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<div id="toc"><ul><li><a class="toc-href" href="#" title="Regularization for Multi-layer Neural Networks in Tensorflow">Regularization for Multi-layer Neural Networks in Tensorflow</a><ul><li><a class="toc-href" href="#Import-libraries" title="Import libraries">Import libraries</a></li><li><a class="toc-href" href="#Load-NotMNIST-dataset" title="Load NotMNIST dataset">Load NotMNIST dataset</a></li><li><a class="toc-href" href="#Reformat-dataset" title="Reformat dataset">Reformat dataset</a><ul><li><a class="toc-href" href="#Using-Accuracy-as-Default-Metric" title="Using Accuracy as Default Metric">Using Accuracy as Default Metric</a></li></ul></li><li><a class="toc-href" href="#3-layer-NN-as-base-model_1" title="3-layer NN as base model">3-layer NN as base model</a><ul><li><a class="toc-href" href="#Hyper-parameters" title="Hyper parameters">Hyper parameters</a></li><li><a class="toc-href" href="#Build-model" title="Build model">Build model</a></li><li><a class="toc-href" href="#Train-model-without-regularization" title="Train model without regularization">Train model without regularization</a></li></ul></li><li><a class="toc-href" href="#L2-regularization_1" title="L2 regularization">L2 regularization</a></li><li><a class="toc-href" href="#Case-of-overfitting" title="Case of overfitting">Case of overfitting</a></li><li><a class="toc-href" href="#Dropout" title="Dropout">Dropout</a></li><li><a class="toc-href" href="#Boost-performance-by-using-Multi-layer-NN" title="Boost performance by using Multi-layer NN">Boost performance by using Multi-layer NN</a></li></ul></li></ul></div>
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Regularization for Multi-layer Neural Networks in Tensorflow
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<p>The goal of this assignment is to explore regularization techniques.
The original notebook can be found <a href="https://github.com/tensorflow/tensorflow/blob/master/tensorflow/examples/udacity/3_regularization.ipynb">here</a></p>
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<h2 id="Import-libraries">Import libraries<a class="anchor-link" href="#Import-libraries">¶</a></h2>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1"># These are all the modules we'll be using later. Make sure you can import them</span>
<span class="c1"># before proceeding further.</span>
<span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">print_function</span>
<span class="kn">from</span> <span class="nn">tqdm</span> <span class="kn">import</span> <span class="n">tnrange</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">tensorflow</span> <span class="k">as</span> <span class="nn">tf</span>
<span class="kn">from</span> <span class="nn">six.moves</span> <span class="kn">import</span> <span class="n">cPickle</span> <span class="k">as</span> <span class="n">pickle</span>
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<h2 id="Load-NotMNIST-dataset">Load NotMNIST dataset<a class="anchor-link" href="#Load-NotMNIST-dataset">¶</a></h2>
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<p>First reload the data we generated in <code>1_notmnist.ipynb</code>.</p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">pickle_file</span> <span class="o">=</span> <span class="s1">'datasets/notMNIST.pickle'</span>
<span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="n">pickle_file</span><span class="p">,</span> <span class="s1">'rb'</span><span class="p">)</span> <span class="k">as</span> <span class="n">f</span><span class="p">:</span>
<span class="n">save</span> <span class="o">=</span> <span class="n">pickle</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
<span class="n">X_train</span> <span class="o">=</span> <span class="n">save</span><span class="p">[</span><span class="s1">'train_dataset'</span><span class="p">]</span>
<span class="n">Y_train</span> <span class="o">=</span> <span class="n">save</span><span class="p">[</span><span class="s1">'train_labels'</span><span class="p">]</span>
<span class="n">X_valid</span> <span class="o">=</span> <span class="n">save</span><span class="p">[</span><span class="s1">'valid_dataset'</span><span class="p">]</span>
<span class="n">Y_valid</span> <span class="o">=</span> <span class="n">save</span><span class="p">[</span><span class="s1">'valid_labels'</span><span class="p">]</span>
<span class="n">X_test</span> <span class="o">=</span> <span class="n">save</span><span class="p">[</span><span class="s1">'test_dataset'</span><span class="p">]</span>
<span class="n">Y_test</span> <span class="o">=</span> <span class="n">save</span><span class="p">[</span><span class="s1">'test_labels'</span><span class="p">]</span>
<span class="k">del</span> <span class="n">save</span> <span class="c1"># hint to help gc free up memory</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'Training set'</span><span class="p">,</span> <span class="n">X_train</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">Y_train</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'Validation set'</span><span class="p">,</span> <span class="n">X_valid</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">Y_valid</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'Test set'</span><span class="p">,</span> <span class="n">X_test</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">Y_test</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
