diff --git a/doc/pub/week42/html/._week42-bs000.html b/doc/pub/week42/html/._week42-bs000.html
index bdb5f998a..d836f3987 100644
--- a/doc/pub/week42/html/._week42-bs000.html
+++ b/doc/pub/week42/html/._week42-bs000.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -392,7 +410,7 @@ MathJax.Hub.Config({
9
10
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs001.html b/doc/pub/week42/html/._week42-bs001.html
index e61672723..6b5cf1166 100644
--- a/doc/pub/week42/html/._week42-bs001.html
+++ b/doc/pub/week42/html/._week42-bs001.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -401,7 +419,7 @@ MathJax.Hub.Config({
10
11
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs002.html b/doc/pub/week42/html/._week42-bs002.html
index 4f774fbe8..adb90d7e3 100644
--- a/doc/pub/week42/html/._week42-bs002.html
+++ b/doc/pub/week42/html/._week42-bs002.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -373,7 +391,7 @@ we will also study the usage of 11
12
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs003.html b/doc/pub/week42/html/._week42-bs003.html
index e8ce13760..736b8e062 100644
--- a/doc/pub/week42/html/._week42-bs003.html
+++ b/doc/pub/week42/html/._week42-bs003.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -390,7 +408,7 @@ and output layer to any given precision.
12
13
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs004.html b/doc/pub/week42/html/._week42-bs004.html
index d8b08302c..72a59fbf2 100644
--- a/doc/pub/week42/html/._week42-bs004.html
+++ b/doc/pub/week42/html/._week42-bs004.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -393,7 +411,7 @@ for the solution to be unique.
13
14
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs005.html b/doc/pub/week42/html/._week42-bs005.html
index cd9f39038..849c19ea5 100644
--- a/doc/pub/week42/html/._week42-bs005.html
+++ b/doc/pub/week42/html/._week42-bs005.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -398,7 +416,7 @@ As described previously, an optimization method could be used to minimize the pa
14
15
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs006.html b/doc/pub/week42/html/._week42-bs006.html
index 01691e7f7..22d2f9d49 100644
--- a/doc/pub/week42/html/._week42-bs006.html
+++ b/doc/pub/week42/html/._week42-bs006.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -400,7 +418,7 @@ The neural net should then find the parameters \( P \) that minimizes the cost f
15
16
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs007.html b/doc/pub/week42/html/._week42-bs007.html
index 7dcef6a2a..ecdd75585 100644
--- a/doc/pub/week42/html/._week42-bs007.html
+++ b/doc/pub/week42/html/._week42-bs007.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -382,7 +400,7 @@ Automatic differentiation is a method of finding the derivatives numerically wit
16
17
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs008.html b/doc/pub/week42/html/._week42-bs008.html
index 4146b5adc..1dfcfff2c 100644
--- a/doc/pub/week42/html/._week42-bs008.html
+++ b/doc/pub/week42/html/._week42-bs008.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -400,7 +418,7 @@ Having an analytical solution at hand, it is possible to use it to compare how w
17
18
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs009.html b/doc/pub/week42/html/._week42-bs009.html
index bf5fd99ed..d61f6ebe0 100644
--- a/doc/pub/week42/html/._week42-bs009.html
+++ b/doc/pub/week42/html/._week42-bs009.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -391,7 +409,7 @@ In this example, \( \gamma = 2 \) and \( g_0 = 10 \).
18
19
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs010.html b/doc/pub/week42/html/._week42-bs010.html
index 47d5983df..819950858 100644
--- a/doc/pub/week42/html/._week42-bs010.html
+++ b/doc/pub/week42/html/._week42-bs010.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
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+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -385,7 +403,7 @@ with \( h_1(x) \) ensuring that \( g_t(x) \) satisfies some conditions and \( h_
19
20
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs011.html b/doc/pub/week42/html/._week42-bs011.html
index 735600d13..57659d870 100644
--- a/doc/pub/week42/html/._week42-bs011.html
+++ b/doc/pub/week42/html/._week42-bs011.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -397,7 +415,7 @@ $$
20
21
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs012.html b/doc/pub/week42/html/._week42-bs012.html
index d154967f2..1b1fa9e4c 100644
--- a/doc/pub/week42/html/._week42-bs012.html
+++ b/doc/pub/week42/html/._week42-bs012.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -406,7 +424,7 @@ is fulfilled as best as possible.
21
22
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs013.html b/doc/pub/week42/html/._week42-bs013.html
index 5c09bfa71..91aa9eec4 100644
--- a/doc/pub/week42/html/._week42-bs013.html
+++ b/doc/pub/week42/html/._week42-bs013.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -402,7 +420,7 @@ for an input value \( x \).
22
23
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs014.html b/doc/pub/week42/html/._week42-bs014.html
index a87f4f87e..dc8704f7a 100644
--- a/doc/pub/week42/html/._week42-bs014.html
+++ b/doc/pub/week42/html/._week42-bs014.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -400,7 +418,7 @@ $$
23
24
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs015.html b/doc/pub/week42/html/._week42-bs015.html
index abfd4e253..57a841ecf 100644
--- a/doc/pub/week42/html/._week42-bs015.html
+++ b/doc/pub/week42/html/._week42-bs015.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -385,7 +403,7 @@ The input layer will consist of \( N_{\text{input} } \) neurons, passing its ele
24
25
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs016.html b/doc/pub/week42/html/._week42-bs016.html
index a6b4c6c17..a8e7a530d 100644
--- a/doc/pub/week42/html/._week42-bs016.html
+++ b/doc/pub/week42/html/._week42-bs016.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -394,7 +412,7 @@ $$
25
26
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs017.html b/doc/pub/week42/html/._week42-bs017.html
index ab6da065a..1bca0dab2 100644
--- a/doc/pub/week42/html/._week42-bs017.html
+++ b/doc/pub/week42/html/._week42-bs017.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -395,7 +413,7 @@ $$
26
27
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs018.html b/doc/pub/week42/html/._week42-bs018.html
index 5372b7921..89053614f 100644
--- a/doc/pub/week42/html/._week42-bs018.html
+++ b/doc/pub/week42/html/._week42-bs018.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -410,7 +428,7 @@ it is assumes that the number of neurons in the output layer is one.
