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<time class="post-full-meta-date" datetime="18 December 2021">18 December 2021</time>
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<h1 class="post-full-title">cs231n - Lecture 6. Hardware and Software</h1>
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<h3 id="deeplearning-software">Deeplearning Software</h3>
<ul>
<li>The point of deep learning frameworks<br />
(1) Quick to develop and test new ideas<br />
(2) Automatically compute gradients<br />
(3) Run it all efficiently on GPU (wrap cuDNN, cuBLAS, OpenCL, etc)</li>
</ul>
<h3 id="computational-graph-example">Computational graph example</h3>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="n">np</span>
<span class="n">np</span><span class="p">.</span><span class="n">random</span><span class="p">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">N</span><span class="p">,</span> <span class="n">D</span> <span class="o">=</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="p">.</span><span class="n">random</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="p">.</span><span class="n">random</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="p">.</span><span class="n">random</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
<span class="n">a</span> <span class="o">=</span> <span class="n">x</span> <span class="o">*</span> <span class="n">y</span>
<span class="n">b</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="n">z</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">np</span><span class="p">.</span><span class="nb">sum</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
<span class="n">grad_c</span> <span class="o">=</span> <span class="mf">1.0</span>
<span class="n">grad_b</span> <span class="o">=</span> <span class="n">grad_c</span> <span class="o">*</span> <span class="n">np</span><span class="p">.</span><span class="n">ones</span><span class="p">((</span><span class="n">N</span><span class="p">,</span> <span class="n">D</span><span class="p">))</span>
<span class="n">grad_a</span> <span class="o">=</span> <span class="n">grad_b</span><span class="p">.</span><span class="n">copy</span><span class="p">()</span>
<span class="n">grad_z</span> <span class="o">=</span> <span class="n">grad_b</span><span class="p">.</span><span class="n">copy</span><span class="p">()</span>
<span class="n">grad_x</span> <span class="o">=</span> <span class="n">grad_a</span> <span class="o">*</span> <span class="n">y</span>
<span class="n">grad_y</span> <span class="o">=</span> <span class="n">grad_a</span> <span class="o">*</span> <span class="n">x</span>
</code></pre></div></div>
<ul>
<li>in Numpy<br />
Good: Clean API, easy to write numeric code<br />
Bad: Have to compute our own gradients and can’t run on GPU</li>
</ul>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kn">import</span> <span class="nn">torch</span>
<span class="n">device</span> <span class="o">=</span> <span class="s">'cuda:0'</span>
<span class="n">N</span><span class="p">,</span> <span class="n">D</span> <span class="o">=</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D</span><span class="p">,</span> <span class="n">requires_grad</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span>
<span class="n">device</span><span class="o">=</span><span class="n">device</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
<span class="n">a</span> <span class="o">=</span> <span class="n">x</span> <span class="o">*</span> <span class="n">y</span>
<span class="n">b</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="n">z</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="nb">sum</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
<span class="n">c</span><span class="p">.</span><span class="n">backward</span><span class="p">()</span>
<span class="k">print</span><span class="p">(</span><span class="n">x</span><span class="p">.</span><span class="n">grad</span><span class="p">)</span>
</code></pre></div></div>
<ul>
<li>in PyTorch<br />
PyTorch handles gradients for us<br />
Can run on GPU</li>
</ul>
<h3 id="pytorch-fundamental-concepts">PyTorch: Fundamental Concepts</h3>
<ul>
<li><code class="language-plaintext highlighter-rouge">torch.Tensor</code>: Like a numpy array, but can run on GPU</li>
<li><code class="language-plaintext highlighter-rouge">torch.autograd</code>: Package for building computational graphs out of Tensors, and automatically computing gradients</li>
<li><code class="language-plaintext highlighter-rouge">torch.nn.Module</code>: A neural network layer; may store state or learnable weights</li>
<li>we are using PyTorch version <em>1.7</em> here</li>
</ul>
<h3 id="pytorch-autograd">PyTorch: Autograd</h3>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="c1"># Running example: Train a two-layer ReLU network on random data with L2 loss
</span><span class="kn">import</span> <span class="nn">torch</span>
<span class="n">N</span><span class="p">,</span> <span class="n">D_in</span><span class="p">,</span> <span class="n">H</span><span class="p">,</span> <span class="n">D_out</span> <span class="o">=</span> <span class="mi">64</span><span class="p">,</span> <span class="mi">1000</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">10</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D_in</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D_out</span><span class="p">)</span>