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<pre>Training set (200000, 28, 28) (200000,)
Validation set (10000, 28, 28) (10000,)
Test set (10000, 28, 28) (10000,)
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<h2 id="Reformat-dataset">Reformat dataset<a class="anchor-link" href="#Reformat-dataset">¶</a></h2>
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<p>Reformat into a shape that's more adapted to the models we're going to train:</p>
<ul>
<li>data as a flat matrix,</li>
<li>labels as float 1-hot encodings.</li>
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<p>As I did in previous notebook, this reformat operation will be different from the operation suggested by the original <a href="https://github.com/tensorflow/tensorflow/blob/master/tensorflow/examples/udacity/3_regularization.ipynb">notebook</a>.</p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">image_size</span> <span class="o">=</span> <span class="mi">28</span>
<span class="n">num_labels</span> <span class="o">=</span> <span class="mi">10</span>
<span class="k">def</span> <span class="nf">reformat</span><span class="p">(</span><span class="n">dataset</span><span class="p">,</span> <span class="n">labels</span><span class="p">):</span>
<span class="n">dataset</span> <span class="o">=</span> <span class="n">dataset</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">image_size</span> <span class="o">*</span> <span class="n">image_size</span><span class="p">))</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span><span class="o">.</span><span class="n">T</span>
<span class="c1"># Map 0 to [1.0, 0.0, 0.0 ...], 1 to [0.0, 1.0, 0.0 ...]</span>
<span class="n">labels</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">num_labels</span><span class="p">)</span> <span class="o">==</span> <span class="n">labels</span><span class="p">[:,</span> <span class="kc">None</span><span class="p">])</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span><span class="o">.</span><span class="n">T</span>
<span class="k">return</span> <span class="n">dataset</span><span class="p">,</span> <span class="n">labels</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">Y_train</span> <span class="o">=</span> <span class="n">reformat</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">Y_train</span><span class="p">)</span>
<span class="n">X_valid</span><span class="p">,</span> <span class="n">Y_valid</span> <span class="o">=</span> <span class="n">reformat</span><span class="p">(</span><span class="n">X_valid</span><span class="p">,</span> <span class="n">Y_valid</span><span class="p">)</span>
<span class="n">X_test</span><span class="p">,</span> <span class="n">Y_test</span> <span class="o">=</span> <span class="n">reformat</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span> <span class="n">Y_test</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'Training set'</span><span class="p">,</span> <span class="n">X_train</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">Y_train</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'Validation set'</span><span class="p">,</span> <span class="n">X_valid</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">Y_valid</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'Test set'</span><span class="p">,</span> <span class="n">X_test</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">X_test</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
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<pre>Training set (784, 200000) (10, 200000)
Validation set (784, 10000) (10, 10000)
Test set (784, 10000) (784, 10000)
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<h3 id="Using-Accuracy-as-Default-Metric">Using Accuracy as Default Metric<a class="anchor-link" href="#Using-Accuracy-as-Default-Metric">¶</a></h3><p>Because as we explored before, there exist no unbalanced problem in the dataset,<br/>
so accuracy alone will be sufficient for evaluating performance of our model on the classification task.</p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">accuracy</span><span class="p">(</span><span class="n">predictions</span><span class="p">,</span> <span class="n">labels</span><span class="p">):</span>
<span class="k">return</span> <span class="p">(</span>
<span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">predictions</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span>
<span class="n">labels</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">))</span> <span class="o">/</span> <span class="n">labels</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="mi">100</span><span class="p">)</span>
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<h2 id="3-layer-NN-as-base-model_1">3-layer NN as base model<a class="anchor-link" href="#3-layer-NN-as-base-model">¶</a></h2><p>In order to test the effect with/without regularization, we will use a little more complex neural network with 2 hidden layers as our base model. And we will be using ReLU as our activation function.</p>