27
28
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs019.html b/doc/pub/week42/html/._week42-bs019.html
index 697a39ca3..68256d1ef 100644
--- a/doc/pub/week42/html/._week42-bs019.html
+++ b/doc/pub/week42/html/._week42-bs019.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -393,7 +411,7 @@ $$
28
29
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs020.html b/doc/pub/week42/html/._week42-bs020.html
index 3c685e5d1..31cd5cb96 100644
--- a/doc/pub/week42/html/._week42-bs020.html
+++ b/doc/pub/week42/html/._week42-bs020.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -394,7 +412,7 @@ In this case we seek a continuous range of values since we are approximating a f
29
30
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs021.html b/doc/pub/week42/html/._week42-bs021.html
index 44bcac8a2..8b7e4e320 100644
--- a/doc/pub/week42/html/._week42-bs021.html
+++ b/doc/pub/week42/html/._week42-bs021.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
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@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -393,7 +411,7 @@ Here, gradient descent with a constant step size has been chosen.
30
31
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs022.html b/doc/pub/week42/html/._week42-bs022.html
index 1fc2c7771..38608ef8d 100644
--- a/doc/pub/week42/html/._week42-bs022.html
+++ b/doc/pub/week42/html/._week42-bs022.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
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+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
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2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -415,7 +433,7 @@ $$
31
32
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs023.html b/doc/pub/week42/html/._week42-bs023.html
index b2df8c5f1..23a977b9c 100644
--- a/doc/pub/week42/html/._week42-bs023.html
+++ b/doc/pub/week42/html/._week42-bs023.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -525,7 +543,7 @@ MathJax.Hub.Config({
32
33
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs024.html b/doc/pub/week42/html/._week42-bs024.html
index 0ae0e62cb..aa491419e 100644
--- a/doc/pub/week42/html/._week42-bs024.html
+++ b/doc/pub/week42/html/._week42-bs024.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -545,7 +563,7 @@ The number of neurons within each hidden layer are given as a list of integers i
33
34
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs025.html b/doc/pub/week42/html/._week42-bs025.html
index f42658e07..0d35b2101 100644
--- a/doc/pub/week42/html/._week42-bs025.html
+++ b/doc/pub/week42/html/._week42-bs025.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -397,7 +415,7 @@ Here, we stay with a more simple approach and implement for comparison, the simp
34
35
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs026.html b/doc/pub/week42/html/._week42-bs026.html
index 928da4c2d..2f9a16bff 100644
--- a/doc/pub/week42/html/._week42-bs026.html
+++ b/doc/pub/week42/html/._week42-bs026.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -393,7 +411,7 @@ In this example, we let \( \alpha = 2 \), \( A = 1 \), and \( g_0 = 1.2 \).
35
36
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs027.html b/doc/pub/week42/html/._week42-bs027.html
index 6407b2344..51a25b4db 100644
--- a/doc/pub/week42/html/._week42-bs027.html
+++ b/doc/pub/week42/html/._week42-bs027.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -398,7 +416,7 @@ $$
36
37
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs028.html b/doc/pub/week42/html/._week42-bs028.html
index ced9a147a..7450e5623 100644
--- a/doc/pub/week42/html/._week42-bs028.html
+++ b/doc/pub/week42/html/._week42-bs028.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -547,7 +565,7 @@ The network will be the similar as for the exponential decay example, but with s
37
38
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs029.html b/doc/pub/week42/html/._week42-bs029.html
index 619d24e31..cab10f322 100644
--- a/doc/pub/week42/html/._week42-bs029.html
+++ b/doc/pub/week42/html/._week42-bs029.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
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+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
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+ ('Convolution Examples: Principle of Superposition and Periodic '
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+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
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@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -501,7 +519,7 @@ extending the program that uses the network using Autograd:
38
39
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs030.html b/doc/pub/week42/html/._week42-bs030.html
index 9968562a5..bfa68bff7 100644
--- a/doc/pub/week42/html/._week42-bs030.html
+++ b/doc/pub/week42/html/._week42-bs030.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
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+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
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+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
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@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -403,7 +421,7 @@ In addition, it could be interesting to see how a typical method for numerically
39
40
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs031.html b/doc/pub/week42/html/._week42-bs031.html
index 1d537b9dd..28043a4c8 100644
--- a/doc/pub/week42/html/._week42-bs031.html
+++ b/doc/pub/week42/html/._week42-bs031.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
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2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -410,7 +428,7 @@ $$
40
41
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs032.html b/doc/pub/week42/html/._week42-bs032.html
index 97df5525e..1cfbb4412 100644
--- a/doc/pub/week42/html/._week42-bs032.html
+++ b/doc/pub/week42/html/._week42-bs032.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
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2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -531,7 +549,7 @@ MathJax.Hub.Config({
41
42
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs033.html b/doc/pub/week42/html/._week42-bs033.html
index fb76e1d1b..06fa1b87e 100644
--- a/doc/pub/week42/html/._week42-bs033.html
+++ b/doc/pub/week42/html/._week42-bs033.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -470,7 +488,7 @@ which makes it possible to solve for the vector \( \boldsymbol{g} \).
