layer:\n",
-    "\n",
-    "$$\n",
-    "\\hat{z}_{1}^{\\mathrm{output}} = \n",
-    "\\begin{pmatrix}\n",
-    "b_1^{\\mathrm{output}} & \\hat{w}_1^{\\mathrm{output}}\n",
-    "\\end{pmatrix}\n",
-    "\\begin{pmatrix}\n",
-    "1  & 1 & \\dots & 1 \\\\\n",
-    "\\hat{x}_1^{\\mathrm{hidden}} & \\hat{x}_2^{\\mathrm{hidden}} & \\dots & \\hat{x}_N^{\\mathrm{hidden}}\n",
-    "\\end{pmatrix}\n",
-    "$$\n",
-    "\n",
-    "In this case we seek a continous range of values since we are\n",
-    "approximating a function. This means that after computing\n",
-    "$\\hat{z}_{1}^{\\mathrm{output}}$ the neural network has finished its\n",
-    "feedforward step, and $\\hat{z}_{1}^{\\mathrm{output}}$ is the final\n",
-    "output of the network.\n",
     "\n",
     "\n",
     "## Setting up the code, feed forward part"
@@ -4472,7 +4333,7 @@
    "source": [
     "## Backpropagation\n",
     "\n",
-    "Now that feedforward can be done, the next step is to decide how the\n",
+    "Now that the feedforward can be done, the next step is to decide how the\n",
     "parameters should change such that they minimize the cost function.\n",
     "\n",
     "Recall that the chosen cost function for this problem is"
@@ -4588,11 +4449,29 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "\n",
+    "
    \n",
+    "\n",
     "$$\n",
-    "\\begin{aligned}\n",
-    "P_{\\mathrm{hidden},\\mathrm{new}} &= P_{\\mathrm{hidden}} - \\lambda \\nabla_{P_{\\mathrm{hidden}}} c(x, P)  \\\\\n",
-    "P_{\\mathrm{output},\\mathrm{new}} &= P_{\\mathrm{output}} - \\lambda \\nabla_{P_{\\mathrm{output}}} c(x, P)  \n",
-    "\\end{aligned}\n",
+    "\\begin{equation}\n",
+    "P_{\\mathrm{hidden},\\mathrm{new}} = P_{\\mathrm{hidden}} - \\lambda \\nabla_{P_{\\mathrm{hidden}}} c(x, P)  \n",
+    "\\label{_auto13} \\tag{20}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "\n",
+    "
    \n",
+    "\n",
+    "$$\n",
+    "\\begin{equation} \n",
+    "P_{\\mathrm{output},\\mathrm{new}} = P_{\\mathrm{output}} - \\lambda \\nabla_{P_{\\mathrm{output}}} c(x, P)  \n",
+    "\\label{_auto14} \\tag{21}\n",
+    "\\end{equation}\n",
     "$$"
    ]
   },
@@ -4664,67 +4543,8 @@
     "P_{\\mathrm{hidden} }^{(N_{\\mathrm{hidden}})}, \\ P_{\\mathrm{output} }\\big\\}$.\n",
     "\n",
     "\n",
-    "## Feed forward again\n",
     "\n",
-    "The feedforward step is similar to as for the neural netowork, but now considering more than one hidden layer. \n",
     "\n",
-    "The $i$-th neuron at layer $l$ recieves the result\n",
-    "$\\hat{x}_j^{(l-1),\\mathrm{hidden} }$ from the $j$-th neuron at layer\n",
-    "$l-1$. The $i$-th neuron at layer $l$ weights all of the elements in\n",
-    "$\\hat{x}_j^{(l-1),\\mathrm{hidden} }$ with a weight vector $w_{i,j}^{(l), \\ \\mathrm{hidden}}$ with as many weigths as there are\n",
-    "elements in$\\hat{x}_j^{(l-1),\\mathrm{hidden} }$, and adds a bias\n",