<span class="n">w1</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">D_in</span><span class="p">,</span> <span class="n">H</span><span class="p">,</span> <span class="n">requires_grad</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span> <span class="c1"># enables autograd
</span><span class="n">w2</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">H</span><span class="p">,</span> <span class="n">D_out</span><span class="p">,</span> <span class="n">requires_grad</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
<span class="n">learning_rate</span> <span class="o">=</span> <span class="mf">1e-6</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">500</span><span class="p">):</span>
<span class="n">h</span> <span class="o">=</span> <span class="n">x</span><span class="p">.</span><span class="n">mm</span><span class="p">(</span><span class="n">w1</span><span class="p">)</span> <span class="c1"># Forward pass
</span> <span class="n">h_relu</span> <span class="o">=</span> <span class="n">h</span><span class="p">.</span><span class="n">clamp</span><span class="p">(</span><span class="nb">min</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="c1"># no need to track intermediate values
</span> <span class="n">y_pred</span> <span class="o">=</span> <span class="n">h_relu</span><span class="p">.</span><span class="n">mm</span><span class="p">(</span><span class="n">w2</span><span class="p">)</span> <span class="c1"># = x.mm(w1).clamp(min=0).mm(w2)
</span> <span class="n">loss</span> <span class="o">=</span> <span class="p">(</span><span class="n">y_pred</span> <span class="o">-</span> <span class="n">y</span><span class="p">).</span><span class="nb">pow</span><span class="p">(</span><span class="mi">2</span><span class="p">).</span><span class="nb">sum</span><span class="p">()</span>
<span class="n">loss_backward</span><span class="p">()</span> <span class="c1"># Compute gradient of loss
</span>
<span class="k">with</span> <span class="n">torch</span><span class="p">.</span><span class="n">no_grad</span><span class="p">():</span> <span class="c1"># Gradient descent
</span> <span class="n">w1</span> <span class="o">-=</span> <span class="n">learning_rate</span> <span class="o">*</span> <span class="n">w1</span><span class="p">.</span><span class="n">grad</span>
<span class="n">w2</span> <span class="o">-=</span> <span class="n">learning_rate</span> <span class="o">*</span> <span class="n">w2</span><span class="p">.</span><span class="n">grad</span>
<span class="n">w1</span><span class="p">.</span><span class="n">grad</span><span class="p">.</span><span class="n">zero_</span><span class="p">()</span>
<span class="n">w2</span><span class="p">.</span><span class="n">grad</span><span class="p">.</span><span class="n">zero_</span><span class="p">()</span>
</code></pre></div></div>
<h3 id="or-you-can-define-your-own">Or you can define your own</h3>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="k">class</span> <span class="nc">MyReLU</span><span class="p">(</span><span class="n">torch</span><span class="p">.</span><span class="n">autograd</span><span class="p">.</span><span class="n">Function</span><span class="p">):</span>
<span class="o">@</span><span class="nb">staticmethod</span>
<span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="c1">#Use ctx object to “cache” values for the backward pass
</span> <span class="n">ctx</span><span class="p">.</span><span class="n">save_for_backward</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="k">return</span> <span class="n">x</span><span class="p">.</span><span class="n">clamp</span><span class="p">(</span><span class="nb">min</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="o">@</span><span class="nb">staticmethod</span>
<span class="k">def</span> <span class="nf">backward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">grad_y</span><span class="p">):</span>
<span class="n">x</span><span class="p">,</span> <span class="o">=</span> <span class="n">ctx</span><span class="p">.</span><span class="n">saved_tensors</span>
<span class="n">grad_input</span> <span class="o">=</span> <span class="n">grad_y</span><span class="p">.</span><span class="n">clone</span><span class="p">()</span>
<span class="n">grad_input</span><span class="p">[</span><span class="n">x</span> <span class="o"><</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">return</span> <span class="n">grad_input</span>
<span class="k">def</span> <span class="nf">my_relu</span><span class="p">(</span><span class="n">x</span><span class="p">):</span> <span class="c1"># a helper function to make it easy to use the new function
</span> <span class="k">return</span> <span class="n">MyReLU</span><span class="p">.</span><span class="nb">apply</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
</code></pre></div></div>
<ul>
<li>Now we can replace <code class="language-plaintext highlighter-rouge">y_pred = x.mm(w1).clamp(min=0).mm(w2)</code> with <code class="language-plaintext highlighter-rouge">y_pred = my_relu(x.mm(w1)).mm(w2)</code>. In practice, do it only when you need custom backward.</li>
</ul>
<h3 id="pytorch-nn">PyTorch: nn</h3>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="c1"># Higher-level wrapper for working with neural nets
</span><span class="kn">import</span> <span class="nn">torch</span>
