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<a class="navbar-brand" href="week45-bs.html">Week 45, Convolutional Neural Networks (CCNs) and Recurrent Neural Networks (RNNs)</a>
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
<ul class="dropdown-menu">
<!-- navigation toc: --> <li><a href="._week45-bs001.html#plans-for-week-45" style="font-size: 80%;"><b>Plans for week 45</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs002.html#material-for-the-lab-sessions-additional-ways-to-present-classification-results-and-other-practicalities" style="font-size: 80%;"><b>Material for the lab sessions, additional ways to present classification results and other practicalities</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs003.html#material-for-lecture-monday-november-4" style="font-size: 80%;"><b>Material for Lecture Monday November 4</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs004.html#convolutional-neural-networks-recognizing-images" style="font-size: 80%;"><b>Convolutional Neural Networks (recognizing images)</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs005.html#what-is-the-difference" style="font-size: 80%;"><b>What is the Difference</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs006.html#neural-networks-vs-cnns" style="font-size: 80%;"><b>Neural Networks vs CNNs</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs007.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>
<!-- navigation toc: --> <li><a href="._week45-bs008.html#regular-nns-don-t-scale-well-to-full-images" style="font-size: 80%;"><b>Regular NNs dont scale well to full images</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs009.html#3d-volumes-of-neurons" style="font-size: 80%;"><b>3D volumes of neurons</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs010.html#layers-used-to-build-cnns" style="font-size: 80%;"><b>Layers used to build CNNs</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs011.html#cnns-in-brief" style="font-size: 80%;"><b>CNNs in brief</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs012.html#a-deep-cnn-model-from-raschka-et-al-https-github-com-rasbt-machine-learning-book" style="font-size: 80%;"><b>A deep CNN model ("From Raschka et al":"https://github.com/rasbt/machine-learning-book")</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs013.html#key-idea" style="font-size: 80%;"><b>Key Idea</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs014.html#building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;"><b>Building convolutional neural networks in Tensorflow and Keras</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs015.html#setting-it-up" style="font-size: 80%;"><b>Setting it up</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs016.html#the-mnist-dataset-again" style="font-size: 80%;"><b>The MNIST dataset again</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs017.html#strong-correlations" style="font-size: 80%;"><b>Strong correlations</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs018.html#layers-of-a-cnn" style="font-size: 80%;"><b>Layers of a CNN</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs019.html#systematic-reduction" style="font-size: 80%;"><b>Systematic reduction</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs020.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;"><b>Prerequisites: Collect and pre-process data</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs021.html#importing-keras-and-tensorflow" style="font-size: 80%;"><b>Importing Keras and Tensorflow</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs022.html#running-with-keras" style="font-size: 80%;"><b>Running with Keras</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs023.html#final-part" style="font-size: 80%;"><b>Final part</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs024.html#final-visualization" style="font-size: 80%;"><b>Final visualization</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs025.html#the-cifar01-data-set" style="font-size: 80%;"><b>The CIFAR01 data set</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs026.html#verifying-the-data-set" style="font-size: 80%;"><b>Verifying the data set</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs027.html#set-up-the-model" style="font-size: 80%;"><b>Set up the model</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs028.html#add-dense-layers-on-top" style="font-size: 80%;"><b>Add Dense layers on top</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs029.html#compile-and-train-the-model" style="font-size: 80%;"><b>Compile and train the model</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs030.html#finally-evaluate-the-model" style="font-size: 80%;"><b>Finally, evaluate the model</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#building-our-own-cnn-code" style="font-size: 80%;"><b>Building our own CNN code</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#list-of-contents" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;List of contents:</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#schedulers" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Schedulers</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#usage-of-schedulers" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Usage of schedulers</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#cost-functions" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Cost functions</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#usage-of-cost-functions" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Usage of cost functions</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#activation-functions" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Activation functions</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#usage-of-activation-functions" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Usage of activation functions</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#convolution" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Convolution</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#layers" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Layers</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#convolution2dlayer-convolution-in-a-hidden-layer" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Convolution2DLayer: convolution in a hidden layer</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#backpropagation-in-the-convolutional-layer" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Backpropagation in the convolutional layer</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#demonstration" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Demonstration</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#pooling-layer" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Pooling Layer</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#flattening-layer" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Flattening Layer</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#fully-connected-layers" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Fully Connected Layers</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#optimized-convolution2dlayer" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Optimized Convolution2DLayer</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#the-convolutional-neural-network-cnn" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;The Convolutional Neural Network (CNN)</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#usage-of-cnn-code" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Usage of CNN code</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#additional-remarks" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Additional Remarks</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#remarks-on-the-speed" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Remarks on the speed</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#convolution-using-separable-kernels" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Convolution using separable kernels</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs031.html#convolution-in-the-fourier-domain" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Convolution in the Fourier domain</a></li>