-    "$b_i^{(l), \\ \\mathrm{hidden} }$:"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\begin{aligned}\n",
-    "z_{i,j}^{(l),\\ \\mathrm{hidden}} &= b_i^{(l), \\ \\mathrm{hidden}} + \\big(\\hat{w}_{i}^{(l), \\ \\mathrm{hidden}}\\big)^T\\hat{x}_j^{(l-1),\\mathrm{hidden} } \\\\\n",
-    "&= \n",
-    "\\begin{pmatrix}\n",
-    "b_i^{(l), \\ \\mathrm{hidden}}  & \\big(\\hat{w}_{i}^{(l), \\ \\mathrm{hidden}}\\big)^T\n",
-    "\\end{pmatrix}\n",
-    "\\begin{pmatrix}\n",
-    "1  \\\\\n",
-    "\\hat{x}_j^{(l-1),\\mathrm{hidden} }\n",
-    "\\end{pmatrix} \n",
-    "\\end{aligned}\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The output from the $i$-th neuron at the hidden layer $l$ becomes a vector $\\hat{z}_{i}^{(l),\\ \\mathrm{hidden}}$:"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\hat{z}_{i}^{(l),\\ \\mathrm{hidden}} &= \\Big(  b_i^{(l), \\ \\mathrm{hidden}} + \\big(\\hat{w}_{i}^{(l), \\ \\mathrm{hidden}}\\big)^T\\hat{x}_1^{(l-1),\\mathrm{hidden} }, \\ \\dots \\ , \\  b_i^{(l), \\ \\mathrm{hidden}} + \\big(\\hat{w}_{i}^{(l), \\ \\mathrm{hidden}}\\big)^T\\hat{x}_{N_{hidden}^{(l-1)}}^{(l-1),\\mathrm{hidden} } \\Big) \\\\\n",
-    "&= \n",
-    "\\begin{pmatrix}\n",
-    "b_i^{(l), \\ \\mathrm{hidden}} & \\big(\\hat{w}_{i}^{(l), \\ \\mathrm{hidden}}\\big)^T\n",
-    "\\end{pmatrix}\n",
-    "\\begin{pmatrix}\n",
-    "1 & 1 & \\dots & 1 \\\\\n",
-    "\\hat{x}_{1}^{(l-1),\\mathrm{hidden} } & \\hat{x}_{2}^{(l-1),\\mathrm{hidden} } & \\dots & \\hat{x}_{N_{hidden}^{(l-1)}}^{(l-1),\\mathrm{hidden} }\n",
-    "\\end{pmatrix}\n",
-    "\\end{aligned}\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
     "## The final parts of the code"
    ]
   },
@@ -4897,7 +4717,7 @@
     "values for the input $\\vec x$ is 10, number of hidden neurons in the\n",
     "hidden layer being 10 and th step size used in gradien descent\n",
     "$\\lambda = 0.001$. The program updates the weights and biases in the\n",
-    "network *num_iter* times. Finally, it plots the results from using the\n",
+    "network for a given number of iterations. Finally, it plots the results from using the\n",
     "neural network along with the analytical solution."
    ]
   },
diff --git a/doc/pub/NeuralNet/ipynb/ipynb-NeuralNet-src.tar.gz b/doc/pub/NeuralNet/ipynb/ipynb-NeuralNet-src.tar.gz
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diff --git a/doc/src/NeuralNet/NeuralNet.do.txt b/doc/src/NeuralNet/NeuralNet.do.txt
index 958c631f5..5c0da3c04 100644
--- a/doc/src/NeuralNet/NeuralNet.do.txt
+++ b/doc/src/NeuralNet/NeuralNet.do.txt
@@ -3214,120 +3214,9 @@ painless.
 For simplicity, we assume that the input is an array 
 $\hat{x}= (x_1, \dots, x_N)$ with $N$ elements. It is at these points the neural
 network should find $P$ such that it fulfills (ref{eq:min}).
+All the ingredients discussed earlier, from the activation function, hidden layers and their weights, biases etc
+are included below.
 