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<h3 id="Hyper-parameters">Hyper parameters<a class="anchor-link" href="#Hyper-parameters">¶</a></h3>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1"># hyper parameters</span>
<span class="n">learning_rate</span> <span class="o">=</span> <span class="mf">1e-2</span>
<span class="n">lamba</span> <span class="o">=</span> <span class="mf">1e-3</span>
<span class="n">keep_prob</span> <span class="o">=</span> <span class="mf">0.5</span>
<span class="n">batch_size</span> <span class="o">=</span> <span class="mi">128</span>
<span class="n">num_steps</span> <span class="o">=</span> <span class="mi">501</span>
<span class="n">n0</span> <span class="o">=</span> <span class="n">image_size</span> <span class="o">*</span> <span class="n">image_size</span> <span class="c1"># input size</span>
<span class="n">n1</span> <span class="o">=</span> <span class="mi">1024</span> <span class="c1"># first hidden layer</span>
<span class="n">n2</span> <span class="o">=</span> <span class="mi">512</span> <span class="c1"># second hidden layer</span>
<span class="n">n3</span> <span class="o">=</span> <span class="mi">256</span> <span class="c1"># third hidden layer</span>
<span class="n">n4</span> <span class="o">=</span> <span class="n">num_labels</span> <span class="c1"># output size</span>
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<h3 id="Build-model">Build model<a class="anchor-link" href="#Build-model">¶</a></h3>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1"># build a model which let us able to choose different optimzation mechnism</span>
<span class="k">def</span> <span class="nf">model</span><span class="p">(</span><span class="n">lamba</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">learning_rate</span><span class="o">=</span><span class="n">learning_rate</span><span class="p">,</span>
<span class="n">keep_prob</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">learning_decay</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
<span class="n">batch_size</span><span class="o">=</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">num_steps</span><span class="o">=</span><span class="n">num_steps</span><span class="p">,</span> <span class="n">n1</span><span class="o">=</span><span class="n">n1</span><span class="p">,</span> <span class="n">n2</span><span class="o">=</span><span class="n">n2</span><span class="p">,</span> <span class="n">n3</span><span class="o">=</span><span class="n">n3</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Train 3-layer NN with following settings:</span>
<span class="sd"> Regularization lambda: {}</span>
<span class="sd"> Learning rate: {}</span>
<span class="sd"> learning_decay: {}</span>
<span class="sd"> keep_prob: {}</span>
<span class="sd"> Batch_size: {}</span>
<span class="sd"> Number of steps: {}</span>
<span class="sd"> n1, n2, n3: {}, {}, {}"""</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">lamba</span><span class="p">,</span> <span class="n">learning_rate</span><span class="p">,</span>
<span class="n">learning_decay</span><span class="p">,</span> <span class="n">keep_prob</span><span class="p">,</span>
<span class="n">batch_size</span><span class="p">,</span> <span class="n">num_steps</span><span class="p">,</span> <span class="n">n1</span><span class="p">,</span> <span class="n">n2</span><span class="p">,</span> <span class="n">n3</span><span class="p">))</span>
<span class="c1"># construct computation graph</span>
<span class="n">graph</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Graph</span><span class="p">()</span>
<span class="k">with</span> <span class="n">graph</span><span class="o">.</span><span class="n">as_default</span><span class="p">():</span>
<span class="c1"># placeholder for mini-batch when training </span>
<span class="n">X</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">placeholder</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">,</span> <span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="n">n0</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">))</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">placeholder</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">,</span> <span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="n">num_labels</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">))</span>
<span class="n">global_step</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="c1"># use all valid/test set</span>
<span class="n">tf_X_valid</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">constant</span><span class="p">(</span><span class="n">X_valid</span><span class="p">)</span>
<span class="n">tf_X_test</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">constant</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="c1"># initialize weights, biases</span>
<span class="c1"># notice that we have two hidden </span>
<span class="c1"># layers so we now have W1, b1, W2, b2, W3, b3</span>
<span class="n">W1</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">truncated_normal</span><span class="p">([</span><span class="n">n1</span><span class="p">,</span> <span class="n">n0</span><span class="p">],</span> <span class="n">stddev</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mf">2.0</span> <span class="o">/</span> <span class="n">n0</span><span class="p">)))</span>
