From 05f321f9856e3bc81b45e57cc9228794369e8801 Mon Sep 17 00:00:00 2001 From: mhjensen Date: Thu, 18 Oct 2018 05:50:28 +0200 Subject: [PATCH] update on neural networks --- doc/pub/LogReg/html/._LogReg-bs000.html | 2 +- doc/pub/LogReg/html/._LogReg-bs018.html | 3 - doc/pub/LogReg/html/._LogReg-bs022.html | 4 - doc/pub/LogReg/html/LogReg-bs.html | 2 +- doc/pub/LogReg/html/LogReg-reveal.html | 10 +- doc/pub/LogReg/html/LogReg-solarized.html | 9 +- doc/pub/LogReg/html/LogReg.html | 9 +- doc/pub/LogReg/ipynb/LogReg.ipynb | 11 +- doc/pub/LogReg/ipynb/ipynb-LogReg-src.tar.gz | Bin 210 -> 209 bytes .../LogReg/pdf/LogReg-beamer-handouts2x3.pdf | Bin 319869 -> 319156 bytes doc/pub/LogReg/pdf/LogReg-beamer.pdf | Bin 306170 -> 305477 bytes doc/pub/LogReg/pdf/LogReg-minted.pdf | Bin 343742 -> 343094 bytes doc/pub/NeuralNet/html/._NeuralNet-bs000.html | 24 +- doc/pub/NeuralNet/html/._NeuralNet-bs001.html | 22 +- doc/pub/NeuralNet/html/._NeuralNet-bs002.html | 22 +- 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doc/pub/NeuralNet/html/._NeuralNet-bs070.html create mode 100644 doc/pub/NeuralNet/html/._NeuralNet-bs071.html create mode 100644 doc/pub/NeuralNet/html/._NeuralNet-bs072.html create mode 100644 doc/src/NeuralNet/figslides/cnn.jpeg create mode 100644 doc/src/NeuralNet/figslides/nn.jpeg diff --git a/doc/pub/LogReg/html/._LogReg-bs000.html b/doc/pub/LogReg/html/._LogReg-bs000.html index 226e1d7bf..8fab13972 100644 --- a/doc/pub/LogReg/html/._LogReg-bs000.html +++ b/doc/pub/LogReg/html/._LogReg-bs000.html @@ -159,7 +159,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Oct 11, 2018

+

Oct 18, 2018


diff --git a/doc/pub/LogReg/html/._LogReg-bs018.html b/doc/pub/LogReg/html/._LogReg-bs018.html index 6e79d2da1..7c367356c 100644 --- a/doc/pub/LogReg/html/._LogReg-bs018.html +++ b/doc/pub/LogReg/html/._LogReg-bs018.html @@ -184,9 +184,6 @@ X_train, X_test, y_train, y_test = skms=0.95 ) -

-Using a small training set yields a better accuracy. This will be discussed in the end. -

diff --git a/doc/pub/LogReg/html/._LogReg-bs022.html b/doc/pub/LogReg/html/._LogReg-bs022.html index a6f6c2ed9..59f3921c8 100644 --- a/doc/pub/LogReg/html/._LogReg-bs022.html +++ b/doc/pub/LogReg/html/._LogReg-bs022.html @@ -196,10 +196,6 @@ training data looks quite good, but as the testing data is so far off we see that we are dealing with an overfit model.

-A previous run with \( 50\% \) of the data used for training yielded a -worse performance than using a smaller training set. This again gives -confidence to the fact that logistic regression is not able to -correctly fit the Ising model as it is not a linear model.

diff --git a/doc/pub/LogReg/html/LogReg-bs.html b/doc/pub/LogReg/html/LogReg-bs.html index 226e1d7bf..8fab13972 100644 --- a/doc/pub/LogReg/html/LogReg-bs.html +++ b/doc/pub/LogReg/html/LogReg-bs.html @@ -159,7 +159,7 @@ MathJax.Hub.Config({

[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Oct 11, 2018

+

Oct 18, 2018


diff --git a/doc/pub/LogReg/html/LogReg-reveal.html b/doc/pub/LogReg/html/LogReg-reveal.html index 2f41dca82..01452dbe0 100644 --- a/doc/pub/LogReg/html/LogReg-reveal.html +++ b/doc/pub/LogReg/html/LogReg-reveal.html @@ -148,7 +148,7 @@ MathJax.Hub.Config({

[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

 
-

Oct 11, 2018

+

Oct 18, 2018


@@ -730,8 +730,6 @@ X_train, X_test, y_train, y_test = skms.train_test_split( test_size=0.95 ) -

-Using a small training set yields a better accuracy. This will be discussed in the end. @@ -952,12 +950,6 @@ that logistic regression is quite inept at predicting the Ising model transition and is therefore highly non-linear. The ROC curve for the training data looks quite good, but as the testing data is so far off we see that we are dealing with an overfit model. - -

-A previous run with \( 50\% \) of the data used for training yielded a -worse performance than using a smaller training set. This again gives -confidence to the fact that logistic regression is not able to -correctly fit the Ising model as it is not a linear model. diff --git a/doc/pub/LogReg/html/LogReg-solarized.html b/doc/pub/LogReg/html/LogReg-solarized.html index 0e21bf0a9..963a161fc 100644 --- a/doc/pub/LogReg/html/LogReg-solarized.html +++ b/doc/pub/LogReg/html/LogReg-solarized.html @@ -101,7 +101,7 @@ MathJax.Hub.Config({

[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Oct 11, 2018

+

Oct 18, 2018


@@ -628,9 +628,6 @@ X_train, X_test, y_train, y_test = skms.train_test_split( test_size=0.95 ) -

-Using a small training set yields a better accuracy. This will be discussed in the end. -











@@ -841,10 +838,6 @@ training data looks quite good, but as the testing data is so far off we see that we are dealing with an overfit model.

-A previous run with \( 50\% \) of the data used for training yielded a -worse performance than using a smaller training set. This again gives -confidence to the fact that logistic regression is not able to -correctly fit the Ising model as it is not a linear model. diff --git a/doc/pub/LogReg/html/LogReg.html b/doc/pub/LogReg/html/LogReg.html index abf1d112a..61b01692f 100644 --- a/doc/pub/LogReg/html/LogReg.html +++ b/doc/pub/LogReg/html/LogReg.html @@ -106,7 +106,7 @@ MathJax.Hub.Config({

[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Oct 11, 2018

+

Oct 18, 2018


@@ -633,9 +633,6 @@ X_train, X_test, y_train, y_test = skms=0.95 ) -

-Using a small training set yields a better accuracy. This will be discussed in the end. -











@@ -846,10 +843,6 @@ training data looks quite good, but as the testing data is so far off we see that we are dealing with an overfit model.