-!split
-===== Feedforward =====
-
-First, a feedforward of the inputs must be done. This means that $\hat{x}$ 
-must be passed through an input layer, a hidden layer and a output
- layer. The input layer in this case, does not need to process the
- data any further. The input layer will consist of $N_{\mathrm{input} }$
- neurons, passing its element to each neuron in the hidden layer.  The
- number of neurons in the hidden layer will be $N_{\mathrm{hidden} }$.
-
-For the $i$-th in the hidden layer with weight $w_i^{\mathrm{hidden} }$
-and bias $b_i^{\mathrm{hidden} }$, the weighting from the $j$-th neuron
-at the input layer is:
-
-!bt
-\begin{aligned}
-z_{i,j}^{\mathrm{hidden}} &= b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}}x_j \\
-&= 
-\begin{pmatrix}
-b_i^{\mathrm{hidden}} & w_i^{\mathrm{hidden}}
-\end{pmatrix}
-\begin{pmatrix}
-1 \\
-x_j
-\end{pmatrix} 
-\end{aligned}
-!et
-
-
-!split 
-===== Result after weighting =====
-
-The result after weighting the input at the $i$-th hidden neuron can be written as a vector:
-!bt
-\begin{aligned}
-\hat{z}_{i}^{\mathrm{hidden}} &= \Big( b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}}x_1 , \ b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}} x_2, \ \dots \, , \ b_i^{\mathrm{hidden}} + w_i^{\mathrm{hidden}} x_N\Big)  \\
-&= 
-\begin{pmatrix}
- b_i^{\mathrm{hidden}}  & w_i^{\mathrm{hidden}}
-\end{pmatrix}
-\begin{pmatrix}
-1  & 1 & \dots & 1 \\
-x_1 & x_2 & \dots & x_N
-\end{pmatrix} \\
-&= \hat{p}_{i, \mathrm{hidden}}^T X
-\end{aligned}
-!et
-
-It is the vector $\hat{p}_{i, \mathrm{hidden}}^T$ that defines each row
-in $P_{\mathrm{hidden} }$, which contains the weights for the neural
-network to minimize according to (ref{eq:min}).
-
-After having found $\hat{z}_{i}^{\mathrm{hidden}} $ for every neuron $i$
-in the hidden layer, the vector will be sent to an activation function
-$a_i(\hat{z})$.  In this example, the sigmoid function has been used:
-
-$$
-f(z) = \frac{1}{1 + \exp{(-z)}}.
-$$
-
-
-!split
-===== Output =====
-
-The output $\hat{x}_i^{\mathrm{hidden}}$from each $i$-th hidden neuron is:
-
-$$
-\hat{x}_i^{\mathrm{hidden} } = f\big(  \hat{z}_{i}^{\mathrm{hidden}} \big).
-$$
-
-The outputs $\hat{x}_i^{\mathrm{hidden} } $ are then sent to the output layer. 
-
-The output layer consist of one neuron in this case, and combines the
-output from each of the neurons in the hidden layers. The output layer
-combines the results from the hidden layer using some weights $
-w_i^{\mathrm{output}}$ and biases $b_i^{\mathrm{output}}$. In this case,
-it is assumes that the number of neurons in the output layer is one.
-
-The procedure of weigthing the output neuron $j$ in the hidden layer
-to the $i$-th neuron in the output layer is similar as for the hidden
-layer described previously.
-
-!bt
-\begin{aligned}
-z_{1,j}^{\mathrm{output}} & = 
-\begin{pmatrix}
-b_1^{\mathrm{output}} & \hat{w}_1^{\mathrm{output}}
-\end{pmatrix}
-\begin{pmatrix}
-1 \\
-\hat{x}_j^{\mathrm{hidden}}
-\end{pmatrix}
-\end{aligned}
-!et
-
-Expressing $z_{1,j}^{\mathrm{output}}$ as a vector gives the following procedure of weighting the inputs from the hidden layer:
-
-$$
-\hat{z}_{1}^{\mathrm{output}} = 
-\begin{pmatrix}
-b_1^{\mathrm{output}} & \hat{w}_1^{\mathrm{output}}
-\end{pmatrix}
-\begin{pmatrix}
-1  & 1 & \dots & 1 \\
-\hat{x}_1^{\mathrm{hidden}} & \hat{x}_2^{\mathrm{hidden}} & \dots & \hat{x}_N^{\mathrm{hidden}}
-\end{pmatrix}
-$$
-
-In this case we seek a continous range of values since we are
-approximating a function. This means that after computing
-$\hat{z}_{1}^{\mathrm{output}}$ the neural network has finished its
-feedforward step, and $\hat{z}_{1}^{\mathrm{output}}$ is the final
-output of the network.
 