<span class="n">W2</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">truncated_normal</span><span class="p">([</span><span class="n">n2</span><span class="p">,</span> <span class="n">n1</span><span class="p">],</span> <span class="n">stddev</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mf">2.0</span> <span class="o">/</span> <span class="n">n1</span><span class="p">)))</span>
<span class="n">W3</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">truncated_normal</span><span class="p">([</span><span class="n">n3</span><span class="p">,</span> <span class="n">n2</span><span class="p">],</span> <span class="n">stddev</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mf">2.0</span> <span class="o">/</span> <span class="n">n2</span><span class="p">)))</span>
<span class="n">W4</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">truncated_normal</span><span class="p">([</span><span class="n">n4</span><span class="p">,</span> <span class="n">n3</span><span class="p">],</span> <span class="n">stddev</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mf">2.0</span> <span class="o">/</span> <span class="n">n3</span><span class="p">)))</span>
<span class="n">b1</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="n">n1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]))</span>
<span class="n">b2</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="n">n2</span><span class="p">,</span> <span class="mi">1</span><span class="p">]))</span>
<span class="n">b3</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="n">n3</span><span class="p">,</span> <span class="mi">1</span><span class="p">]))</span>
<span class="n">b4</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="n">n4</span><span class="p">,</span> <span class="mi">1</span><span class="p">]))</span>
<span class="c1"># training computation</span>
<span class="n">Z1</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">W1</span><span class="p">,</span> <span class="n">X</span><span class="p">)</span> <span class="o">+</span> <span class="n">b1</span>
<span class="n">A1</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span><span class="n">Z1</span><span class="p">)</span> <span class="k">if</span> <span class="n">keep_prob</span> <span class="o">==</span> <span class="mi">1</span> <span class="k">else</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">dropout</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span><span class="n">Z1</span><span class="p">),</span> <span class="n">keep_prob</span><span class="p">)</span>
<span class="n">Z2</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">W2</span><span class="p">,</span> <span class="n">A1</span><span class="p">)</span> <span class="o">+</span> <span class="n">b2</span>
<span class="n">A2</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span><span class="n">Z2</span><span class="p">)</span> <span class="k">if</span> <span class="n">keep_prob</span> <span class="o">==</span> <span class="mi">1</span> <span class="k">else</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">dropout</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span><span class="n">Z2</span><span class="p">),</span> <span class="n">keep_prob</span><span class="p">)</span>
<span class="n">Z3</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">W3</span><span class="p">,</span> <span class="n">A2</span><span class="p">)</span> <span class="o">+</span> <span class="n">b3</span>
<span class="n">A3</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span><span class="n">Z3</span><span class="p">)</span> <span class="k">if</span> <span class="n">keep_prob</span> <span class="o">==</span> <span class="mi">1</span> <span class="k">else</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">dropout</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span><span class="n">Z3</span><span class="p">),</span> <span class="n">keep_prob</span><span class="p">)</span>
<span class="n">Z4</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">W4</span><span class="p">,</span> <span class="n">A3</span><span class="p">)</span> <span class="o">+</span> <span class="n">b4</span>
<span class="n">loss</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">reduce_mean</span><span class="p">(</span>
<span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">softmax_cross_entropy_with_logits</span><span class="p">(</span>
<span class="n">labels</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">Y</span><span class="p">),</span> <span class="n">logits</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">Z4</span><span class="p">)))</span>
<span class="k">if</span> <span class="n">lamba</span><span class="p">:</span>
<span class="n">loss</span> <span class="o">+=</span> <span class="n">lamba</span> <span class="o">*</span> \
<span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">l2_loss</span><span class="p">(</span><span class="n">W1</span><span class="p">)</span> <span class="o">+</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">l2_loss</span><span class="p">(</span><span class="n">W2</span><span class="p">)</span> <span class="o">+</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">l2_loss</span><span class="p">(</span><span class="n">W3</span><span class="p">)</span> <span class="o">+</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">l2_loss</span><span class="p">(</span><span class="n">W4</span><span class="p">))</span>