<span class="n">N</span><span class="p">,</span> <span class="n">D_in</span><span class="p">,</span> <span class="n">H</span><span class="p">,</span> <span class="n">D_out</span> <span class="o">=</span> <span class="mi">64</span><span class="p">,</span> <span class="mi">1000</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">10</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D_in</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D_out</span><span class="p">)</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">nn</span><span class="p">.</span><span class="n">Sequential</span><span class="p">(</span>
<span class="n">torch</span><span class="p">.</span><span class="n">nn</span><span class="p">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">D_in</span><span class="p">,</span> <span class="n">H</span><span class="p">),</span>
<span class="n">torch</span><span class="p">.</span><span class="n">nn</span><span class="p">.</span><span class="n">ReLU</span><span class="p">(),</span>
<span class="n">torch</span><span class="p">.</span><span class="n">nn</span><span class="p">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">H</span><span class="p">,</span> <span class="n">D_out</span><span class="p">))</span>
<span class="n">learning_rate</span> <span class="o">=</span> <span class="mf">1e-2</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">500</span><span class="p">):</span>
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">model</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">loss</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">nn</span><span class="p">.</span><span class="n">functional</span><span class="p">.</span><span class="n">mse_loss</span><span class="p">(</span><span class="n">y_pred</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">loss</span><span class="p">.</span><span class="n">backward</span><span class="p">()</span>
<span class="k">with</span> <span class="n">torch</span><span class="p">.</span><span class="n">no_grad</span><span class="p">():</span>
<span class="k">for</span> <span class="n">param</span> <span class="ow">in</span> <span class="n">model</span><span class="p">.</span><span class="n">parameters</span><span class="p">():</span>
<span class="n">param</span> <span class="o">-=</span> <span class="n">learning_rate</span> <span class="o">*</span> <span class="n">param</span><span class="p">.</span><span class="n">grad</span>
<span class="n">model</span><span class="p">.</span><span class="n">zero_grad</span><span class="p">()</span>
</code></pre></div></div>
<h3 id="pytorch-optim">PyTorch: optim</h3>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kn">import</span> <span class="nn">torch</span>
<span class="n">N</span><span class="p">,</span> <span class="n">D_in</span><span class="p">,</span> <span class="n">H</span><span class="p">,</span> <span class="n">D_out</span> <span class="o">=</span> <span class="mi">64</span><span class="p">,</span> <span class="mi">1000</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">10</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D_in</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D_out</span><span class="p">)</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">nn</span><span class="p">.</span><span class="n">Sequential</span><span class="p">(</span>
<span class="n">torch</span><span class="p">.</span><span class="n">nn</span><span class="p">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">D_in</span><span class="p">,</span> <span class="n">H</span><span class="p">),</span>
<span class="n">torch</span><span class="p">.</span><span class="n">nn</span><span class="p">.</span><span class="n">ReLU</span><span class="p">(),</span>
<span class="n">torch</span><span class="p">.</span><span class="n">nn</span><span class="p">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">H</span><span class="p">,</span> <span class="n">D_out</span><span class="p">))</span>
<span class="n">learning_rate</span> <span class="o">=</span> <span class="mf">1e-4</span>
<span class="n">optimizer</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">optim</span><span class="p">.</span><span class="n">Adam</span><span class="p">(</span><span class="n">model</span><span class="p">.</span><span class="n">parameters</span><span class="p">(),</span>
<span class="n">lr</span><span class="o">=</span><span class="n">learning_rate</span><span class="p">)</span> <span class="c1"># different update rules
</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">500</span><span class="p">):</span>
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">model</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">loss</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">nn</span><span class="p">.</span><span class="n">functional</span><span class="p">.</span><span class="n">mse_loss</span><span class="p">(</span><span class="n">y_pred</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">loss</span><span class="p">.</span><span class="n">backward</span><span class="p">()</span>
<span class="n">optimizer</span><span class="p">.</span><span class="n">step</span><span class="p">()</span>
<span class="n">optimizer</span><span class="p">.</span><span class="n">zero_grad</span><span class="p">()</span>
</code></pre></div></div>
<h3 id="pytorch-define-new-modules">PyTorch: Define new Modules</h3>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kn">import</span> <span class="nn">torch</span>