-A previous run with \( 50\% \) of the data used for training yielded a -worse performance than using a smaller training set. This again gives -confidence to the fact that logistic regression is not able to -correctly fit the Ising model as it is not a linear model. diff --git a/doc/pub/LogReg/ipynb/LogReg.ipynb b/doc/pub/LogReg/ipynb/LogReg.ipynb index 5a9d85a4f..2ad1a345d 100644 --- a/doc/pub/LogReg/ipynb/LogReg.ipynb +++ b/doc/pub/LogReg/ipynb/LogReg.ipynb @@ -10,7 +10,7 @@ " \n", "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n", "\n", - "Date: **Oct 11, 2018**\n", + "Date: **Oct 18, 2018**\n", "\n", "Copyright 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n", "\n", @@ -782,8 +782,6 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Using a small training set yields a better accuracy. This will be discussed in the end.\n", - "\n", "## Logistic regression\n", "\n", "Logistic regression is a linear model for classification. Recalling\n", @@ -1078,12 +1076,7 @@ "that logistic regression is quite inept at predicting the Ising model\n", "transition and is therefore highly non-linear. The ROC curve for the\n", "training data looks quite good, but as the testing data is so far off\n", - "we see that we are dealing with an overfit model.\n", - "\n", - "A previous run with $50\\%$ of the data used for training yielded a\n", - "worse performance than using a smaller training set. This again gives\n", - "confidence to the fact that logistic regression is not able to\n", - "correctly fit the Ising model as it is not a linear model." + "we see that we are dealing with an overfit model." ] } ], diff --git a/doc/pub/LogReg/ipynb/ipynb-LogReg-src.tar.gz b/doc/pub/LogReg/ipynb/ipynb-LogReg-src.tar.gz index 61efa703778f211c579c0968b368b2dd1fa2d890..1a28dae2419e20c37fb03780d6df71952530a89b 100644 GIT binary patch literal 209 zcmb2|=3wY}eLR|h`R)0GSxklk#|qEe9kn?)spRgLm=*0!O&;+In+na>`kHiJsI3lX zt{pLMu+AbYeP!!wV`7u^( zWAyHIpMERmEa}yoA3f>L!xxirZXUe2lAGT&#N5H JFlaC^004;*W&{8L literal 210 zcmb2|=3odD-yhAu{Pz68EG9#NV}*bw7q9>OPaiipY_K`b&c;rE^`}TR^Tkt)KJT1UlsKz+)y<`Lmv;%qUO#*2#jcr> zfys$qT&}$J`&D@6=(3Mf{+(@ob7+0>;~Qnwspp@H{yb;@XzTaLFn#Bj$rA*+Zy))g z=f5#}_qtE*iaASq_2x%Sx^w)Zy1E%p((P;F^38XB`8CTjwlTuV^Mnub*INMbJLgN3vp=hAndkKJy5E)RCqw!J@t4Hx(!*VuPCfVmFot4~TpUZe7T8rpHHuew| zFNDgQqPiXGtmM*Fm@P>I(x1!>yT8|G%dkZ0wrzm#IRgM= z-o)>GEHm0<9e$T198PGNb}5|IbfaFvt$)*IfPDBtX2>2$+8TMs>@Z5$3^(=^sbrin 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MathJax.Hub.Config({

  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -278,7 +296,7 @@ MathJax.Hub.Config({
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Oct 16, 2018