<span class="c1"># optimizer</span>
<span class="k">if</span> <span class="n">learning_decay</span><span class="p">:</span>
<span class="n">learning_rate</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">train</span><span class="o">.</span><span class="n">exponential_decay</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">global_step</span><span class="p">,</span> <span class="mi">5000</span><span class="p">,</span> <span class="mf">0.80</span><span class="p">,</span> <span class="n">staircase</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">optimizer</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">train</span><span class="o">.</span><span class="n">GradientDescentOptimizer</span><span class="p">(</span><span class="n">learning_rate</span><span class="p">)</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">loss</span><span class="p">,</span> <span class="n">global_step</span><span class="o">=</span><span class="n">global_step</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">optimizer</span> <span class="o">=</span> <span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">train</span>
<span class="o">.</span><span class="n">GradientDescentOptimizer</span><span class="p">(</span><span class="n">learning_rate</span><span class="p">)</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">loss</span><span class="p">))</span>
<span class="c1"># valid / test prediction</span>
<span class="n">Y_pred</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">softmax</span><span class="p">(</span><span class="n">Z4</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">Y_vaild_pred</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">softmax</span><span class="p">(</span>
<span class="n">tf</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">W4</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span>
<span class="n">tf</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">W3</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span>
<span class="n">tf</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">W2</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span>
<span class="n">tf</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">W1</span><span class="p">,</span> <span class="n">tf_X_valid</span><span class="p">)</span> <span class="o">+</span> <span class="n">b1</span><span class="p">))</span> <span class="o">+</span> <span class="n">b2</span><span class="p">))</span> <span class="o">+</span> <span class="n">b3</span><span class="p">))</span> <span class="o">+</span> <span class="n">b4</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">Y_test_pred</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">softmax</span><span class="p">(</span>
<span class="n">tf</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">W4</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span>
<span class="n">tf</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">W3</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span>
<span class="n">tf</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">W2</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span>
<span class="n">tf</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">W1</span><span class="p">,</span> <span class="n">tf_X_test</span><span class="p">)</span> <span class="o">+</span> <span class="n">b1</span><span class="p">))</span> <span class="o">+</span> <span class="n">b2</span><span class="p">))</span> <span class="o">+</span> <span class="n">b3</span><span class="p">))</span> <span class="o">+</span> <span class="n">b4</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="c1"># define training</span>
<span class="k">with</span> <span class="n">tf</span><span class="o">.</span><span class="n">Session</span><span class="p">(</span><span class="n">graph</span><span class="o">=</span><span class="n">graph</span><span class="p">)</span> <span class="k">as</span> <span class="n">sess</span><span class="p">:</span>
<span class="c1"># initialized parameters</span>
<span class="n">tf</span><span class="o">.</span><span class="n">global_variables_initializer</span><span class="p">()</span><span class="o">.</span><span class="n">run</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Initialized"</span><span class="p">)</span>
<span class="k">for</span> <span class="n">step</span> <span class="ow">in</span> <span class="n">tnrange</span><span class="p">(</span><span class="n">num_steps</span><span class="p">):</span>
<span class="c1"># generate randomized mini-batches from training data</span>
<span class="n">offset</span> <span class="o">=</span> <span class="p">(</span><span class="n">step</span> <span class="o">*</span> <span class="n">batch_size</span><span class="p">)</span> <span class="o">%</span> <span class="p">(</span><span class="n">Y_train</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">batch_size</span><span class="p">)</span>