<span class="k">class</span> <span class="nc">TwoLayerNet</span><span class="p">(</span><span class="n">torch</span><span class="p">.</span><span class="n">nn</span><span class="p">.</span><span class="n">Module</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">D_in</span><span class="p">,</span> <span class="n">H</span><span class="p">,</span> <span class="n">D_out</span><span class="p">):</span> <span class="c1"># init sets up two children
</span> <span class="nb">super</span><span class="p">(</span><span class="n">TwoLayerNet</span><span class="p">,</span> <span class="bp">self</span><span class="p">).</span><span class="n">__init__</span><span class="p">()</span>
<span class="bp">self</span><span class="p">.</span><span class="n">linear1</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">nn</span><span class="p">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">D_in</span><span class="p">,</span> <span class="n">H</span><span class="p">)</span>
<span class="bp">self</span><span class="p">.</span><span class="n">linear2</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">nn</span><span class="p">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">H</span><span class="p">,</span> <span class="n">D_out</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
<span class="n">h_relu</span> <span class="o">=</span> <span class="bp">self</span><span class="p">.</span><span class="n">linear1</span><span class="p">(</span><span class="n">x</span><span class="p">).</span><span class="n">clamp</span><span class="p">(</span><span class="nb">min</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">y_pred</span> <span class="o">=</span> <span class="bp">self</span><span class="p">.</span><span class="n">linear2</span><span class="p">(</span><span class="n">h_relu</span><span class="p">)</span>
<span class="k">return</span> <span class="n">y_pred</span>
<span class="n">N</span><span class="p">,</span> <span class="n">D_in</span><span class="p">,</span> <span class="n">H</span><span class="p">,</span> <span class="n">D_out</span> <span class="o">=</span> <span class="mi">64</span><span class="p">,</span> <span class="mi">1000</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">10</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D_in</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D_out</span><span class="p">)</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">TwoLayerNet</span><span class="p">(</span><span class="n">D_in</span><span class="p">,</span> <span class="n">H</span><span class="p">,</span> <span class="n">D_out</span><span class="p">)</span>
<span class="n">optimizer</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">optim</span><span class="p">.</span><span class="n">SGD</span><span class="p">(</span><span class="n">model</span><span class="p">.</span><span class="n">parameters</span><span class="p">(),</span> <span class="n">lr</span><span class="o">=</span><span class="mf">1e-4</span><span class="p">)</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">500</span><span class="p">):</span>
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">model</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">loss</span> <span class="o">=</span> <span class="n">torch</span><span class="p">.</span><span class="n">nn</span><span class="p">.</span><span class="n">functional</span><span class="p">.</span><span class="n">mse_loss</span><span class="p">(</span><span class="n">y_pred</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">loss</span><span class="p">.</span><span class="n">backward</span><span class="p">()</span>
<span class="n">optimizer</span><span class="p">.</span><span class="n">step</span><span class="p">()</span>
<span class="n">optimizer</span><span class="p">.</span><span class="n">zero_grad</span><span class="p">()</span>
</code></pre></div></div>
<h3 id="pytorch-pretrained-models">PyTorch: Pretrained Models</h3>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kn">import</span> <span class="nn">torch</span>
<span class="kn">import</span> <span class="nn">torchvision</span>
<span class="n">alexnet</span> <span class="o">=</span> <span class="n">torchvision</span><span class="p">.</span><span class="n">models</span><span class="p">.</span><span class="n">alexnet</span><span class="p">(</span><span class="n">pretrained</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
<span class="n">vgg16</span> <span class="o">=</span> <span class="n">torchvision</span><span class="p">.</span><span class="n">models</span><span class="p">.</span><span class="n">vgg16</span><span class="p">(</span><span class="n">pretrained</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
<span class="n">resnet101</span> <span class="o">=</span> <span class="n">torchvision</span><span class="p">.</span><span class="n">models</span><span class="p">.</span><span class="n">resnet101</span><span class="p">(</span><span class="n">pretrained</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
</code></pre></div></div>
<h3 id="tensorflow-24">TensorFlow 2.4</h3>
<ul>
<li>Default dynamic graph, optionally static.</li>
</ul>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="n">np</span>
<span class="kn">import</span> <span class="nn">tensorflow</span> <span class="k">as</span> <span class="n">tf</span>