    +

    Oct 18, 2018


    @@ -302,7 +320,7 @@ MathJax.Hub.Config({

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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs001.html b/doc/pub/NeuralNet/html/._NeuralNet-bs001.html index 44fc3a92a..d0d16e154 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs001.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs001.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -287,7 +305,7 @@ a weight variable.
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs002.html b/doc/pub/NeuralNet/html/._NeuralNet-bs002.html index 773a1f14a..1484e01b5 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs002.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs002.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -337,7 +355,7 @@ humanities to life science and medicine.
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs003.html b/doc/pub/NeuralNet/html/._NeuralNet-bs003.html index 209d7fcaa..acab1f6e4 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs003.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs003.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -302,7 +320,7 @@ methods we discussed earlier.
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs004.html b/doc/pub/NeuralNet/html/._NeuralNet-bs004.html index 2a5f5c51d..e16bd4030 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs004.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs004.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -294,7 +312,7 @@ to all nodes in the subsequent layer, making this a so-called
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -303,7 +321,7 @@ recognition.
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs006.html b/doc/pub/NeuralNet/html/._NeuralNet-bs006.html index 6831a5e64..6754a02ac 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs006.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs006.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -295,7 +313,7 @@ especially well-suited for handwriting and speech recognition.
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -296,7 +314,7 @@ type of NN due the unusual activation functions.
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -294,7 +312,7 @@ Such networks are often called multilayer perceptrons (MLPs).
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -299,7 +317,7 @@ as to not restrict the range of output values.
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -300,7 +318,7 @@ of the outputs of all neurons in the previous layer.
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs011.html b/doc/pub/NeuralNet/html/._NeuralNet-bs011.html index 243c723e7..8108d0808 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs011.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs011.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -329,7 +347,7 @@ is obtained.
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs012.html b/doc/pub/NeuralNet/html/._NeuralNet-bs012.html index 64ed07ca4..2e541f417 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs012.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs012.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -311,7 +329,7 @@ $$
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs013.html b/doc/pub/NeuralNet/html/._NeuralNet-bs013.html index 20788e1fb..bbfd21bef 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs013.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs013.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -302,7 +320,7 @@ variables are the input values \( x_n \).
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs014.html b/doc/pub/NeuralNet/html/._NeuralNet-bs014.html index 12aebdafd..58fac7d48 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs014.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs014.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -311,7 +329,7 @@ flexibility of a neural network.
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs015.html b/doc/pub/NeuralNet/html/._NeuralNet-bs015.html index 75f455d95..3c1726864 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs015.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs015.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -321,7 +339,7 @@ $$
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs016.html b/doc/pub/NeuralNet/html/._NeuralNet-bs016.html index 20ab2d14a..c39087df0 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs016.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs016.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -305,7 +323,7 @@ used as input to the activation functions. For each operation
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs017.html b/doc/pub/NeuralNet/html/._NeuralNet-bs017.html index 1dfbd2c6a..8243ecf0d 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs017.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs017.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -299,7 +317,7 @@ for a FFNN to fulfill the universal approximation theorem
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs018.html b/doc/pub/NeuralNet/html/._NeuralNet-bs018.html index 2fba6eb34..58c8df7d1 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs018.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs018.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -307,7 +325,7 @@ $$
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs019.html b/doc/pub/NeuralNet/html/._NeuralNet-bs019.html index 4eebc4d90..1627ddc42 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs019.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs019.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -369,7 +387,7 @@ plt.show()
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs020.html b/doc/pub/NeuralNet/html/._NeuralNet-bs020.html index 316612137..c6f019e20 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs020.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs020.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -320,7 +338,7 @@ like logistic regression or linear regression and their modifications on the oth
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs021.html b/doc/pub/NeuralNet/html/._NeuralNet-bs021.html index e32373ef4..aeb78b86a 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs021.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs021.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -310,7 +328,7 @@ the potential of being universal approximators.
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs022.html b/doc/pub/NeuralNet/html/._NeuralNet-bs022.html index f443fdbe5..0ca3daeea 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs022.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs022.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -316,7 +334,7 @@ classes.
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs023.html b/doc/pub/NeuralNet/html/._NeuralNet-bs023.html index a151443c8..ddb3d9ee7 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs023.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs023.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -320,7 +338,7 @@ $$
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs024.html b/doc/pub/NeuralNet/html/._NeuralNet-bs024.html index 8a560f656..a84556e61 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs024.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs024.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -304,7 +322,7 @@ $$
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs025.html b/doc/pub/NeuralNet/html/._NeuralNet-bs025.html index d4ce1524f..a019ba831 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs025.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs025.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -307,7 +325,7 @@ $$
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs026.html b/doc/pub/NeuralNet/html/._NeuralNet-bs026.html index 8dce9b6dd..d14fddab4 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs026.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs026.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -332,7 +350,7 @@ $$
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs027.html b/doc/pub/NeuralNet/html/._NeuralNet-bs027.html index 566cdd8b4..7d157fdea 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs027.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs027.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
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  • CNNs in more detail
    • @@ -299,7 +317,7 @@ That is, the error \( \delta_j^L \) is exactly equal to the rate of change of th
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs028.html b/doc/pub/NeuralNet/html/._NeuralNet-bs028.html index c73902140..971b0940a 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs028.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs028.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -344,7 +362,7 @@ one \( L-1 \) in terms of the errors in the final output layer.
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs029.html b/doc/pub/NeuralNet/html/._NeuralNet-bs029.html index f73bea6ea..47accb760 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs029.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs029.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -314,7 +332,7 @@ We are now ready to set up the algorithm for back propagation and learning the w
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs030.html b/doc/pub/NeuralNet/html/._NeuralNet-bs030.html index dc50afb97..ffcbd9ab7 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs030.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs030.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -358,7 +376,7 @@ Here it is convenient to use stochastic gradient descent (see the examples below
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs031.html b/doc/pub/NeuralNet/html/._NeuralNet-bs031.html index 4925bb7b7..a4388a5ab 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs031.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs031.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -320,7 +338,7 @@ of our network.
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs032.html b/doc/pub/NeuralNet/html/._NeuralNet-bs032.html index e8c29bd5d..5aa45a9d1 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs032.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs032.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -342,7 +360,7 @@ The back propagation equations need now only a small change, namely the definiti
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs033.html b/doc/pub/NeuralNet/html/._NeuralNet-bs033.html index 433191a0c..534e425c8 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs033.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs033.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -330,7 +348,7 @@ In case we use another activation function than the logistic one, we need to eva
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs034.html b/doc/pub/NeuralNet/html/._NeuralNet-bs034.html index bebeeab0c..5b88a5aac 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs034.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs034.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -304,7 +322,7 @@ which in case of the simply binary model reduces to having \( i=j \).
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs035.html b/doc/pub/NeuralNet/html/._NeuralNet-bs035.html index 1382acec1..9b2d5be58 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs035.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs035.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -298,7 +316,7 @@ One can identify a set of key steps when using neural networks to solve supervis
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs036.html b/doc/pub/NeuralNet/html/._NeuralNet-bs036.html index f1c2fc395..3c51f6cae 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs036.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs036.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -377,7 +395,7 @@ plt.show()
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs037.html b/doc/pub/NeuralNet/html/._NeuralNet-bs037.html index dd46359f6..1d430d6cd 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs037.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs037.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -331,7 +349,7 @@ X_train, X_test, Y_train, Y_test = train_tes
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs038.html b/doc/pub/NeuralNet/html/._NeuralNet-bs038.html index 669d2bb60..bbcf02dfb 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs038.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs038.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -328,7 +346,7 @@ which is inspired by probability theory (see logistic regression) and was most c
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs039.html b/doc/pub/NeuralNet/html/._NeuralNet-bs039.html index d0a8591d9..c26adfb30 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs039.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs039.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -327,7 +345,7 @@ weights to the output layer.
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs040.html b/doc/pub/NeuralNet/html/._NeuralNet-bs040.html index 842f99d27..cfac09502 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs040.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs040.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -318,7 +336,7 @@ output_bias = np49
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs041.html b/doc/pub/NeuralNet/html/._NeuralNet-bs041.html index 156e55d98..73b5bd0ea 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs041.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs041.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -309,7 +327,7 @@ $$ a_{j}^{L} = \frac{\exp{(z_j^{L})}}
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs042.html b/doc/pub/NeuralNet/html/._NeuralNet-bs042.html index 044950df5..79fc6c9b1 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs042.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs042.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -357,7 +375,7 @@ predictions = predict(X_train)
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs043.html b/doc/pub/NeuralNet/html/._NeuralNet-bs043.html index 504ed3872..883927f4b 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs043.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs043.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -313,7 +331,7 @@ you got the correct label. The probability of category \( c \) is given by the s
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -322,7 +340,7 @@ The various optmization methods, with codes and algorithms, are discussed in o
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -315,7 +333,7 @@ calculate the gradient efficently.
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -396,7 +414,7 @@ lmbd = 0.0155
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
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  • CNNs in more detail
    • @@ -302,7 +320,7 @@ Andrew Ng goes through some of these considerations in this 56
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -395,7 +413,7 @@ being realizations of this object with different hyperparameters. An implementat
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -317,7 +335,7 @@ test_predict = dnn58
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -315,7 +333,7 @@ DNN_numpy = np.
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
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  • CNNs in more detail
    • @@ -324,7 +342,7 @@ plt.show()
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    • diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs052.html b/doc/pub/NeuralNet/html/._NeuralNet-bs052.html index c8112b974..c69327d25 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs052.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs052.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
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  • CNNs in more detail
    • @@ -321,7 +339,7 @@ DNN_scikit = np
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
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  • CNNs in brief
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  • CNNs in more detail
    • @@ -324,7 +342,7 @@ plt.show()
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -297,7 +315,7 @@ NumPy arrays.
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -327,7 +345,7 @@ and/or if you use anaconda, just write (or install from the graphical use
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -348,7 +366,7 @@ X_train, X_test, Y_train, Y_test = train_tes
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -426,6 +444,8 @@ MathJax.Hub.Config({
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -358,6 +376,9 @@ writer.add_graph(tf65
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
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  • 3D volumes of neurons
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  • Layers used to build CNNs
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  • CNNs in brief
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  • CNNs in more detail
    • @@ -378,6 +396,10 @@ plt.show()
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -307,6 +325,11 @@ learn at widely different speeds
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -307,6 +325,12 @@ better than the logistic function in deep networks).
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
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  • Layers used to build CNNs
    • +
  • CNNs in brief
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  • CNNs in more detail
    • @@ -312,6 +330,13 @@ fast to compute).
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
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  • Layers used to build CNNs
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  • CNNs in brief
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  • CNNs in more detail
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
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  • CNNs in more detail
    • @@ -294,6 +312,12 @@ bootstrap to evaluate other activation functions.
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -315,6 +333,12 @@ supervised learning.
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  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -280,8 +298,9 @@ Here we list some of the important limitations of supervised neural network base
  • Many problems are not about prediction. In natural science we are often interested in learning something about the underlying distribution that generates the data. In this case, it is often difficult to cast these ideas in a supervised learning setting. While the problems are related, it is possible to make good predictions with a wrong model. The model might or might not be useful for understanding the underlying science.
    • -Some of these remarks are particular to DNNs, others are shared by all supervised learning methods. This motivates the use of unsupervised methods which in part circumnavigate these problems. +Some of these remarks are particular to DNNs, others are shared by all supervised learning methods. This motivates the use of unsupervised methods which in part circumvent these problems. +

      @@ -297,6 +316,13 @@ Some of these remarks are particular to DNNs, others are shared by all supervise
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    diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs067.html b/doc/pub/NeuralNet/html/._NeuralNet-bs067.html new file mode 100644 index 000000000..04710ab6c --- /dev/null +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs067.html @@ -0,0 +1,352 @@ + + + + + + + +Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning +
    + +
    + +
    +
    + + +
    + +

     

     

     

    + + + + +

    Convolutional Neural Networks (recognizing images)

    + +

    +Convolutional Neural Networks (CNN) are very similar to ordinary Neural Networks. + +