42
43
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs034.html b/doc/pub/week42/html/._week42-bs034.html
index 5c9bc5e58..cbb761dc8 100644
--- a/doc/pub/week42/html/._week42-bs034.html
+++ b/doc/pub/week42/html/._week42-bs034.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -574,7 +592,7 @@ We can then compare the result from this numerical scheme with the output from o
43
44
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs035.html b/doc/pub/week42/html/._week42-bs035.html
index 57dd558e5..507cfa53d 100644
--- a/doc/pub/week42/html/._week42-bs035.html
+++ b/doc/pub/week42/html/._week42-bs035.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -395,7 +413,7 @@ where \( f \) is an expression involving all kinds of possible mixed derivatives
44
45
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs036.html b/doc/pub/week42/html/._week42-bs036.html
index 1ebc9758c..251e92dd9 100644
--- a/doc/pub/week42/html/._week42-bs036.html
+++ b/doc/pub/week42/html/._week42-bs036.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
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+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -395,7 +413,7 @@ The role of the function \( h_2(x_1,\dots,x_N,N(x_1,\dots,x_N,P)) \), is to ensu
45
46
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs037.html b/doc/pub/week42/html/._week42-bs037.html
index 80370e53a..832b00ada 100644
--- a/doc/pub/week42/html/._week42-bs037.html
+++ b/doc/pub/week42/html/._week42-bs037.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
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+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -395,7 +413,7 @@ $$
46
47
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs038.html b/doc/pub/week42/html/._week42-bs038.html
index 5dc91ccc6..4d67376ae 100644
--- a/doc/pub/week42/html/._week42-bs038.html
+++ b/doc/pub/week42/html/._week42-bs038.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
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+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
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+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
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@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -391,7 +409,7 @@ $$
47
48
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs039.html b/doc/pub/week42/html/._week42-bs039.html
index 01b9a0f48..ef2217815 100644
--- a/doc/pub/week42/html/._week42-bs039.html
+++ b/doc/pub/week42/html/._week42-bs039.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
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+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -397,7 +415,7 @@ with \( u(x) \) being some given function.
48
49
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs040.html b/doc/pub/week42/html/._week42-bs040.html
index 44cf7c4b5..1de5b9aa6 100644
--- a/doc/pub/week42/html/._week42-bs040.html
+++ b/doc/pub/week42/html/._week42-bs040.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
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+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -404,7 +422,7 @@ First, we will look into how Autograd could be used in a network tailored to sol
49
50
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs041.html b/doc/pub/week42/html/._week42-bs041.html
index 107456adf..1c46d4057 100644
--- a/doc/pub/week42/html/._week42-bs041.html
+++ b/doc/pub/week42/html/._week42-bs041.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -434,7 +452,7 @@ network at each possible pair \( (x,t) \), given an array for the desired
50
51
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs042.html b/doc/pub/week42/html/._week42-bs042.html
index 8744d2672..64db9f808 100644
--- a/doc/pub/week42/html/._week42-bs042.html
+++ b/doc/pub/week42/html/._week42-bs042.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -401,7 +419,7 @@ since \( (0) = u(1) = 0 \) and \( u(x) = \sin(\pi x) \).
51
52
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs043.html b/doc/pub/week42/html/._week42-bs043.html
index 9815fe948..26ac6cfd9 100644
--- a/doc/pub/week42/html/._week42-bs043.html
+++ b/doc/pub/week42/html/._week42-bs043.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -439,7 +457,7 @@ mixed derivatives of \( g(x,t) \).
52
53
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs044.html b/doc/pub/week42/html/._week42-bs044.html
index 255c41526..63fe51927 100644
--- a/doc/pub/week42/html/._week42-bs044.html
+++ b/doc/pub/week42/html/._week42-bs044.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -623,7 +641,7 @@ Using TensorFlow results in a much better execution time. Try it!