<span class="n">N</span><span class="p">,</span> <span class="n">D</span><span class="p">,</span> <span class="n">H</span> <span class="o">=</span> <span class="mi">64</span><span class="p">,</span> <span class="mi">1000</span><span class="p">,</span> <span class="mi">100</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">convert_to_tensor</span><span class="p">(</span><span class="n">np</span><span class="p">.</span><span class="n">random</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D</span><span class="p">),</span> <span class="n">np</span><span class="p">.</span><span class="n">float32</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">convert_to_tensor</span><span class="p">(</span><span class="n">np</span><span class="p">.</span><span class="n">random</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D</span><span class="p">),</span> <span class="n">np</span><span class="p">.</span><span class="n">float32</span><span class="p">)</span>
<span class="n">w1</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">tf</span><span class="p">.</span><span class="n">random</span><span class="p">.</span><span class="n">uniform</span><span class="p">((</span><span class="n">D</span><span class="p">,</span> <span class="n">H</span><span class="p">)))</span> <span class="c1"># weights
</span><span class="n">w2</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">tf</span><span class="p">.</span><span class="n">random</span><span class="p">.</span><span class="n">uniform</span><span class="p">((</span><span class="n">H</span><span class="p">,</span> <span class="n">D</span><span class="p">)))</span> <span class="c1"># weights
</span>
<span class="n">learning_rate</span> <span class="o">=</span> <span class="mf">1e-6</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">50</span><span class="p">):</span>
<span class="k">with</span> <span class="n">tf</span><span class="p">.</span><span class="n">GradientTape</span><span class="p">()</span> <span class="k">as</span> <span class="n">tape</span><span class="p">:</span> <span class="c1"># build dynamic graph
</span> <span class="n">h</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">maximum</span><span class="p">(</span><span class="n">tf</span><span class="p">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">w1</span><span class="p">),</span> <span class="mi">0</span><span class="p">)</span> <span class="c1"># forward pass
</span> <span class="n">y_pred</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">h</span><span class="p">,</span> <span class="n">w2</span><span class="p">)</span>
<span class="n">diff</span> <span class="o">=</span> <span class="n">y_pred</span> <span class="o">-</span> <span class="n">y</span>
<span class="n">loss</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">reduce_mean</span><span class="p">(</span><span class="n">tf</span><span class="p">.</span><span class="n">reduce_sum</span><span class="p">(</span><span class="n">diff</span> <span class="o">**</span> <span class="mi">2</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">))</span>
<span class="n">gradients</span> <span class="o">=</span> <span class="n">tape</span><span class="p">.</span><span class="n">gradient</span><span class="p">(</span><span class="n">loss</span><span class="p">,</span> <span class="p">[</span><span class="n">w1</span><span class="p">,</span> <span class="n">w2</span><span class="p">])</span> <span class="c1"># backward pass
</span> <span class="n">w1</span><span class="p">.</span><span class="n">assign</span><span class="p">(</span><span class="n">w1</span> <span class="o">-</span> <span class="n">learning_rate</span> <span class="o">*</span> <span class="n">gradients</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="c1"># gradient descent
</span> <span class="n">w2</span><span class="p">.</span><span class="n">assign</span><span class="p">(</span><span class="n">w2</span> <span class="o">-</span> <span class="n">learning_rate</span> <span class="o">*</span> <span class="n">gradients</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
</code></pre></div></div>
<h3 id="keras-high-level-wrapper">Keras: High-level Wrapper</h3>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="n">np</span>
<span class="kn">import</span> <span class="nn">tensorflow</span> <span class="k">as</span> <span class="n">tf</span>
<span class="n">N</span><span class="p">,</span> <span class="n">D</span><span class="p">,</span> <span class="n">H</span> <span class="o">=</span> <span class="mi">64</span><span class="p">,</span> <span class="mi">1000</span><span class="p">,</span> <span class="mi">100</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">convert_to_tensor</span><span class="p">(</span><span class="n">np</span><span class="p">.</span><span class="n">random</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D</span><span class="p">),</span> <span class="n">np</span><span class="p">.</span><span class="n">float32</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">convert_to_tensor</span><span class="p">(</span><span class="n">np</span><span class="p">.</span><span class="n">random</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D</span><span class="p">),</span> <span class="n">np</span><span class="p">.</span><span class="n">float32</span><span class="p">)</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">keras</span><span class="p">.</span><span class="n">Sequential</span><span class="p">()</span>