    +They are made up of neurons that have learnable weights and +biases. Each neuron receives some inputs, performs a dot product and +optionally follows it with a non-linearity. The whole network still +expresses a single differentiable score function: from the raw image +pixels on one end to class scores at the other. And they still have a +loss function (for example Softmax) on the last (fully-connected) layer +and all the tips/tricks we developed for learning regular Neural +Networks still apply (back propagation, gradient descent etc etc). + +

    +What is the difference? CNN architectures make the explicit assumption that +the inputs are images, which allows us to encode certain properties +into the architecture. These then make the forward function more +efficient to implement and vastly reduce the amount of parameters in +the network. + +

    +Here we provide only a superficial overview, for the more interested, we recommend highly the course +IN5400 – Machine Learning for Image Analysis +and the slides of CS231. + +

    +

    + +

    + + +
    + + + + + + + +
    + +
    + + + + + + diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs068.html b/doc/pub/NeuralNet/html/._NeuralNet-bs068.html new file mode 100644 index 000000000..0102625d7 --- /dev/null +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs068.html @@ -0,0 +1,346 @@ + + + + + + + +Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning +
    + +
    + +
    +
    + + +
    + +

     

     

     

    + + + + +

    Regular NNs don’t scale well to full images

    + +

    +As an example, consider +an image of size \( 32\times 32\times 3 \) (32 wide, 32 high, 3 color channels), so a +single fully-connected neuron in a first hidden layer of a regular +Neural Network would have \( 32*32*3 = 3072 \) weights. This amount still +seems manageable, but clearly this fully-connected structure does not +scale to larger images. For example, an image of more respectable +size, say \( 200\times 200\times 3 \), would lead to neurons that have +\( 200*200*3 =120,000 \) weights. Moreover, we would almost certainly want to have +several such neurons, so the parameters would add up quickly! Clearly, +this full connectivity is wasteful and the huge number of parameters +would quickly lead to overfitting. + +

    +

    +
    +

    Figure 1: A regular 3-layer Neural Network.

    +

    +
    + +

    +

    + +

    + + +
    + + + + + + + +
    + +
    + + + + + + diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs069.html b/doc/pub/NeuralNet/html/._NeuralNet-bs069.html new file mode 100644 index 000000000..39574af44 --- /dev/null +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs069.html @@ -0,0 +1,360 @@ + + + + + + + +Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning +
    + +
    + +
    +
    + + +
    + +

     

     

     

    + + + + +

    3D volumes of neurons

    + +

    +Convolutional Neural Networks take advantage of the fact that the +input consists of images and they constrain the architecture in a more +sensible way. + +

    +In particular, unlike a regular Neural Network, the +layers of a CNN have neurons arranged in 3 dimensions: width, +height, depth. (Note that the word depth here refers to the third +dimension of an activation volume, not to the depth of a full Neural +Network, which can refer to the total number of layers in a network.) + +

    +To understand it better, the above example of an image +with an input volume of +activations has dimensions \( 32\times 32\times 3 \) (width, height, +depth respectively). + +

    +The neurons in a layer will +only be connected to a small region of the layer before it, instead of +all of the neurons in a fully-connected manner. Moreover, the final +output layer could for this specific image have dimensions \( 1\times 1 times 10 \), +because by the +end of the CNN architecture we will reduce the full image into a +single vector of class scores, arranged along the depth +dimension. + +

    +

    +
    +

    Figure 2: A CNN arranges its neurons in three dimensions (width, height, depth), as visualized in one of the layers. Every layer of a CNN transforms the 3D input volume to a 3D output volume of neuron activations. In this example, the red input layer holds the image, so its width and height would be the dimensions of the image, and the depth would be 3 (Red, Green, Blue channels).

    +

    +
    + +

    +

    + +

    + + +
    + + + + + + + +
    + +
    + + + + + + diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs070.html b/doc/pub/NeuralNet/html/._NeuralNet-bs070.html new file mode 100644 index 000000000..98d604cdb --- /dev/null +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs070.html @@ -0,0 +1,345 @@ + + + + + + + +Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning +
    + +
    + +
    +
    + + +
    + +

     

     

     

    + + + + +

    Layers used to build CNNs

    + +

    +A simple CNN is a sequence of layers, and every layer of a CNN +transforms one volume of activations to another through a +differentiable function. We use three main types of layers to build +CNN architectures: Convolutional Layer, Pooling Layer, and +Fully-Connected Layer (exactly as seen in regular Neural Networks). We +will stack these layers to form a full CNN architecture. + +

    +A simple CNN for image classification could have the architecture: + +

      +
    • INPUT (\( 32\times 32 \times 3 \)) will hold the raw pixel values of the image, in this case an image of width 32, height 32, and with three color channels R,G,B.
      • +
    • CONV layer will compute the output of neurons that are connected to local regions in the input, each computing a dot product between their weights and a small region they are connected to in the input volume. This may result in volume such as \( [32\times 32\times 12] \) if we decided to use 12 filters.
      • +
    • RELU layer will apply an elementwise activation function, such as the \( max(0,x) \) thresholding at zero. This leaves the size of the volume unchanged (\( [32\times 32\times 12] \)).
      • +
    • POOL layer will perform a downsampling operation along the spatial dimensions (width, height), resulting in volume such as \( [16\times 16\times 12] \).
      • +
    • FC (i.e. fully-connected) layer will compute the class scores, resulting in volume of size \( [1\times 1\times 10] \), where each of the 10 numbers correspond to a class score, such as among the 10 categories of the MNIST images we considered above . As with ordinary Neural Networks and as the name implies, each neuron in this layer will be connected to all the numbers in the previous volume.
      • +
    + +In this way, CNNs transform the original image layer by layer from the original pixel values to the final class scores. Note that some layers contain parameters and other don’t. In particular, the CONV/FC layers perform transformations that are a function of not only the activations in the input volume, but also of the parameters (the weights and biases of the neurons). On the other hand, the RELU/POOL layers will implement a fixed function. The parameters in the CONV/FC layers will be trained with gradient descent so that the class scores that the CNN computes are consistent with the labels in the training set for each image. + +

    +

    + +

    + + +
    + + + + + + + +
    + +
    + + + + + + diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs071.html b/doc/pub/NeuralNet/html/._NeuralNet-bs071.html new file mode 100644 index 000000000..a80853360 --- /dev/null +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs071.html @@ -0,0 +1,333 @@ + + + + + + + +Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning +
    + +
    + +
    +
    + + +
    + +

     

     

     

    + + + + +

    CNNs in brief

    + +

    +In summary: + +

      +
    • A CNN architecture is in the simplest case a list of Layers that transform the image volume into an output volume (e.g. holding the class scores)
      • +
    • There are a few distinct types of Layers (e.g. CONV/FC/RELU/POOL are by far the most popular)
      • +
    • Each Layer accepts an input 3D volume and transforms it to an output 3D volume through a differentiable function
      • +
    • Each Layer may or may not have parameters (e.g. CONV/FC do, RELU/POOL don’t)
      • +
    • Each Layer may or may not have additional hyperparameters (e.g. CONV/FC/POOL do, RELU doesn’t)
      • +
    + +

    + +

    + + +
    + + + + + + + +
    + +
    + + + + + + diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs072.html b/doc/pub/NeuralNet/html/._NeuralNet-bs072.html new file mode 100644 index 000000000..6061892ba --- /dev/null +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs072.html @@ -0,0 +1,323 @@ + + + + + + + +Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning +
    + +
    + +
    +
    + + +
    + +

