Morten Hjorth-Jensen
377 lines
25 KiB
HTML
377 lines
25 KiB
HTML
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<title>Week 44, Convolutional Neural Networks (CNN)</title>
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('Material for Lecture Thursday November 2',
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('Convolutional Neural Networks (recognizing images)',
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'regular-nns-don-t-scale-well-to-full-images'),
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('Layers used to build CNNs',
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('Further Dimensionality Remarks',
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('CNNs in more detail', 2, None, 'cnns-in-more-detail'),
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('No zero padding, unit strides',
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('Strong correlations', 2, None, 'strong-correlations'),
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('Layers of a CNN', 2, None, 'layers-of-a-cnn'),
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('Prerequisites: Collect and pre-process data',
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('Importing Keras and Tensorflow',
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('Running with Keras', 2, None, 'running-with-keras'),
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('Final part', 2, None, 'final-part'),
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('Final visualization', 2, None, 'final-visualization'),
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('The CIFAR01 data set', 2, None, 'the-cifar01-data-set'),
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('Verifying the data set', 2, None, 'verifying-the-data-set'),
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('Set up the model', 2, None, 'set-up-the-model'),
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('Add Dense layers on top', 2, None, 'add-dense-layers-on-top'),
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('Compile and train the model',
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('Optimized Convolution2DLayer',
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('Convolution using separable kernels',
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<a class="navbar-brand" href="week44-bs.html">Week 44, Convolutional Neural Networks (CNN)</a>
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week44-bs001.html#plan-for-week-44" style="font-size: 80%;"><b>Plan for week 44</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs002.html#material-for-lecture-thursday-november-2" style="font-size: 80%;"><b>Material for Lecture Thursday November 2</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs003.html#convolutional-neural-networks-recognizing-images" style="font-size: 80%;"><b>Convolutional Neural Networks (recognizing images)</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs004.html#what-is-the-difference" style="font-size: 80%;"><b>What is the Difference</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs005.html#neural-networks-vs-cnns" style="font-size: 80%;"><b>Neural Networks vs CNNs</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs006.html#why-cnns-for-images-sound-files-medical-images-from-ct-scans-etc" style="font-size: 80%;"><b>Why CNNS for images, sound files, medical images from CT scans etc?</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs007.html#regular-nns-don-t-scale-well-to-full-images" style="font-size: 80%;"><b>Regular NNs don’t scale well to full images</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs008.html#3d-volumes-of-neurons" style="font-size: 80%;"><b>3D volumes of neurons</b></a></li>
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<!-- navigation toc: --> <li><a href="#layers-used-to-build-cnns" style="font-size: 80%;"><b>Layers used to build CNNs</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs010.html#transforming-images" style="font-size: 80%;"><b>Transforming images</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs011.html#cnns-in-brief" style="font-size: 80%;"><b>CNNs in brief</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs012.html#key-idea" style="font-size: 80%;"><b>Key Idea</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs013.html#mathematics-of-cnns" style="font-size: 80%;"><b>Mathematics of CNNs</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs014.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;"><b>Convolution Examples: Polynomial multiplication</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs015.html#efficient-polynomial-multiplication" style="font-size: 80%;"><b>Efficient Polynomial Multiplication</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs016.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;"><b>A more efficient way of coding the above Convolution</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs017.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;"><b>Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs018.html#simple-code-example" style="font-size: 80%;"><b>Simple Code Example</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs019.html#wrapping-up-fourier-transforms" style="font-size: 80%;"><b>Wrapping up Fourier transforms</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs020.html#finding-the-coefficients" style="font-size: 80%;"><b>Finding the Coefficients</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs021.html#final-words-on-fourier-transforms" style="font-size: 80%;"><b>Final words on Fourier Transforms</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs021.html#fourier-transforms-and-convolution" style="font-size: 80%;"> Fourier transforms and convolution</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs021.html#two-dimensional-objects" style="font-size: 80%;"><b>Two-dimensional Objects</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs022.html#more-on-dimensionalities" style="font-size: 80%;"><b>More on Dimensionalities</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs023.html#further-dimensionality-remarks" style="font-size: 80%;"><b>Further Dimensionality Remarks</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs024.html#cnns-in-more-detail" style="font-size: 80%;"><b>CNNs in more detail</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs025.html#pooling" style="font-size: 80%;"><b>Pooling</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs026.html#no-zero-padding-unit-strides" style="font-size: 80%;"><b>No zero padding, unit strides</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs027.html#zero-padding-unit-strides" style="font-size: 80%;"><b>Zero padding, unit strides</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs028.html#half-same-padding" style="font-size: 80%;"><b>Half (same) padding</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs029.html#full-padding" style="font-size: 80%;"><b>Full padding</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs030.html#pooling-arithmetic" style="font-size: 80%;"><b>Pooling arithmetic</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs031.