352 lines
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HTML
352 lines
20 KiB
HTML
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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="._week41-bs001.html#plan-for-week-41" style="font-size: 80%;">Plan for week 41</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs002.html#videos-on-neural-networks" style="font-size: 80%;">Videos on Neural Networks</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs003.html#review-of-the-back-propagation-algorithm" style="font-size: 80%;">Review of the back propagation algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs004.html#setting-up-the-back-propagation-algorithm" style="font-size: 80%;">Setting up the Back propagation algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs005.html#setting-up-a-multi-layer-perceptron-model-for-classification" style="font-size: 80%;">Setting up a Multi-layer perceptron model for classification</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs006.html#defining-the-cost-function" style="font-size: 80%;">Defining the cost function</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs007.html#example-binary-classification-problem" style="font-size: 80%;">Example: binary classification problem</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs008.html#the-softmax-function" style="font-size: 80%;">The Softmax function</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs009.html#developing-a-code-for-doing-neural-networks-with-back-propagation" style="font-size: 80%;">Developing a code for doing neural networks with back propagation</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs036.html#collect-and-pre-process-data" style="font-size: 80%;">Collect and pre-process data</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs011.html#train-and-test-datasets" style="font-size: 80%;">Train and test datasets</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs012.html#define-model-and-architecture" style="font-size: 80%;">Define model and architecture</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs013.html#layers" style="font-size: 80%;">Layers</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs014.html#weights-and-biases" style="font-size: 80%;">Weights and biases</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs015.html#feed-forward-pass" style="font-size: 80%;">Feed-forward pass</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs016.html#matrix-multiplications" style="font-size: 80%;">Matrix multiplications</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs017.html#choose-cost-function-and-optimizer" style="font-size: 80%;">Choose cost function and optimizer</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs018.html#optimizing-the-cost-function" style="font-size: 80%;">Optimizing the cost function</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs019.html#regularization" style="font-size: 80%;">Regularization</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs020.html#matrix-multiplication" style="font-size: 80%;">Matrix multiplication</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs021.html#improving-performance" style="font-size: 80%;">Improving performance</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs022.html#full-object-oriented-implementation" style="font-size: 80%;">Full object-oriented implementation</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs023.html#evaluate-model-performance-on-test-data" style="font-size: 80%;">Evaluate model performance on test data</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs024.html#adjust-hyperparameters" style="font-size: 80%;">Adjust hyperparameters</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs027.html#visualization" style="font-size: 80%;">Visualization</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs026.html#scikit-learn-implementation" style="font-size: 80%;">scikit-learn implementation</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs027.html#visualization" style="font-size: 80%;">Visualization</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs028.html#testing-our-code-for-the-xor-or-and-and-gates" style="font-size: 80%;">Testing our code for the XOR, OR and AND gates</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs029.html#the-and-and-xor-gates" style="font-size: 80%;">The AND and XOR Gates</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs030.html#representing-the-data-sets" style="font-size: 80%;">Representing the Data Sets</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs031.html#setting-up-the-neural-network" style="font-size: 80%;">Setting up the Neural Network</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs032.html#the-code-using-scikit-learn" style="font-size: 80%;">The Code using Scikit-Learn</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs033.html#building-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">Building neural networks in Tensorflow and Keras</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs034.html#tensorflow" style="font-size: 80%;">Tensorflow</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs035.html#using-keras" style="font-size: 80%;">Using Keras</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs036.html#collect-and-pre-process-data" style="font-size: 80%;">Collect and pre-process data</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs037.html#the-breast-cancer-data-now-with-keras" style="font-size: 80%;">The Breast Cancer Data, now with Keras</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs038.html#fine-tuning-neural-network-hyperparameters" style="font-size: 80%;">Fine-tuning neural network hyperparameters</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs039.html#hidden-layers" style="font-size: 80%;">Hidden layers</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs040.html#which-activation-function-should-i-use" style="font-size: 80%;">Which activation function should I use?</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs041.html#is-the-logistic-activation-function-sigmoid-our-choice" style="font-size: 80%;">Is the Logistic activation function (Sigmoid) our choice?</a></li>
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<!-- navigation toc: --> <li><a href="#the-derivative-of-the-logistic-funtion" style="font-size: 80%;">The derivative of the Logistic funtion</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs043.html#the-relu-function-family" style="font-size: 80%;">The RELU function family</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs044.html#which-activation-function-should-we-use" style="font-size: 80%;">Which activation function should we use?</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs045.html#more-on-activation-functions-output-layers" style="font-size: 80%;">More on activation functions, output layers</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs046.html#batch-normalization" style="font-size: 80%;">Batch Normalization</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs047.html#dropout" style="font-size: 80%;">Dropout</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs048.html#gradient-clipping" style="font-size: 80%;">Gradient Clipping</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs049.html#a-very-nice-website-on-neural-networks" style="font-size: 80%;">A very nice website on Neural Networks</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs050.html#a-top-down-perspective-on-neural-networks" style="font-size: 80%;">A top-down perspective on Neural networks</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs051.html#limitations-of-supervised-learning-with-deep-networks" style="font-size: 80%;">Limitations of supervised learning with deep networks</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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</div> <!-- end of navigation bar -->
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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="part0042"></a>
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<!-- !split -->
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<h2 id="the-derivative-of-the-logistic-funtion" class="anchor">The derivative of the Logistic funtion </h2>
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<p>Looking at the logistic activation function, when inputs become large
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(negative or positive), the function saturates at 0 or 1, with a
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derivative extremely close to 0. Thus when backpropagation kicks in,
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it has virtually no gradient to propagate back through the network,
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and what little gradient exists keeps getting diluted as
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backpropagation progresses down through the top layers, so there is
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really nothing left for the lower layers.
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</p>
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<p>In their paper, Glorot and Bengio propose a way to significantly
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alleviate this problem. We need the signal to flow properly in both
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directions: in the forward direction when making predictions, and in
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the reverse direction when backpropagating gradients. We don’t want
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the signal to die out, nor do we want it to explode and saturate. For
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the signal to flow properly, the authors argue that we need the
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variance of the outputs of each layer to be equal to the variance of
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its inputs, and we also need the gradients to have equal variance
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before and after flowing through a layer in the reverse direction.
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</p>
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<p>One of the insights in the 2010 paper by Glorot and Bengio was that
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the vanishing/exploding gradients problems were in part due to a poor
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choice of activation function. Until then most people had assumed that
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if Nature had chosen to use roughly sigmoid activation functions in
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biological neurons, they must be an excellent choice. But it turns out
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that other activation functions behave much better in deep neural
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networks, in particular the ReLU activation function, mostly because
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it does not saturate for positive values (and also because it is quite
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fast to compute).
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</p>
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<p>
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<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
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<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
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<!-- Bootstrap footer
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<footer>
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<a href="https://..."><img width="250" align=right src="https://..."></a>
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</footer>
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-->
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<center style="font-size:80%">
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<!-- copyright only on the titlepage -->
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</center>
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</body>
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</html>
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