     

     

     

    + + + + +

    CNNs in more detail

    + +

    +More material to come with examples. + +

    + +

    + + +
    + + + + + + + +
    + +
    + + + + + + diff --git a/doc/pub/NeuralNet/html/NeuralNet-bs.html b/doc/pub/NeuralNet/html/NeuralNet-bs.html index 55accbec3..2280e9a0e 100644 --- a/doc/pub/NeuralNet/html/NeuralNet-bs.html +++ b/doc/pub/NeuralNet/html/NeuralNet-bs.html @@ -140,7 +140,19 @@ Automatically generated HTML file from DocOnce source ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -244,6 +256,12 @@ MathJax.Hub.Config({
  • Which activation function should we use?
  • A top-down perspective on Neural networks
  • Limitations of supervised learning with deep networks
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • CNNs in brief
    • +
  • CNNs in more detail
    • @@ -278,7 +296,7 @@ MathJax.Hub.Config({
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Oct 16, 2018

    +

    Oct 18, 2018


    @@ -302,7 +320,7 @@ MathJax.Hub.Config({

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    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

     
    -

    Oct 16, 2018

    +

    Oct 18, 2018


    @@ -3085,7 +3085,153 @@ Here we list some of the important limitations of supervised neural network base

    -Some of these remarks are particular to DNNs, others are shared by all supervised learning methods. This motivates the use of unsupervised methods which in part circumnavigate these problems. +Some of these remarks are particular to DNNs, others are shared by all supervised learning methods. This motivates the use of unsupervised methods which in part circumvent these problems. + + + +

    +

    Convolutional Neural Networks (recognizing images)

    + +

    +Convolutional Neural Networks (CNN) are very similar to ordinary Neural Networks. + +

    +They are made up of neurons that have learnable weights and +biases. Each neuron receives some inputs, performs a dot product and +optionally follows it with a non-linearity. The whole network still +expresses a single differentiable score function: from the raw image +pixels on one end to class scores at the other. And they still have a +loss function (for example Softmax) on the last (fully-connected) layer +and all the tips/tricks we developed for learning regular Neural +Networks still apply (back propagation, gradient descent etc etc). + +

    +What is the difference? CNN architectures make the explicit assumption that +the inputs are images, which allows us to encode certain properties +into the architecture. These then make the forward function more +efficient to implement and vastly reduce the amount of parameters in +the network. + +

    +Here we provide only a superficial overview, for the more interested, we recommend highly the course +IN5400 – Machine Learning for Image Analysis +and the slides of CS231. +

    + + +
    +

    Regular NNs don’t scale well to full images

    + +

    +As an example, consider +an image of size \( 32\times 32\times 3 \) (32 wide, 32 high, 3 color channels), so a +single fully-connected neuron in a first hidden layer of a regular +Neural Network would have \( 32*32*3 = 3072 \) weights. This amount still +seems manageable, but clearly this fully-connected structure does not +scale to larger images. For example, an image of more respectable +size, say \( 200\times 200\times 3 \), would lead to neurons that have +\( 200*200*3 =120,000 \) weights. Moreover, we would almost certainly want to have +several such neurons, so the parameters would add up quickly! Clearly, +this full connectivity is wasteful and the huge number of parameters +would quickly lead to overfitting. + +

    +

    +
    +

    Figure 1: A regular 3-layer Neural Network.

    +

    +
    +
    + + +
    +

    3D volumes of neurons

    + +

    +Convolutional Neural Networks take advantage of the fact that the +input consists of images and they constrain the architecture in a more +sensible way. + +

    +In particular, unlike a regular Neural Network, the +layers of a CNN have neurons arranged in 3 dimensions: width, +height, depth. (Note that the word depth here refers to the third +dimension of an activation volume, not to the depth of a full Neural +Network, which can refer to the total number of layers in a network.) + +

    +To understand it better, the above example of an image +with an input volume of +activations has dimensions \( 32\times 32\times 3 \) (width, height, +depth respectively). + +

    +The neurons in a layer will +only be connected to a small region of the layer before it, instead of +all of the neurons in a fully-connected manner. Moreover, the final +output layer could for this specific image have dimensions \( 1\times 1 times 10 \), +because by the +end of the CNN architecture we will reduce the full image into a +single vector of class scores, arranged along the depth +dimension. + +

    +

    +
    +

    Figure 2: A CNN arranges its neurons in three dimensions (width, height, depth), as visualized in one of the layers. Every layer of a CNN transforms the 3D input volume to a 3D output volume of neuron activations. In this example, the red input layer holds the image, so its width and height would be the dimensions of the image, and the depth would be 3 (Red, Green, Blue channels).

    +

    +
    +
    + + +
    +

    Layers used to build CNNs

    + +

    +A simple CNN is a sequence of layers, and every layer of a CNN +transforms one volume of activations to another through a +differentiable function. We use three main types of layers to build +CNN architectures: Convolutional Layer, Pooling Layer, and +Fully-Connected Layer (exactly as seen in regular Neural Networks). We +will stack these layers to form a full CNN architecture. + +

    +A simple CNN for image classification could have the architecture: + +

      +

    • INPUT (\( 32\times 32 \times 3 \)) will hold the raw pixel values of the image, in this case an image of width 32, height 32, and with three color channels R,G,B.
      • +

    • CONV layer will compute the output of neurons that are connected to local regions in the input, each computing a dot product between their weights and a small region they are connected to in the input volume. This may result in volume such as \( [32\times 32\times 12] \) if we decided to use 12 filters.
      • +

    • RELU layer will apply an elementwise activation function, such as the \( max(0,x) \) thresholding at zero. This leaves the size of the volume unchanged (\( [32\times 32\times 12] \)).
      • +

    • POOL layer will perform a downsampling operation along the spatial dimensions (width, height), resulting in volume such as \( [16\times 16\times 12] \).
      • +

    • FC (i.e. fully-connected) layer will compute the class scores, resulting in volume of size \( [1\times 1\times 10] \), where each of the 10 numbers correspond to a class score, such as among the 10 categories of the MNIST images we considered above . As with ordinary Neural Networks and as the name implies, each neuron in this layer will be connected to all the numbers in the previous volume.
      • +
    +

    + +In this way, CNNs transform the original image layer by layer from the original pixel values to the final class scores. Note that some layers contain parameters and other don’t. In particular, the CONV/FC layers perform transformations that are a function of not only the activations in the input volume, but also of the parameters (the weights and biases of the neurons). On the other hand, the RELU/POOL layers will implement a fixed function. The parameters in the CONV/FC layers will be trained with gradient descent so that the class scores that the CNN computes are consistent with the labels in the training set for each image. +

    + + +
    +

    CNNs in brief

    + +

    +In summary: + +

      +

    • A CNN architecture is in the simplest case a list of Layers that transform the image volume into an output volume (e.g. holding the class scores)
      • +

    • There are a few distinct types of Layers (e.g. CONV/FC/RELU/POOL are by far the most popular)
      • +

    • Each Layer accepts an input 3D volume and transforms it to an output 3D volume through a differentiable function
      • +

    • Each Layer may or may not have parameters (e.g. CONV/FC do, RELU/POOL don’t)
      • +

    • Each Layer may or may not have additional hyperparameters (e.g. CONV/FC/POOL do, RELU doesn’t)
      • +
    +
    + + +
    +

    CNNs in more detail

    + +

    +More material to come with examples.