53
54
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs045.html b/doc/pub/week42/html/._week42-bs045.html
index 69e2c3381..b0c8b4810 100644
--- a/doc/pub/week42/html/._week42-bs045.html
+++ b/doc/pub/week42/html/._week42-bs045.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -401,7 +419,7 @@ where \( \frac{\partial g(x,t)}{\partial t} \Big |_{t = 0} \) means the derivati
54
55
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs046.html b/doc/pub/week42/html/._week42-bs046.html
index 56450bb71..7028af6e7 100644
--- a/doc/pub/week42/html/._week42-bs046.html
+++ b/doc/pub/week42/html/._week42-bs046.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -402,7 +420,7 @@ In this example, let \( c = 1 \) and \( u(x) = \sin(\pi x) \) and \( v(x) = -\pi
55
56
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs047.html b/doc/pub/week42/html/._week42-bs047.html
index 2ee79c61e..c2dc521fc 100644
--- a/doc/pub/week42/html/._week42-bs047.html
+++ b/doc/pub/week42/html/._week42-bs047.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -396,7 +414,7 @@ Note that this trial solution satisfies the conditions only if \( u(0) = v(0) =
56
57
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs048.html b/doc/pub/week42/html/._week42-bs048.html
index d3b52cf64..df1bdba67 100644
--- a/doc/pub/week42/html/._week42-bs048.html
+++ b/doc/pub/week42/html/._week42-bs048.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -384,7 +402,7 @@ $$
57
58
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs049.html b/doc/pub/week42/html/._week42-bs049.html
index 3d66dc95c..786b57a9f 100644
--- a/doc/pub/week42/html/._week42-bs049.html
+++ b/doc/pub/week42/html/._week42-bs049.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -601,7 +619,7 @@ MathJax.Hub.Config({
58
59
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- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs050.html b/doc/pub/week42/html/._week42-bs050.html
index 860c886a0..71ff8ed29 100644
--- a/doc/pub/week42/html/._week42-bs050.html
+++ b/doc/pub/week42/html/._week42-bs050.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -383,7 +401,7 @@ MathJax.Hub.Config({
59
60
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs051.html b/doc/pub/week42/html/._week42-bs051.html
index bad554ea4..eaecaa6c0 100644
--- a/doc/pub/week42/html/._week42-bs051.html
+++ b/doc/pub/week42/html/._week42-bs051.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -411,7 +429,7 @@ Another good read is the article here 60
61
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs052.html b/doc/pub/week42/html/._week42-bs052.html
index b3e8dbea1..bbf7e558a 100644
--- a/doc/pub/week42/html/._week42-bs052.html
+++ b/doc/pub/week42/html/._week42-bs052.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -386,7 +404,7 @@ before the transformation.
61
62
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs053.html b/doc/pub/week42/html/._week42-bs053.html
index 72cd50ce9..badd1e515 100644
--- a/doc/pub/week42/html/._week42-bs053.html
+++ b/doc/pub/week42/html/._week42-bs053.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -400,7 +418,7 @@ in the input).
62
63
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs054.html b/doc/pub/week42/html/._week42-bs054.html
index cc257de62..d0c2972f9 100644
--- a/doc/pub/week42/html/._week42-bs054.html
+++ b/doc/pub/week42/html/._week42-bs054.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -400,7 +418,7 @@ would quickly lead to possible overfitting.
63
64
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs055.html b/doc/pub/week42/html/._week42-bs055.html
index f61725188..37b126799 100644
--- a/doc/pub/week42/html/._week42-bs055.html
+++ b/doc/pub/week42/html/._week42-bs055.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -412,7 +430,7 @@ dimension.
64
65
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs056.html b/doc/pub/week42/html/._week42-bs056.html
index 9a6a3f3bb..d4b0d36c3 100644
--- a/doc/pub/week42/html/._week42-bs056.html
+++ b/doc/pub/week42/html/._week42-bs056.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -395,7 +413,7 @@ A simple CNN for image classification could have the architecture:
65
66
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs057.html b/doc/pub/week42/html/._week42-bs057.html
index 20e29e590..ceca9f7f2 100644
--- a/doc/pub/week42/html/._week42-bs057.html
+++ b/doc/pub/week42/html/._week42-bs057.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -391,7 +409,7 @@ are consistent with the labels in the training set for each image.
66
67
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs058.html b/doc/pub/week42/html/._week42-bs058.html
index 6ad72e677..89b2ce73c 100644
--- a/doc/pub/week42/html/._week42-bs058.html
+++ b/doc/pub/week42/html/._week42-bs058.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -393,7 +411,7 @@ and the slides of 67
68
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs059.html b/doc/pub/week42/html/._week42-bs059.html
index f6ce5856f..539716f0c 100644
--- a/doc/pub/week42/html/._week42-bs059.html
+++ b/doc/pub/week42/html/._week42-bs059.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -349,18 +367,41 @@ MathJax.Hub.Config({
-CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+Mathematics of CNNs
-As discussed above, CNNs are neural networks built from the assumption that the inputs
-to the network are 2D images. This is important because the number of features or pixels in images
-grows very fast with the image size, and an enormous number of weights and biases are needed in order to build an accurate network.
+The mathematics of CNNs is based on the mathematical operation of
+convolution. In mathematics (in particular in functional analysis),
+convolution is represented by matheematical operation (integration,
+summation etc) on two function in order to produce a third function
+that expresses how the shape of one gets modified by the other.
+Convolution has a plethora of applications in a variety of disciplines, spanning from statistics to signal processing, computer vision, solutions of differential equations,linear algebra, engineering, and yes, machine learning.
-As before, we still have our input, a hidden layer and an output. What's novel about convolutional networks
-are the convolutional and pooling layers stacked in pairs between the input and the hidden layer.
-In addition, the data is no longer represented as a 2D feature matrix, instead each input is a number of 2D
-matrices, typically 1 for each color dimension (Red, Green, Blue).
+Mathematically, convolution is defined as follows (one-dimensional example):
+Let us define a continuous function \( y(t) \) given by
+$$
+y(t) = \int x(a) w(t-a) da,
+$$
+
+where \( x(a) \) represents a so-called input and \( w(t-a) \) is normally called the weight function or kernel.
+
+
+The above integral is written in a more compact form as
+$$
+y(t) = \left(x * w\right)(t).
+$$
+
+
+The discretized version reads
+$$
+y(t) = \sum_{a=-\infty}^{a=\infty}x(a)w(t-a).
+$$
+
+Computing the inverse of the above convolution operations is known as deconvolution.
+
+
+How can we use this? And what does it mean? Let us study some familiar examples first.