<span class="n">batch_X</span> <span class="o">=</span> <span class="n">X_train</span><span class="p">[:,</span> <span class="n">offset</span><span class="p">:(</span><span class="n">offset</span> <span class="o">+</span> <span class="n">batch_size</span><span class="p">)]</span>
<span class="n">batch_Y</span> <span class="o">=</span> <span class="n">Y_train</span><span class="p">[:,</span> <span class="n">offset</span><span class="p">:(</span><span class="n">offset</span> <span class="o">+</span> <span class="n">batch_size</span><span class="p">)]</span>
<span class="c1"># train model</span>
<span class="n">_</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">batch_Y_pred</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span>
<span class="p">[</span><span class="n">optimizer</span><span class="p">,</span> <span class="n">loss</span><span class="p">,</span> <span class="n">Y_pred</span><span class="p">],</span> <span class="n">feed_dict</span><span class="o">=</span><span class="p">{</span><span class="n">X</span><span class="p">:</span> <span class="n">batch_X</span><span class="p">,</span> <span class="n">Y</span><span class="p">:</span> <span class="n">batch_Y</span><span class="p">})</span>
<span class="k">if</span> <span class="p">(</span><span class="n">step</span> <span class="o">%</span> <span class="mi">200</span> <span class="o">==</span> <span class="mi">0</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'Minibatch loss at step </span><span class="si">{}</span><span class="s1">: </span><span class="si">{:.3f}</span><span class="s1">. batch acc: </span><span class="si">{:.1f}</span><span class="s1">%, Valid acc: </span><span class="si">{:.1f}</span><span class="s1">%.'</span>\
<span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">step</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span>
<span class="n">accuracy</span><span class="p">(</span><span class="n">batch_Y_pred</span><span class="p">,</span> <span class="n">batch_Y</span><span class="p">),</span>
<span class="n">accuracy</span><span class="p">(</span><span class="n">Y_vaild_pred</span><span class="o">.</span><span class="n">eval</span><span class="p">(),</span> <span class="n">Y_valid</span><span class="p">)))</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'Test acc: </span><span class="si">{:.1f}</span><span class="s1">%'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">accuracy</span><span class="p">(</span><span class="n">Y_test_pred</span><span class="o">.</span><span class="n">eval</span><span class="p">(),</span> <span class="n">Y_test</span><span class="p">)))</span>
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<h3 id="Train-model-without-regularization">Train model without regularization<a class="anchor-link" href="#Train-model-without-regularization">¶</a></h3>
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">model</span><span class="p">(</span><span class="n">learning_rate</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">num_steps</span><span class="o">=</span><span class="mi">1601</span><span class="p">)</span>
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<pre>
Train 3-layer NN with following settings:
Regularization lambda: 0
Learning rate: 0.5
learning_decay: False
keep_prob: 1
Batch_size: 128
Number of steps: 1601
n1, n2, n3: 1024, 512, 256
Initialized
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<pre>Minibatch loss at step 0: 2.374. batch acc: 14.1%, Valid acc: 28.4%.
Minibatch loss at step 200: 0.600. batch acc: 82.0%, Valid acc: 84.9%.
Minibatch loss at step 400: 0.429. batch acc: 89.8%, Valid acc: 85.8%.
Minibatch loss at step 600: 0.372. batch acc: 87.5%, Valid acc: 85.7%.
Minibatch loss at step 800: 0.454. batch acc: 89.1%, Valid acc: 87.7%.
Minibatch loss at step 1000: 0.374. batch acc: 87.5%, Valid acc: 88.1%.
Minibatch loss at step 1200: 0.251. batch acc: 91.4%, Valid acc: 88.8%.
Minibatch loss at step 1400: 0.397. batch acc: 89.8%, Valid acc: 89.0%.
Minibatch loss at step 1600: 0.470. batch acc: 82.0%, Valid acc: 88.9%.
Test acc: 94.2%
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<h2 id="L2-regularization_1">L2 regularization<a class="anchor-link" href="#L2-regularization">¶</a></h2><p>Introduce and tune L2 regularization for the models. Remember that L2 amounts to adding a penalty on the norm of the weights to the loss. In TensorFlow, you can compute the L2 loss for a tensor <code>t</code> using <code>nn.l2_loss(t)</code>. The right amount of regularization should improve your validation / test accuracy.</p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1"># for lamda in [1 / 10 ** i for i in list(np.arange(1, 4))]:</span>
<span class="c1"># model(lamba=lamda)</span>
<span class="n">model</span><span class="p">(</span><span class="n">lamba</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">learning_rate</span><span class="o">=</span><span class="mf">0.01</span><span class="p">)</span>
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Train 3-layer NN with following settings:
Regularization lambda: 0.1
Optimizer: sgd
Learning rate: 0.01
Batch_size: 128
Number of steps: 501
n1, n2: 512, 256
Initialized
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<pre>Minibatch loss at step 0: 22969.777. batch acc: 9.4%, Valid acc: 19.3%.