    diff --git a/doc/pub/NeuralNet/html/NeuralNet-solarized.html b/doc/pub/NeuralNet/html/NeuralNet-solarized.html index 1421708b8..52fb79998 100644 --- a/doc/pub/NeuralNet/html/NeuralNet-solarized.html +++ b/doc/pub/NeuralNet/html/NeuralNet-solarized.html @@ -160,7 +160,19 @@ div { text-align: justify; text-justify: inter-word; } ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -202,7 +214,7 @@ MathJax.Hub.Config({
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Oct 16, 2018

    +

    Oct 18, 2018












    @@ -2923,7 +2935,151 @@ Here we list some of the important limitations of supervised neural network base

  • Many problems are not about prediction. In natural science we are often interested in learning something about the underlying distribution that generates the data. In this case, it is often difficult to cast these ideas in a supervised learning setting. While the problems are related, it is possible to make good predictions with a wrong model. The model might or might not be useful for understanding the underlying science.
    • -Some of these remarks are particular to DNNs, others are shared by all supervised learning methods. This motivates the use of unsupervised methods which in part circumnavigate these problems. +Some of these remarks are particular to DNNs, others are shared by all supervised learning methods. This motivates the use of unsupervised methods which in part circumvent these problems. + +

    +









    + +

    Convolutional Neural Networks (recognizing images)

    + +

    +Convolutional Neural Networks (CNN) are very similar to ordinary Neural Networks. + +

    +They are made up of neurons that have learnable weights and +biases. Each neuron receives some inputs, performs a dot product and +optionally follows it with a non-linearity. The whole network still +expresses a single differentiable score function: from the raw image +pixels on one end to class scores at the other. And they still have a +loss function (for example Softmax) on the last (fully-connected) layer +and all the tips/tricks we developed for learning regular Neural +Networks still apply (back propagation, gradient descent etc etc). + +

    +What is the difference? CNN architectures make the explicit assumption that +the inputs are images, which allows us to encode certain properties +into the architecture. These then make the forward function more +efficient to implement and vastly reduce the amount of parameters in +the network. + +

    +Here we provide only a superficial overview, for the more interested, we recommend highly the course +IN5400 – Machine Learning for Image Analysis +and the slides of CS231. + +

    +









    + +

    Regular NNs don’t scale well to full images

    + +

    +As an example, consider +an image of size \( 32\times 32\times 3 \) (32 wide, 32 high, 3 color channels), so a +single fully-connected neuron in a first hidden layer of a regular +Neural Network would have \( 32*32*3 = 3072 \) weights. This amount still +seems manageable, but clearly this fully-connected structure does not +scale to larger images. For example, an image of more respectable +size, say \( 200\times 200\times 3 \), would lead to neurons that have +\( 200*200*3 =120,000 \) weights. Moreover, we would almost certainly want to have +several such neurons, so the parameters would add up quickly! Clearly, +this full connectivity is wasteful and the huge number of parameters +would quickly lead to overfitting. + +

    +

    +
    +

    Figure 1: A regular 3-layer Neural Network.

    +

    +
    + +

    +









    + +

    3D volumes of neurons

    + +

    +Convolutional Neural Networks take advantage of the fact that the +input consists of images and they constrain the architecture in a more +sensible way. + +

    +In particular, unlike a regular Neural Network, the +layers of a CNN have neurons arranged in 3 dimensions: width, +height, depth. (Note that the word depth here refers to the third +dimension of an activation volume, not to the depth of a full Neural +Network, which can refer to the total number of layers in a network.) + +

    +To understand it better, the above example of an image +with an input volume of +activations has dimensions \( 32\times 32\times 3 \) (width, height, +depth respectively). + +

    +The neurons in a layer will +only be connected to a small region of the layer before it, instead of +all of the neurons in a fully-connected manner. Moreover, the final +output layer could for this specific image have dimensions \( 1\times 1 times 10 \), +because by the +end of the CNN architecture we will reduce the full image into a +single vector of class scores, arranged along the depth +dimension. + +

    +

    +
    +

    Figure 2: A CNN arranges its neurons in three dimensions (width, height, depth), as visualized in one of the layers. Every layer of a CNN transforms the 3D input volume to a 3D output volume of neuron activations. In this example, the red input layer holds the image, so its width and height would be the dimensions of the image, and the depth would be 3 (Red, Green, Blue channels).

    +

    +
    + +

    + + +

    Layers used to build CNNs

    + +

    +A simple CNN is a sequence of layers, and every layer of a CNN +transforms one volume of activations to another through a +differentiable function. We use three main types of layers to build +CNN architectures: Convolutional Layer, Pooling Layer, and +Fully-Connected Layer (exactly as seen in regular Neural Networks). We +will stack these layers to form a full CNN architecture. + +

    +A simple CNN for image classification could have the architecture: + +

      +
    • INPUT (\( 32\times 32 \times 3 \)) will hold the raw pixel values of the image, in this case an image of width 32, height 32, and with three color channels R,G,B.
      • +
    • CONV layer will compute the output of neurons that are connected to local regions in the input, each computing a dot product between their weights and a small region they are connected to in the input volume. This may result in volume such as \( [32\times 32\times 12] \) if we decided to use 12 filters.
      • +
    • RELU layer will apply an elementwise activation function, such as the \( max(0,x) \) thresholding at zero. This leaves the size of the volume unchanged (\( [32\times 32\times 12] \)).
      • +
    • POOL layer will perform a downsampling operation along the spatial dimensions (width, height), resulting in volume such as \( [16\times 16\times 12] \).
      • +
    • FC (i.e. fully-connected) layer will compute the class scores, resulting in volume of size \( [1\times 1\times 10] \), where each of the 10 numbers correspond to a class score, such as among the 10 categories of the MNIST images we considered above . As with ordinary Neural Networks and as the name implies, each neuron in this layer will be connected to all the numbers in the previous volume.
      • +
    + +In this way, CNNs transform the original image layer by layer from the original pixel values to the final class scores. Note that some layers contain parameters and other don’t. In particular, the CONV/FC layers perform transformations that are a function of not only the activations in the input volume, but also of the parameters (the weights and biases of the neurons). On the other hand, the RELU/POOL layers will implement a fixed function. The parameters in the CONV/FC layers will be trained with gradient descent so that the class scores that the CNN computes are consistent with the labels in the training set for each image. + +

    +









    + +

    CNNs in brief

    + +

    +In summary: + +

      +
    • A CNN architecture is in the simplest case a list of Layers that transform the image volume into an output volume (e.g. holding the class scores)
      • +
    • There are a few distinct types of Layers (e.g. CONV/FC/RELU/POOL are by far the most popular)
      • +
    • Each Layer accepts an input 3D volume and transforms it to an output 3D volume through a differentiable function
      • +
    • Each Layer may or may not have parameters (e.g. CONV/FC do, RELU/POOL don’t)
      • +
    • Each Layer may or may not have additional hyperparameters (e.g. CONV/FC/POOL do, RELU doesn’t)
      • +
    + +