@@ -388,7 +429,7 @@ matrices, typically 1 for each color dimension (Red, Green, Blue).
68
69
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs060.html b/doc/pub/week42/html/._week42-bs060.html
index 2cfb751fa..a05956e0b 100644
--- a/doc/pub/week42/html/._week42-bs060.html
+++ b/doc/pub/week42/html/._week42-bs060.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -349,14 +367,11 @@ MathJax.Hub.Config({
-Setting it up
+Convolution Examples: Polynomial multiplication
-It means that to represent the entire
-dataset of images, we require a 4D matrix or tensor. This tensor has the dimensions:
-$$
-(n_{inputs},\, n_{pixels, width},\, n_{pixels, height},\, depth) .
-$$
+We have already met such an example in project 1 when we tried to set up the design matrix for a two-dimensional function.
+Let us remind of this and recast it in terms of the mathematical operation of convolution.
@@ -384,7 +399,7 @@ $$
69
70
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs061.html b/doc/pub/week42/html/._week42-bs061.html
index 136743ddb..a3b57b303 100644
--- a/doc/pub/week42/html/._week42-bs061.html
+++ b/doc/pub/week42/html/._week42-bs061.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -349,20 +367,7 @@ MathJax.Hub.Config({
-The MNIST dataset again
-
-
-The MNIST dataset consists of grayscale images with a pixel size of
-\( 28\times 28 \), meaning we require \( 28 \times 28 = 724 \) weights to each
-neuron in the first hidden layer.
-
-
-If we were to analyze images of size \( 128\times 128 \) we would require
-\( 128 \times 128 = 16384 \) weights to each neuron. Even worse if we were
-dealing with color images, as most images are, we have an image matrix
-of size \( 128\times 128 \) for each color dimension (Red, Green, Blue),
-meaning 3 times the number of weights \( = 49152 \) are required for every
-single neuron in the first hidden layer.
+
Convolution Examples: Probability Theory
@@ -390,7 +395,7 @@ single neuron in the first hidden layer.
70
71
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs062.html b/doc/pub/week42/html/._week42-bs062.html
index c4f97e513..f9461869d 100644
--- a/doc/pub/week42/html/._week42-bs062.html
+++ b/doc/pub/week42/html/._week42-bs062.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -349,20 +367,176 @@ MathJax.Hub.Config({
-Strong correlations
+
-Images typically have strong local correlations, meaning that a small
-part of the image varies little from its neighboring regions. If for
-example we have an image of a blue car, we can roughly assume that a
-small blue part of the image is surrounded by other blue regions.
+If one has several driving forces, \( F(t)=\sum_n F_n(t) \), one can find
+the particular solution to each \( F_n \), \( x_{pn}(t) \), and the particular
+solution for the entire driving force is
+
+$$
+\begin{equation}
+x_p(t)=\sum_nx_{pn}(t).
+\tag{21}
+\end{equation}
+$$
-Therefore, instead of connecting every single pixel to a neuron in the
-first hidden layer, as we have previously done with deep neural
-networks, we can instead connect each neuron to a small part of the
-image (in all 3 RGB depth dimensions). The size of each small area is
-fixed, and known as a receptive.
+This is known as the principal of superposition. It only applies when
+the homogenous equation is linear. If there were an anharmonic term
+such as \( x^3 \) in the homogenous equation, then when one summed various
+solutions, \( x=(\sum_n x_n)^2 \), one would get cross
+terms. Superposition is especially useful when \( F(t) \) can be written
+as a sum of sinusoidal terms, because the solutions for each
+sinusoidal (sine or cosine) term is analytic, as we saw above.
+
+
+Driving forces are often periodic, even when they are not
+sinusoidal. Periodicity implies that for some time \( \tau \)
+
+$$
+\begin{eqnarray}
+F(t+\tau)=F(t).
+\end{eqnarray}
+$$
+
+
+One example of a non-sinusoidal periodic force is a square wave. Many
+components in electric circuits are non-linear, e.g. diodes, which
+makes many wave forms non-sinusoidal even when the circuits are being
+driven by purely sinusoidal sources.
+
+
+The code here shows a typical example of such a square wave generated using the functionality included in the scipy Python package. We have used a period of \( \tau=0.2 \).
+
+
+
+
+
import numpy as np
+import math
+from scipy import signal
+import matplotlib.pyplot as plt
+
+# number of points
+n = 500
+# start and final times
+t0 = 0.0
+tn = 1.0
+# Period
+t = np.linspace(t0, tn, n, endpoint=False)
+SqrSignal = np.zeros(n)
+SqrSignal = 1.0+signal.square(2*np.pi*5*t)
+plt.plot(t, SqrSignal)
+plt.ylim(-0.5, 2.5)
+plt.show()
+
+For the sinusoidal example the
+period is \( \tau=2\pi/\omega \). However, higher harmonics can also
+satisfy the periodicity requirement. In general, any force that
+satisfies the periodicity requirement can be expressed as a sum over
+harmonics,
+
+$$
+\begin{equation}
+F(t)=\frac{f_0}{2}+\sum_{n>0} f_n\cos(2n\pi t/\tau)+g_n\sin(2n\pi t/\tau).
+\tag{22}
+\end{equation}
+$$
+
+
+We can write down the answer for
+\( x_{pn}(t) \), by substituting \( f_n/m \) or \( g_n/m \) for \( F_0/m \). By
+writing each factor \( 2n\pi t/\tau \) as \( n\omega t \), with \( \omega\equiv
+2\pi/\tau \),
+
+$$
+\begin{equation}
+\tag{23}
+F(t)=\frac{f_0}{2}+\sum_{n>0}f_n\cos(n\omega t)+g_n\sin(n\omega t).