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;"><b>CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs032.html#setting-it-up" style="font-size: 80%;"><b>Setting it up</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs033.html#the-mnist-dataset-again" style="font-size: 80%;"><b>The MNIST dataset again</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs034.html#strong-correlations" style="font-size: 80%;"><b>Strong correlations</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs035.html#layers-of-a-cnn" style="font-size: 80%;"><b>Layers of a CNN</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs036.html#systematic-reduction" style="font-size: 80%;"><b>Systematic reduction</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs037.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;"><b>Prerequisites: Collect and pre-process data</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs038.html#importing-keras-and-tensorflow" style="font-size: 80%;"><b>Importing Keras and Tensorflow</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs039.html#running-with-keras" style="font-size: 80%;"><b>Running with Keras</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs040.html#final-part" style="font-size: 80%;"><b>Final part</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs041.html#final-visualization" style="font-size: 80%;"><b>Final visualization</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs042.html#the-cifar01-data-set" style="font-size: 80%;"><b>The CIFAR01 data set</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs043.html#verifying-the-data-set" style="font-size: 80%;"><b>Verifying the data set</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs044.html#set-up-the-model" style="font-size: 80%;"><b>Set up the model</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs045.html#add-dense-layers-on-top" style="font-size: 80%;"><b>Add Dense layers on top</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs046.html#compile-and-train-the-model" style="font-size: 80%;"><b>Compile and train the model</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs047.html#finally-evaluate-the-model" style="font-size: 80%;"><b>Finally, evaluate the model</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#building-our-own-cnn-code" style="font-size: 80%;"><b>Building our own CNN code</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#list-of-contents" style="font-size: 80%;"> List of contents:</a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#schedulers" style="font-size: 80%;"> Schedulers</a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#usage-of-schedulers" style="font-size: 80%;"> Usage of schedulers</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#cost-functions" style="font-size: 80%;"> Cost functions</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#usage-of-cost-functions" style="font-size: 80%;"> Usage of cost functions</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#activation-functions" style="font-size: 80%;"> Activation functions</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#usage-of-activation-functions" style="font-size: 80%;"> Usage of activation functions</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#convolution" style="font-size: 80%;"> Convolution</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#layers" style="font-size: 80%;"> Layers</a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#convolution2dlayer-convolution-in-a-hidden-layer" style="font-size: 80%;"> Convolution2DLayer: convolution in a hidden layer</a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#backpropagation-in-the-convolutional-layer" style="font-size: 80%;"> Backpropagation in the convolutional layer</a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#demonstration" style="font-size: 80%;"> Demonstration</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#pooling-layer" style="font-size: 80%;"> Pooling Layer</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#flattening-layer" style="font-size: 80%;"> Flattening Layer</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#fully-connected-layers" style="font-size: 80%;"> Fully Connected Layers</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#optimized-convolution2dlayer" style="font-size: 80%;"> Optimized Convolution2DLayer</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs048.html#the-convolutional-neural-network-cnn" style="font-size: 80%;"> The Convolutional Neural Network (CNN)</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs048.html#usage-of-cnn-code" style="font-size: 80%;"> Usage of CNN code</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs048.html#additional-remarks" style="font-size: 80%;"> Additional Remarks</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs048.html#remarks-on-the-speed" style="font-size: 80%;"> Remarks on the speed</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs048.html#convolution-using-separable-kernels" style="font-size: 80%;"> Convolution using separable kernels</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs048.html#convolution-in-the-fourier-domain" style="font-size: 80%;"> Convolution in the Fourier domain</a></li>
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</li>
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<div class="container">
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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<a name="part0009"></a>
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<!-- !split -->
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<h2 id="layers-used-to-build-cnns" class="anchor">Layers used to build CNNs </h2>
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<p>A simple CNN is a sequence of layers, and every layer of a CNN
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transforms one volume of activations to another through a
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differentiable function. We use three main types of layers to build
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CNN architectures: Convolutional Layer, Pooling Layer, and
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Fully-Connected Layer (exactly as seen in regular Neural Networks). We
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will stack these layers to form a full CNN architecture.
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</p>
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<p>A simple CNN for image classification could have the architecture:</p>
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<ul>
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<li> <b>INPUT</b> (\( 32\times 32 \times 3 \)) 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.</li>
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<li> <b>CONV</b> (convolutional )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.</li>
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<li> <b>RELU</b> layer will apply an elementwise activation function, such as the \( max(0,x) \) thresholding at zero. This leaves the size of the volume unchanged (\( [32\times 32\times 12] \)).</li>
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<li> <b>POOL</b> (pooling) layer will perform a downsampling operation along the spatial dimensions (width, height), resulting in volume such as \( [16\times 16\times 12] \).</li>
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<li> <b>FC</b> (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.</li>
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