    + +

    CNNs in more detail

    + +

    +More material to come with examples. diff --git a/doc/pub/NeuralNet/html/NeuralNet.html b/doc/pub/NeuralNet/html/NeuralNet.html index 6c767d090..f38aa6a9d 100644 --- a/doc/pub/NeuralNet/html/NeuralNet.html +++ b/doc/pub/NeuralNet/html/NeuralNet.html @@ -165,7 +165,19 @@ div { text-align: justify; text-justify: inter-word; } ('Limitations of supervised learning with deep networks', 2, None, - '___sec65')]} + '___sec65'), + ('Convolutional Neural Networks (recognizing images)', + 2, + None, + '___sec66'), + ('Regular NNs don’t scale well to full images', + 2, + None, + '___sec67'), + ('3D volumes of neurons', 2, None, '___sec68'), + ('Layers used to build CNNs', 2, None, '___sec69'), + ('CNNs in brief', 2, None, '___sec70'), + ('CNNs in more detail', 2, None, '___sec71')]} end of tocinfo --> @@ -207,7 +219,7 @@ MathJax.Hub.Config({

    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Oct 16, 2018

    +

    Oct 18, 2018












    @@ -2928,7 +2940,151 @@ Here we list some of the important limitations of supervised neural network base

  • Many problems are not about prediction. In natural science we are often interested in learning something about the underlying distribution that generates the data. In this case, it is often difficult to cast these ideas in a supervised learning setting. While the problems are related, it is possible to make good predictions with a wrong model. The model might or might not be useful for understanding the underlying science.
    • -Some of these remarks are particular to DNNs, others are shared by all supervised learning methods. This motivates the use of unsupervised methods which in part circumnavigate these problems. +Some of these remarks are particular to DNNs, others are shared by all supervised learning methods. This motivates the use of unsupervised methods which in part circumvent these problems. + +

    +









    + +

    Convolutional Neural Networks (recognizing images)

    + +

    +Convolutional Neural Networks (CNN) are very similar to ordinary Neural Networks. + +

    +They are made up of neurons that have learnable weights and +biases. Each neuron receives some inputs, performs a dot product and +optionally follows it with a non-linearity. The whole network still +expresses a single differentiable score function: from the raw image +pixels on one end to class scores at the other. And they still have a +loss function (for example Softmax) on the last (fully-connected) layer +and all the tips/tricks we developed for learning regular Neural +Networks still apply (back propagation, gradient descent etc etc). + +

    +What is the difference? CNN architectures make the explicit assumption that +the inputs are images, which allows us to encode certain properties +into the architecture. These then make the forward function more +efficient to implement and vastly reduce the amount of parameters in +the network. + +

    +Here we provide only a superficial overview, for the more interested, we recommend highly the course +IN5400 – Machine Learning for Image Analysis +and the slides of CS231. + +

    +









    + +

    Regular NNs don’t scale well to full images

    + +

    +As an example, consider +an image of size \( 32\times 32\times 3 \) (32 wide, 32 high, 3 color channels), so a +single fully-connected neuron in a first hidden layer of a regular +Neural Network would have \( 32*32*3 = 3072 \) weights. This amount still +seems manageable, but clearly this fully-connected structure does not +scale to larger images. For example, an image of more respectable +size, say \( 200\times 200\times 3 \), would lead to neurons that have +\( 200*200*3 =120,000 \) weights. Moreover, we would almost certainly want to have +several such neurons, so the parameters would add up quickly! Clearly, +this full connectivity is wasteful and the huge number of parameters +would quickly lead to overfitting. + +

    +

    +
    +

    Figure 1: A regular 3-layer Neural Network.

    +

    +
    + +

    +









    + +

    3D volumes of neurons

    + +

    +Convolutional Neural Networks take advantage of the fact that the +input consists of images and they constrain the architecture in a more +sensible way. + +

    +In particular, unlike a regular Neural Network, the +layers of a CNN have neurons arranged in 3 dimensions: width, +height, depth. (Note that the word depth here refers to the third +dimension of an activation volume, not to the depth of a full Neural +Network, which can refer to the total number of layers in a network.) + +

    +To understand it better, the above example of an image +with an input volume of +activations has dimensions \( 32\times 32\times 3 \) (width, height, +depth respectively). + +

    +The neurons in a layer will +only be connected to a small region of the layer before it, instead of +all of the neurons in a fully-connected manner. Moreover, the final +output layer could for this specific image have dimensions \( 1\times 1 times 10 \), +because by the +end of the CNN architecture we will reduce the full image into a +single vector of class scores, arranged along the depth +dimension. + +

    +

    +
    +

    Figure 2: A CNN arranges its neurons in three dimensions (width, height, depth), as visualized in one of the layers. Every layer of a CNN transforms the 3D input volume to a 3D output volume of neuron activations. In this example, the red input layer holds the image, so its width and height would be the dimensions of the image, and the depth would be 3 (Red, Green, Blue channels).

    +

    +
    + +

    + + +

    Layers used to build CNNs

    + +

    +A simple CNN is a sequence of layers, and every layer of a CNN +transforms one volume of activations to another through a +differentiable function. We use three main types of layers to build +CNN architectures: Convolutional Layer, Pooling Layer, and +Fully-Connected Layer (exactly as seen in regular Neural Networks). We +will stack these layers to form a full CNN architecture. + +

    +A simple CNN for image classification could have the architecture: + +

      +
    • INPUT (\( 32\times 32 \times 3 \)) will hold the raw pixel values of the image, in this case an image of width 32, height 32, and with three color channels R,G,B.
      • +
    • CONV layer will compute the output of neurons that are connected to local regions in the input, each computing a dot product between their weights and a small region they are connected to in the input volume. This may result in volume such as \( [32\times 32\times 12] \) if we decided to use 12 filters.
      • +
    • RELU layer will apply an elementwise activation function, such as the \( max(0,x) \) thresholding at zero. This leaves the size of the volume unchanged (\( [32\times 32\times 12] \)).
      • +
    • POOL layer will perform a downsampling operation along the spatial dimensions (width, height), resulting in volume such as \( [16\times 16\times 12] \).
      • +
    • FC (i.e. fully-connected) layer will compute the class scores, resulting in volume of size \( [1\times 1\times 10] \), where each of the 10 numbers correspond to a class score, such as among the 10 categories of the MNIST images we considered above . As with ordinary Neural Networks and as the name implies, each neuron in this layer will be connected to all the numbers in the previous volume.
      • +
    + +In this way, CNNs transform the original image layer by layer from the original pixel values to the final class scores. Note that some layers contain parameters and other don’t. In particular, the CONV/FC layers perform transformations that are a function of not only the activations in the input volume, but also of the parameters (the weights and biases of the neurons). On the other hand, the RELU/POOL layers will implement a fixed function. The parameters in the CONV/FC layers will be trained with gradient descent so that the class scores that the CNN computes are consistent with the labels in the training set for each image. + +

    +









    + +

    CNNs in brief

    + +

    +In summary: + +

      +
    • A CNN architecture is in the simplest case a list of Layers that transform the image volume into an output volume (e.g. holding the class scores)
      • +
    • There are a few distinct types of Layers (e.g. CONV/FC/RELU/POOL are by far the most popular)
      • +
    • Each Layer accepts an input 3D volume and transforms it to an output 3D volume through a differentiable function
      • +
    • Each Layer may or may not have parameters (e.g. CONV/FC do, RELU/POOL don’t)
      • +
    • Each Layer may or may not have additional hyperparameters (e.g. CONV/FC/POOL do, RELU doesn’t)
      • +
    + +