Minibatch loss at step 200: 13876.185. batch acc: 74.2%, Valid acc: 75.2%.
Minibatch loss at step 400: 9266.566. batch acc: 78.1%, Valid acc: 74.3%.
Test acc: 81.4%
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<h2 id="Case-of-overfitting">Case of overfitting<a class="anchor-link" href="#Case-of-overfitting">¶</a></h2><p>Let's demonstrate an extreme case of overfitting. Restrict your training data to just a few batches. What happens?</p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">model</span><span class="p">(</span><span class="n">num_steps</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
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Train 3-layer NN with following settings:
Regularization lambda: 0
Learning rate: 0.01
learning_decay: False
keep_prob: 1
Batch_size: 128
Number of steps: 10
n1, n2, n3: 1024, 512, 256
Initialized
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<pre>Minibatch loss at step 0: 2.442. batch acc: 8.6%, Valid acc: 11.4%.
Test acc: 20.7%
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<h2 id="Dropout">Dropout<a class="anchor-link" href="#Dropout">¶</a></h2><p>Introduce Dropout on the hidden layer of the neural network. Remember: Dropout should only be introduced during training, not evaluation, otherwise your evaluation results would be stochastic as well. TensorFlow provides <code>nn.dropout()</code> for that, but you have to make sure it's only inserted during training.</p>
<p>What happens to our extreme overfitting case?</p>
<p><img src="images/dropout1_kiank.mp4"/></p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">model</span><span class="p">(</span><span class="n">num_steps</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">keep_prob</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
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<pre>
Train 3-layer NN with following settings:
Regularization lambda: 0
Learning rate: 0.01
learning_decay: False
keep_prob: 0.5
Batch_size: 128
Number of steps: 10
n1, n2, n3: 1024, 512, 256
Initialized
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<pre>Minibatch loss at step 0: 2.784. batch acc: 7.0%, Valid acc: 10.0%.
Test acc: 17.3%
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<h2 id="Boost-performance-by-using-Multi-layer-NN">Boost performance by using Multi-layer NN<a class="anchor-link" href="#Boost-performance-by-using-Multi-layer-NN">¶</a></h2><p>Try to get the best performance you can using a multi-layer model! The best reported test accuracy using a deep network is <a href="http://yaroslavvb.blogspot.com/2011/09/notmnist-dataset.html?showComment=1391023266211#c8758720086795711595">97.1%</a>.</p>
<p>One avenue you can explore is to add multiple layers.</p>
<p>Another one is to use learning rate decay:</p>
<pre><code>global_step = tf.Variable(0) # count the number of steps taken.
learning_rate = tf.train.exponential_decay(0.5, global_step, ...)
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss, global_step=global_step)
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">model</span><span class="p">(</span><span class="n">learning_decay</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">num_steps</span><span class="o">=</span><span class="mi">1501</span><span class="p">,</span> <span class="n">lamba</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">keep_prob</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
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Train 3-layer NN with following settings:
Regularization lambda: 0
Learning rate: 0.01
learning_decay: True
keep_prob: 1
Batch_size: 128
Number of steps: 1501
n1, n2, n3: 1024, 512, 256
Initialized
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<pre>Minibatch loss at step 0: 2.395. batch acc: 12.5%, Valid acc: 37.0%.
Minibatch loss at step 200: 0.589. batch acc: 82.0%, Valid acc: 84.7%.
Minibatch loss at step 400: 0.409. batch acc: 89.1%, Valid acc: 86.2%.
Minibatch loss at step 600: 0.396. batch acc: 88.3%, Valid acc: 86.5%.
Minibatch loss at step 800: 0.435. batch acc: 88.3%, Valid acc: 87.6%.
Minibatch loss at step 1000: 0.407. batch acc: 85.2%, Valid acc: 88.5%.
Minibatch loss at step 1200: 0.262. batch acc: 91.4%, Valid acc: 88.9%.
Minibatch loss at step 1400: 0.411. batch acc: 87.5%, Valid acc: 88.8%.
Test acc: 94.3%
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