+\end{equation}
+$$
+
+
+The solutions for \( x(t) \) then come from replacing \( \omega \) with
+\( n\omega \) for each term in the particular solution,
+
+$$
+\begin{eqnarray}
+x_p(t)&=&\frac{f_0}{2k}+\sum_{n>0} \alpha_n\cos(n\omega t-\delta_n)+\beta_n\sin(n\omega t-\delta_n),\\
+\nonumber
+\alpha_n&=&\frac{f_n/m}{\sqrt{((n\omega)^2-\omega_0^2)+4\beta^2n^2\omega^2}},\\
+\nonumber
+\beta_n&=&\frac{g_n/m}{\sqrt{((n\omega)^2-\omega_0^2)+4\beta^2n^2\omega^2}},\\
+\nonumber
+\delta_n&=&\tan^{-1}\left(\frac{2\beta n\omega}{\omega_0^2-n^2\omega^2}\right).
+\end{eqnarray}
+$$
+
+
+Because the forces have been applied for a long time, any non-zero
+damping eliminates the homogenous parts of the solution, so one need
+only consider the particular solution for each \( n \).
+
+
+The problem will considered solved if one can find expressions for the
+coefficients \( f_n \) and \( g_n \), even though the solutions are expressed
+as an infinite sum. The coefficients can be extracted from the
+function \( F(t) \) by
+
+$$
+\begin{eqnarray}
+\tag{24}
+f_n&=&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~F(t)\cos(2n\pi t/\tau),\\
+\nonumber
+g_n&=&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~F(t)\sin(2n\pi t/\tau).
+\end{eqnarray}
+$$
+
+
+To check the consistency of these expressions and to verify
+Eq. (24), one can insert the expansion of \( F(t) \) in
+Eq. (23) into the expression for the coefficients in
+Eq. (24) and see whether
+
+$$
+\begin{eqnarray}
+f_n&=?&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~\left\{
+\frac{f_0}{2}+\sum_{m>0}f_m\cos(m\omega t)+g_m\sin(m\omega t)
+\right\}\cos(n\omega t).
+\end{eqnarray}
+$$
+
+
+Immediately, one can throw away all the terms with \( g_m \) because they
+convolute an even and an odd function. The term with \( f_0/2 \)
+disappears because \( \cos(n\omega t) \) is equally positive and negative
+over the interval and will integrate to zero. For all the terms
+\( f_m\cos(m\omega t) \) appearing in the sum, one can use angle addition
+formulas to see that \( \cos(m\omega t)\cos(n\omega
+t)=(1/2)(\cos[(m+n)\omega t]+\cos[(m-n)\omega t] \). This will integrate
+to zero unless \( m=n \). In that case the \( m=n \) term gives
+
+$$
+\begin{equation}
+\int_{-\tau/2}^{\tau/2}dt~\cos^2(m\omega t)=\frac{\tau}{2},
+\tag{25}
+\end{equation}
+$$
+
+
+and
+
+$$
+\begin{eqnarray}
+f_n&=?&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~f_n/2\\
+\nonumber
+&=&f_n~\checkmark.
+\end{eqnarray}
+$$
+
+
+The same method can be used to check for the consistency of \( g_n \).
@@ -390,7 +564,7 @@ fixed, and known as a 71
72
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs063.html b/doc/pub/week42/html/._week42-bs063.html
index 8758ce04d..332aeb540 100644
--- a/doc/pub/week42/html/._week42-bs063.html
+++ b/doc/pub/week42/html/._week42-bs063.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -347,26 +365,20 @@ MathJax.Hub.Config({
-
+
-Layers of a CNN
-The layers of a convolutional neural network arrange neurons in 3D: width, height and depth.
-The input image is typically a square matrix of depth 3.
+CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
-A convolution is performed on the image which outputs
-a 3D volume of neurons. The weights to the input are arranged in a number of 2D matrices, known as filters.
+As discussed above, CNNs are neural networks built from the assumption that the inputs
+to the network are 2D images. This is important because the number of features or pixels in images
+grows very fast with the image size, and an enormous number of weights and biases are needed in order to build an accurate network.
-Each filter slides along the input image, taking the dot product
-between each small part of the image and the filter, in all depth
-dimensions. This is then passed through a non-linear function,
-typically the Rectified Linear (ReLu) function, which serves as the
-activation of the neurons in the first convolutional layer. This is
-further passed through a pooling layer, which reduces the size of the
-convolutional layer, e.g. by taking the maximum or average across some
-small regions, and this serves as input to the next convolutional
-layer.
+As before, we still have our input, a hidden layer and an output. What's novel about convolutional networks
+are the convolutional and pooling layers stacked in pairs between the input and the hidden layer.
+In addition, the data is no longer represented as a 2D feature matrix, instead each input is a number of 2D
+matrices, typically 1 for each color dimension (Red, Green, Blue).
@@ -394,7 +406,7 @@ layer.