 
 !split
@@ -3381,7 +3270,7 @@ def neural_network(params, x):
 !split
 ===== Backpropagation =====
 
-Now that feedforward can be done, the next step is to decide how the
+Now that the feedforward can be done, the next step is to decide how the
 parameters should change such that they minimize the cost function.
 
 Recall that the chosen cost function for this problem is 
@@ -3468,10 +3357,10 @@ This means that $P_{\mathrm{hidden} }$ and $P_{\mathrm{output} }$ is
 updated by
 
 !bt
-\begin{aligned}
+\begin{align}
 P_{\mathrm{hidden},\mathrm{new}} &= P_{\mathrm{hidden}} - \lambda \nabla_{P_{\mathrm{hidden}}} c(x, P)  \\
 P_{\mathrm{output},\mathrm{new}} &= P_{\mathrm{output}} - \lambda \nabla_{P_{\mathrm{output}}} c(x, P)  
-\end{aligned}
+\end{align}
 !et
 
 This might look like a cumberstone to set up the correct expression
@@ -3528,47 +3417,7 @@ P_{\mathrm{hidden} }^{(1)}, \ P_{\mathrm{hidden} }^{(2)}, \ \dots , \
 P_{\mathrm{hidden} }^{(N_{\mathrm{hidden}})}, \ P_{\mathrm{output} }\big\}$.
 
 
-!split
-===== Feed forward again =====
 
-The feedforward step is similar to as for the neural netowork, but now considering more than one hidden layer. 
-
-The $i$-th neuron at layer $l$ recieves the result
-$\hat{x}_j^{(l-1),\mathrm{hidden} }$ from the $j$-th neuron at layer
-$l-1$. The $i$-th neuron at layer $l$ weights all of the elements in
-$\hat{x}_j^{(l-1),\mathrm{hidden} }$ with a weight vector $w_{i,j}^{(l), \ \mathrm{hidden}}$ with as many weigths as there are
-elements in$\hat{x}_j^{(l-1),\mathrm{hidden} }$, and adds a bias
-$b_i^{(l), \ \mathrm{hidden} }$:
-
-!bt
-\begin{aligned}
-z_{i,j}^{(l),\ \mathrm{hidden}} &= b_i^{(l), \ \mathrm{hidden}} + \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T\hat{x}_j^{(l-1),\mathrm{hidden} } \\
-&= 
-\begin{pmatrix}
-b_i^{(l), \ \mathrm{hidden}}  & \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T
-\end{pmatrix}
-\begin{pmatrix}
-1  \\
-\hat{x}_j^{(l-1),\mathrm{hidden} }
-\end{pmatrix} 
-\end{aligned}
-!et
-
-The output from the $i$-th neuron at the hidden layer $l$ becomes a vector $\hat{z}_{i}^{(l),\ \mathrm{hidden}}$:
-
-!bt
-\begin{aligned}
-\hat{z}_{i}^{(l),\ \mathrm{hidden}} &= \Big(  b_i^{(l), \ \mathrm{hidden}} + \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T\hat{x}_1^{(l-1),\mathrm{hidden} }, \ \dots \ , \  b_i^{(l), \ \mathrm{hidden}} + \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T\hat{x}_{N_{hidden}^{(l-1)}}^{(l-1),\mathrm{hidden} } \Big) \\
-&= 
-\begin{pmatrix}
-b_i^{(l), \ \mathrm{hidden}} & \big(\hat{w}_{i}^{(l), \ \mathrm{hidden}}\big)^T
-\end{pmatrix}
-\begin{pmatrix}
-1 & 1 & \dots & 1 \\
-\hat{x}_{1}^{(l-1),\mathrm{hidden} } & \hat{x}_{2}^{(l-1),\mathrm{hidden} } & \dots & \hat{x}_{N_{hidden}^{(l-1)}}^{(l-1),\mathrm{hidden} }
-\end{pmatrix}
-\end{aligned}
-!et
 
 !split
 ===== The final parts of the code =====
@@ -3710,7 +3559,7 @@ The code below solves the ODE using a neural network. The number of
 values for the input $\vec x$ is 10, number of hidden neurons in the
 hidden layer being 10 and th step size used in gradien descent
 $\lambda = 0.001$. The program updates the weights and biases in the
-network *num_iter* times. Finally, it plots the results from using the
+network for a given number of iterations. Finally, it plots the results from using the
 neural network along with the analytical solution.