    + +

    CNNs in more detail

    + +

    +More material to come with examples. diff --git a/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb b/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb index f4a238955..85ac78395 100644 --- a/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb +++ b/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb @@ -10,7 +10,7 @@ " \n", "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n", "\n", - "Date: **Oct 16, 2018**\n", + "Date: **Oct 18, 2018**\n", "\n", "Copyright 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n", "\n", @@ -3307,7 +3307,135 @@ "\n", "* **Many problems are not about prediction.** In natural science we are often interested in learning something about the underlying distribution that generates the data. In this case, it is often difficult to cast these ideas in a supervised learning setting. While the problems are related, it is possible to make good predictions with a *wrong* model. The model might or might not be useful for understanding the underlying science.\n", "\n", - "Some of these remarks are particular to DNNs, others are shared by all supervised learning methods. This motivates the use of unsupervised methods which in part circumnavigate these problems." + "Some of these remarks are particular to DNNs, others are shared by all supervised learning methods. This motivates the use of unsupervised methods which in part circumvent these problems.\n", + "\n", + "\n", + "## Convolutional Neural Networks (recognizing images)\n", + "\n", + "Convolutional Neural Networks (CNN) are very similar to ordinary Neural Networks.\n", + "\n", + "They are made up of neurons that have learnable weights and\n", + "biases. Each neuron receives some inputs, performs a dot product and\n", + "optionally follows it with a non-linearity. The whole network still\n", + "expresses a single differentiable score function: from the raw image\n", + "pixels on one end to class scores at the other. And they still have a\n", + "loss function (for example Softmax) on the last (fully-connected) layer\n", + "and all the tips/tricks we developed for learning regular Neural\n", + "Networks still apply (back propagation, gradient descent etc etc).\n", + "\n", + "What is the difference? **CNN architectures make the explicit assumption that\n", + "the inputs are images, which allows us to encode certain properties\n", + "into the architecture. These then make the forward function more\n", + "efficient to implement and vastly reduce the amount of parameters in\n", + "the network.**\n", + "\n", + "Here we provide only a superficial overview, for the more interested, we recommend highly the course\n", + "[IN5400 – Machine Learning for Image Analysis](https://www.uio.no/studier/emner/matnat/ifi/IN5400/index-eng.html)\n", + "and the slides of [CS231](http://cs231n.github.io/convolutional-networks/).\n", + "\n", + "## Regular NNs don’t scale well to full images\n", + "\n", + "As an example, consider\n", + "an image of size $32\\times 32\\times 3$ (32 wide, 32 high, 3 color channels), so a\n", + "single fully-connected neuron in a first hidden layer of a regular\n", + "Neural Network would have $32*32*3 = 3072$ weights. This amount still\n", + "seems manageable, but clearly this fully-connected structure does not\n", + "scale to larger images. For example, an image of more respectable\n", + "size, say $200\\times 200\\times 3$, would lead to neurons that have \n", + "$200*200*3 =120,000$ weights. Moreover, we would almost certainly want to have\n", + "several such neurons, so the parameters would add up quickly! Clearly,\n", + "this full connectivity is wasteful and the huge number of parameters\n", + "would quickly lead to overfitting.\n", + "\n", + "\n", + "\n", + "\n", + "

    A regular 3-layer Neural Network.

    \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "## 3D volumes of neurons\n", + "\n", + "Convolutional Neural Networks take advantage of the fact that the\n", + "input consists of images and they constrain the architecture in a more\n", + "sensible way. \n", + "\n", + "In particular, unlike a regular Neural Network, the\n", + "layers of a CNN have neurons arranged in 3 dimensions: width,\n", + "height, depth. (Note that the word depth here refers to the third\n", + "dimension of an activation volume, not to the depth of a full Neural\n", + "Network, which can refer to the total number of layers in a network.)\n", + "\n", + "To understand it better, the above example of an image \n", + "with an input volume of\n", + "activations has dimensions $32\\times 32\\times 3$ (width, height,\n", + "depth respectively). \n", + "\n", + "The neurons in a layer will\n", + "only be connected to a small region of the layer before it, instead of\n", + "all of the neurons in a fully-connected manner. Moreover, the final\n", + "output layer could for this specific image have dimensions $1\\times 1 times 10$, \n", + "because by the\n", + "end of the CNN architecture we will reduce the full image into a\n", + "single vector of class scores, arranged along the depth\n", + "dimension. \n", + "\n", + "\n", + "\n", + "\n", + "

    A CNN arranges its neurons in three dimensions (width, height, depth), as visualized in one of the layers. Every layer of a CNN transforms the 3D input volume to a 3D output volume of neuron activations. In this example, the red input layer holds the image, so its width and height would be the dimensions of the image, and the depth would be 3 (Red, Green, Blue channels).

    \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "## Layers used to build CNNs\n", + "\n", + "\n", + "A simple CNN is a sequence of layers, and every layer of a CNN\n", + "transforms one volume of activations to another through a\n", + "differentiable function. We use three main types of layers to build\n", + "CNN architectures: Convolutional Layer, Pooling Layer, and\n", + "Fully-Connected Layer (exactly as seen in regular Neural Networks). We\n", + "will stack these layers to form a full CNN architecture.\n", + "\n", + "A simple CNN for image classification could have the architecture:\n", + "\n", + "* INPUT ($32\\times 32 \\times 3$) will hold the raw pixel values of the image, in this case an image of width 32, height 32, and with three color channels R,G,B.\n", + "\n", + "* CONV layer will compute the output of neurons that are connected to local regions in the input, each computing a dot product between their weights and a small region they are connected to in the input volume. This may result in volume such as $[32\\times 32\\times 12]$ if we decided to use 12 filters.\n", + "\n", + "* RELU layer will apply an elementwise activation function, such as the $max(0,x)$ thresholding at zero. This leaves the size of the volume unchanged ($[32\\times 32\\times 12]$).\n", + "\n", + "* POOL layer will perform a downsampling operation along the spatial dimensions (width, height), resulting in volume such as $[16\\times 16\\times 12]$.\n", + "\n", + "* FC (i.e. fully-connected) layer will compute the class scores, resulting in volume of size $[1\\times 1\\times 10]$, where each of the 10 numbers correspond to a class score, such as among the 10 categories of the MNIST images we considered above . As with ordinary Neural Networks and as the name implies, each neuron in this layer will be connected to all the numbers in the previous volume.\n", + "\n", + "In this way, CNNs transform the original image layer by layer from the original pixel values to the final class scores. Note that some layers contain parameters and other don’t. In particular, the CONV/FC layers perform transformations that are a function of not only the activations in the input volume, but also of the parameters (the weights and biases of the neurons). On the other hand, the RELU/POOL layers will implement a fixed function. The parameters in the CONV/FC layers will be trained with gradient descent so that the class scores that the CNN computes are consistent with the labels in the training set for each image.\n", + "\n", + "\n", + "## CNNs in brief\n", + "\n", + "In summary:\n", + "\n", + "* A CNN architecture is in the simplest case a list of Layers that transform the image volume into an output volume (e.g. holding the class scores)\n", + "\n", + "* There are a few distinct types of Layers (e.g. CONV/FC/RELU/POOL are by far the most popular)\n", + "\n", + "* Each Layer accepts an input 3D volume and transforms it to an output 3D volume through a differentiable function\n", + "\n", + "* Each Layer may or may not have parameters (e.g. CONV/FC do, RELU/POOL don’t)\n", + "\n", + "* Each Layer may or may not have additional hyperparameters (e.g. CONV/FC/POOL do, RELU doesn’t)\n", + "\n", + "## CNNs in more detail\n", + "\n", + "More material to come with examples." ] } ], diff --git 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