72
73
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs064.html b/doc/pub/week42/html/._week42-bs064.html
index 5dadf870b..1b3079d7f 100644
--- a/doc/pub/week42/html/._week42-bs064.html
+++ b/doc/pub/week42/html/._week42-bs064.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -349,17 +367,14 @@ MathJax.Hub.Config({
-Systematic reduction
+Setting it up
-By systematically reducing the size of the input volume, through
-convolution and pooling, the network should create representations of
-small parts of the input, and then from them assemble representations
-of larger areas. The final pooling layer is flattened to serve as
-input to a hidden layer, such that each neuron in the final pooling
-layer is connected to every single neuron in the hidden layer. This
-then serves as input to the output layer, e.g. a softmax output for
-classification.
+It means that to represent the entire
+dataset of images, we require a 4D matrix or tensor. This tensor has the dimensions:
+$$
+(n_{inputs},\, n_{pixels, width},\, n_{pixels, height},\, depth) .
+$$
@@ -387,7 +402,7 @@ classification.
73
74
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs065.html b/doc/pub/week42/html/._week42-bs065.html
index c7c7dec6a..8b920ef6f 100644
--- a/doc/pub/week42/html/._week42-bs065.html
+++ b/doc/pub/week42/html/._week42-bs065.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -349,51 +367,21 @@ MathJax.Hub.Config({
-Prerequisites: Collect and pre-process data
+The MNIST dataset again
+
+The MNIST dataset consists of grayscale images with a pixel size of
+\( 28\times 28 \), meaning we require \( 28 \times 28 = 724 \) weights to each
+neuron in the first hidden layer.
-
-
# import necessary packages
-import numpy as np
-import matplotlib.pyplot as plt
-from sklearn import datasets
+
+If we were to analyze images of size \( 128\times 128 \) we would require
+\( 128 \times 128 = 16384 \) weights to each neuron. Even worse if we were
+dealing with color images, as most images are, we have an image matrix
+of size \( 128\times 128 \) for each color dimension (Red, Green, Blue),
+meaning 3 times the number of weights \( = 49152 \) are required for every
+single neuron in the first hidden layer.
-
-# ensure the same random numbers appear every time
-np.random.seed(0)
-
-# display images in notebook
-%matplotlib inline
-plt.rcParams['figure.figsize'] = (12,12)
-
-
-# download MNIST dataset
-digits = datasets.load_digits()
-
-# define inputs and labels
-inputs = digits.images
-labels = digits.target
-
-# RGB images have a depth of 3
-# our images are grayscale so they should have a depth of 1
-inputs = inputs[:,:,:,np.newaxis]
-
-print("inputs = (n_inputs, pixel_width, pixel_height, depth) = " + str(inputs.shape))
-print("labels = (n_inputs) = " + str(labels.shape))
-
-
-# choose some random images to display
-n_inputs = len(inputs)
-indices = np.arange(n_inputs)
-random_indices = np.random.choice(indices, size=5)
-
-for i, image in enumerate(digits.images[random_indices]):
- plt.subplot(1, 5, i+1)
- plt.axis('off')
- plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')
- plt.title("Label: %d" % digits.target[random_indices[i]])
-plt.show()
-
@@ -420,7 +408,7 @@ plt.show()
74
75
...
- 76
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs066.html b/doc/pub/week42/html/._week42-bs066.html
index a460c99ee..e1c0abda7 100644
--- a/doc/pub/week42/html/._week42-bs066.html
+++ b/doc/pub/week42/html/._week42-bs066.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -349,33 +367,21 @@ MathJax.Hub.Config({
-Importing Keras and Tensorflow
+Strong correlations
+
+Images typically have strong local correlations, meaning that a small
+part of the image varies little from its neighboring regions. If for
+example we have an image of a blue car, we can roughly assume that a
+small blue part of the image is surrounded by other blue regions.
-
-
from tensorflow.keras import datasets, layers, models
-from tensorflow.keras.layers import Input
-from tensorflow.keras.models import Sequential #This allows appending layers to existing models
-from tensorflow.keras.layers import Dense #This allows defining the characteristics of a particular layer
-from tensorflow.keras import optimizers #This allows using whichever optimiser we want (sgd,adam,RMSprop)
-from tensorflow.keras import regularizers #This allows using whichever regularizer we want (l1,l2,l1_l2)
-from tensorflow.keras.utils import to_categorical #This allows using categorical cross entropy as the cost function
-#from tensorflow.keras import Conv2D
-#from tensorflow.keras import MaxPooling2D
-#from tensorflow.keras import Flatten
+
+Therefore, instead of connecting every single pixel to a neuron in the
+first hidden layer, as we have previously done with deep neural
+networks, we can instead connect each neuron to a small part of the
+image (in all 3 RGB depth dimensions). The size of each small area is
+fixed, and known as a receptive.
-from sklearn.model_selection import train_test_split
-
-# representation of labels
-labels = to_categorical(labels)
-
-# split into train and test data
-# one-liner from scikit-learn library
-train_size = 0.8
-test_size = 1 - train_size
-X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,
- test_size=test_size)
-
@@ -401,6 +407,8 @@ X_train, X_test, Y_train, Y_test = train_tes
74
75
76
+ ...
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs067.html b/doc/pub/week42/html/._week42-bs067.html
index b17dcb4a2..4c18556fe 100644
--- a/doc/pub/week42/html/._week42-bs067.html
+++ b/doc/pub/week42/html/._week42-bs067.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -349,38 +367,25 @@ MathJax.Hub.Config({
-Running with Keras
+Layers of a CNN
+The layers of a convolutional neural network arrange neurons in 3D: width, height and depth.
+The input image is typically a square matrix of depth 3.
+A convolution is performed on the image which outputs
+a 3D volume of neurons. The weights to the input are arranged in a number of 2D matrices, known as filters.