<!-- navigation toc: --> <li><a href="._week45-bs032.html#from-ffnns-and-cnns-to-recurrent-neural-networks-rnns" style="font-size: 80%;"><b>From FFNNs and CNNs to recurrent neural networks (RNNs)</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs033.html#feedback-connections" style="font-size: 80%;"><b>Feedback connections</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs034.html#vanishing-gradients" style="font-size: 80%;"><b>Vanishing gradients</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs035.html#recurrent-neural-networks-rnns-overarching-view" style="font-size: 80%;"><b>Recurrent neural networks (RNNs): Overarching view</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs036.html#sequential-data-only" style="font-size: 80%;"><b>Sequential data only?</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs037.html#differential-equations" style="font-size: 80%;"><b>Differential equations</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs038.html#a-simple-example" style="font-size: 80%;"><b>A simple example</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs039.html#rnns" style="font-size: 80%;"><b>RNNs</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs040.html#what-kinds-of-behaviour-can-rnns-exhibit" style="font-size: 80%;"><b>What kinds of behaviour can RNNs exhibit?</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs041.html#basic-layout-figures-from-sebastian-rashcka-et-al-machine-learning-with-sickit-learn-and-pytorch-https-sebastianraschka-com-blog-2022-ml-pytorch-book-html" style="font-size: 80%;"><b>Basic layout, "Figures from Sebastian Rashcka et al, Machine learning with Sickit-Learn and PyTorch":"https://sebastianraschka.com/blog/2022/ml-pytorch-book.html"</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs042.html#solving-differential-equations-with-rnns" style="font-size: 80%;"><b>Solving differential equations with RNNs</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs043.html#two-first-order-differential-equations" style="font-size: 80%;"><b>Two first-order differential equations</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs044.html#velocity-only" style="font-size: 80%;"><b>Velocity only</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs045.html#linking-with-rnns" style="font-size: 80%;"><b>Linking with RNNs</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs046.html#minor-rewrite" style="font-size: 80%;"><b>Minor rewrite</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs047.html#rnns-in-more-detail" style="font-size: 80%;"><b>RNNs in more detail</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs048.html#rnns-in-more-detail-part-2" style="font-size: 80%;"><b>RNNs in more detail, part 2</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs049.html#rnns-in-more-detail-part-3" style="font-size: 80%;"><b>RNNs in more detail, part 3</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs050.html#rnns-in-more-detail-part-4" style="font-size: 80%;"><b>RNNs in more detail, part 4</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs051.html#rnns-in-more-detail-part-5" style="font-size: 80%;"><b>RNNs in more detail, part 5</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs052.html#rnns-in-more-detail-part-6" style="font-size: 80%;"><b>RNNs in more detail, part 6</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs053.html#rnns-in-more-detail-part-7" style="font-size: 80%;"><b>RNNs in more detail, part 7</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs054.html#backpropagation-through-time" style="font-size: 80%;"><b>Backpropagation through time</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs055.html#the-backward-pass-is-linear" style="font-size: 80%;"><b>The backward pass is linear</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs056.html#the-problem-of-exploding-or-vanishing-gradients" style="font-size: 80%;"><b>The problem of exploding or vanishing gradients</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs057.html#mathematical-setup" style="font-size: 80%;"><b>Mathematical setup</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs058.html#back-propagation-in-time-through-figures-part-1" style="font-size: 80%;"><b>Back propagation in time through figures, part 1</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs059.html#back-propagation-in-time-part-2" style="font-size: 80%;"><b>Back propagation in time, part 2</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs060.html#back-propagation-in-time-part-3" style="font-size: 80%;"><b>Back propagation in time, part 3</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs061.html#back-propagation-in-time-part-4" style="font-size: 80%;"><b>Back propagation in time, part 4</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs062.html#back-propagation-in-time-in-equations" style="font-size: 80%;"><b>Back propagation in time in equations</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs063.html#chain-rule-again" style="font-size: 80%;"><b>Chain rule again</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs064.html#gradients-of-loss-functions" style="font-size: 80%;"><b>Gradients of loss functions</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs065.html#summary-of-rnns" style="font-size: 80%;"><b>Summary of RNNs</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs066.html#summary-of-a-typical-rnn" style="font-size: 80%;"><b>Summary of a typical RNN</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs067.html#four-effective-ways-to-learn-an-rnn-and-preparing-for-next-week" style="font-size: 80%;"><b>Four effective ways to learn an RNN and preparing for next week</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs068.html#gating-mechanism-long-short-term-memory-lstm" style="font-size: 80%;"><b>Gating mechanism: Long Short Term Memory (LSTM)</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs069.html#implementing-a-memory-cell-in-a-neural-network" style="font-size: 80%;"><b>Implementing a memory cell in a neural network</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs070.html#lstm-details" style="font-size: 80%;"><b>LSTM details</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs071.html#basic-layout" style="font-size: 80%;"><b>Basic layout</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs072.html#more-lstm-details" style="font-size: 80%;"><b>More LSTM details</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs073.html#the-forget-gate" style="font-size: 80%;"><b>The forget gate</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs074.html#input-gate" style="font-size: 80%;"><b>Input gate</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs075.html#forget-and-input" style="font-size: 80%;"><b>Forget and input</b></a></li>
<!-- navigation toc: --> <li><a href="._week45-bs076.html#output-gate" style="font-size: 80%;"><b>Output gate</b></a></li>
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<h1>Week 45, Convolutional Neural Networks (CCNs) and Recurrent Neural Networks (RNNs)</h1>
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<b>Morten Hjorth-Jensen</b>
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<b>Department of Physics, University of Oslo</b>
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<h4>November 4-8</h4>
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