-
-
def create_convolutional_neural_network_keras(input_shape, receptive_field,
- n_filters, n_neurons_connected, n_categories,
- eta, lmbd):
- model = Sequential()
- model.add(layers.Conv2D(n_filters, (receptive_field, receptive_field), input_shape=input_shape, padding='same',
- activation='relu', kernel_regularizer=regularizers.l2(lmbd)))
- model.add(layers.MaxPooling2D(pool_size=(2, 2)))
- model.add(layers.Flatten())
- model.add(layers.Dense(n_neurons_connected, activation='relu', kernel_regularizer=regularizers.l2(lmbd)))
- model.add(layers.Dense(n_categories, activation='softmax', kernel_regularizer=regularizers.l2(lmbd)))
-
- sgd = optimizers.SGD(lr=eta)
- model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])
-
- return model
+
+Each filter slides along the input image, taking the dot product
+between each small part of the image and the filter, in all depth
+dimensions. This is then passed through a non-linear function,
+typically the Rectified Linear (ReLu) function, which serves as the
+activation of the neurons in the first convolutional layer. This is
+further passed through a pooling layer, which reduces the size of the
+convolutional layer, e.g. by taking the maximum or average across some
+small regions, and this serves as input to the next convolutional
+layer.
-epochs = 100
-batch_size = 100
-input_shape = X_train.shape[1:4]
-receptive_field = 3
-n_filters = 10
-n_neurons_connected = 50
-n_categories = 10
-
-eta_vals = np.logspace(-5, 1, 7)
-lmbd_vals = np.logspace(-5, 1, 7)
-
@@ -405,6 +410,9 @@ lmbd_vals = np.
74
75
76
+ 77
+ ...
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs068.html b/doc/pub/week42/html/._week42-bs068.html
index 8b6d68051..4af7f5239 100644
--- a/doc/pub/week42/html/._week42-bs068.html
+++ b/doc/pub/week42/html/._week42-bs068.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -349,28 +367,18 @@ MathJax.Hub.Config({
-Final part
+Systematic reduction
+By systematically reducing the size of the input volume, through
+convolution and pooling, the network should create representations of
+small parts of the input, and then from them assemble representations
+of larger areas. The final pooling layer is flattened to serve as
+input to a hidden layer, such that each neuron in the final pooling
+layer is connected to every single neuron in the hidden layer. This
+then serves as input to the output layer, e.g. a softmax output for
+classification.
-
-
CNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
-
-for i, eta in enumerate(eta_vals):
- for j, lmbd in enumerate(lmbd_vals):
- CNN = create_convolutional_neural_network_keras(input_shape, receptive_field,
- n_filters, n_neurons_connected, n_categories,
- eta, lmbd)
- CNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)
- scores = CNN.evaluate(X_test, Y_test)
-
- CNN_keras[i][j] = CNN
-
- print("Learning rate = ", eta)
- print("Lambda = ", lmbd)
- print("Test accuracy: %.3f" % scores[1])
- print()
-
@@ -394,6 +402,10 @@ MathJax.Hub.Config({
74
75
76
+ 77
+ 78
+ ...
+ 80
»
diff --git a/doc/pub/week42/html/._week42-bs069.html b/doc/pub/week42/html/._week42-bs069.html
index 2a2669f5f..a6d31362f 100644
--- a/doc/pub/week42/html/._week42-bs069.html
+++ b/doc/pub/week42/html/._week42-bs069.html
@@ -189,6 +189,20 @@ Automatically generated HTML file from DocOnce source
'layers-used-to-build-cnns'),
('Transforming images', 2, None, 'transforming-images'),
('CNNs in brief', 2, None, 'cnns-in-brief'),
+ ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+ ('Convolution Examples: Polynomial multiplication',
+ 2,
+ None,
+ 'convolution-examples-polynomial-multiplication'),
+ ('Convolution Examples: Probability Theory',
+ 2,
+ None,
+ 'convolution-examples-probability-theory'),
+ ('Convolution Examples: Principle of Superposition and Periodic '
+ 'Forces (Fourier Transforms)',
+ 2,
+ None,
+ 'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
('CNNs in more detail, building convolutional neural networks in '
'Tensorflow and Keras',
2,
@@ -317,23 +331,27 @@ MathJax.Hub.Config({
Layers used to build CNNs
Transforming images
CNNs in brief
- CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
- Setting it up
- The MNIST dataset again
- Strong correlations
- Layers of a CNN
- Systematic reduction
- Prerequisites: Collect and pre-process data
- Importing Keras and Tensorflow
- Running with Keras
- Final part
- Final visualization
- The CIFAR01 data set
- Verifying the data set
- Set up the model
- Add Dense layers on top
- Compile and train the model
- Finally, evaluate the model
+ Mathematics of CNNs
+ Convolution Examples: Polynomial multiplication
+ Convolution Examples: Probability Theory
+ Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
+ CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
+ Setting it up
+ The MNIST dataset again
+ Strong correlations
+ Layers of a CNN
+ Systematic reduction
+ Prerequisites: Collect and pre-process data
+ Importing Keras and Tensorflow
+ Running with Keras
+ Final part
+ Final visualization
+ The CIFAR01 data set
+ Verifying the data set
+ Set up the model
+ Add Dense layers on top
+ Compile and train the model
+ Finally, evaluate the model
@@ -349,40 +367,49 @@ MathJax.Hub.Config({
-Final visualization
-
+Prerequisites: Collect and pre-process data
-