<span class="n">model</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">tf</span><span class="p">.</span><span class="n">keras</span><span class="p">.</span><span class="n">layers</span><span class="p">.</span><span class="n">Dense</span><span class="p">(</span><span class="n">H</span><span class="p">,</span> <span class="n">input_shape</span><span class="o">=</span><span class="p">(</span><span class="n">D</span><span class="p">,),</span>
<span class="n">activation</span><span class="o">=</span><span class="n">tf</span><span class="p">.</span><span class="n">nn</span><span class="p">.</span><span class="n">relu</span><span class="p">))</span>
<span class="n">model</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">tf</span><span class="p">.</span><span class="n">keras</span><span class="p">.</span><span class="n">layers</span><span class="p">.</span><span class="n">Dense</span><span class="p">(</span><span class="n">D</span><span class="p">))</span>
<span class="n">optimizer</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">optimizers</span><span class="p">.</span><span class="n">SGD</span><span class="p">(</span><span class="mf">1e-1</span><span class="p">)</span>
<span class="n">losses</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">50</span><span class="p">):</span>
<span class="k">with</span> <span class="n">tf</span><span class="p">.</span><span class="n">GradientTape</span><span class="p">()</span> <span class="k">as</span> <span class="n">tape</span><span class="p">:</span>
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">model</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">loss</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">losses</span><span class="p">.</span><span class="n">MeanSquaredError</span><span class="p">()(</span><span class="n">y_pred</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">gradients</span> <span class="o">=</span> <span class="n">tape</span><span class="p">.</span><span class="n">gradient</span><span class="p">(</span>
<span class="n">loss</span><span class="p">,</span> <span class="n">model</span><span class="p">.</span><span class="n">trainable_variables</span><span class="p">)</span>
<span class="n">optimizer</span><span class="p">.</span><span class="n">apply_gradients</span><span class="p">(</span>
<span class="nb">zip</span><span class="p">(</span><span class="n">gradients</span><span class="p">,</span> <span class="n">model</span><span class="p">.</span><span class="n">trainable_variables</span><span class="p">))</span>
</code></pre></div></div>
<ul>
<li>
<p>We can make use of different update rules with <code class="language-plaintext highlighter-rouge">tf.optimizers.{}</code> and predefined loss functions as well.</p>
</li>
<li>
<p>Keras can handle the training loop;</p>
</li>
</ul>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">N</span><span class="p">,</span> <span class="n">D</span><span class="p">,</span> <span class="n">H</span> <span class="o">=</span> <span class="mi">64</span><span class="p">,</span> <span class="mi">1000</span><span class="p">,</span> <span class="mi">100</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">convert_to_tensor</span><span class="p">(</span><span class="n">np</span><span class="p">.</span><span class="n">random</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D</span><span class="p">),</span> <span class="n">np</span><span class="p">.</span><span class="n">float32</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">convert_to_tensor</span><span class="p">(</span><span class="n">np</span><span class="p">.</span><span class="n">random</span><span class="p">.</span><span class="n">randn</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D</span><span class="p">),</span> <span class="n">np</span><span class="p">.</span><span class="n">float32</span><span class="p">)</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">keras</span><span class="p">.</span><span class="n">Sequential</span><span class="p">()</span>
<span class="n">model</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">tf</span><span class="p">.</span><span class="n">keras</span><span class="p">.</span><span class="n">layers</span><span class="p">.</span><span class="n">Dense</span><span class="p">(</span><span class="n">H</span><span class="p">,</span> <span class="n">input_shape</span><span class="o">=</span><span class="p">(</span><span class="n">D</span><span class="p">,),</span>
<span class="n">activation</span><span class="o">=</span><span class="n">tf</span><span class="p">.</span><span class="n">nn</span><span class="p">.</span><span class="n">relu</span><span class="p">))</span>
<span class="n">model</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">tf</span><span class="p">.</span><span class="n">keras</span><span class="p">.</span><span class="n">layers</span><span class="p">.</span><span class="n">Dense</span><span class="p">(</span><span class="n">D</span><span class="p">))</span>
<span class="n">optimizer</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">optimizers</span><span class="p">.</span><span class="n">SGD</span><span class="p">(</span><span class="mf">1e-1</span><span class="p">)</span>
<span class="n">model</span><span class="p">.</span><span class="nb">compile</span><span class="p">(</span><span class="n">loss</span><span class="o">=</span><span class="n">tf</span><span class="p">.</span><span class="n">keras</span><span class="p">.</span><span class="n">losses</span><span class="p">.</span><span class="n">MeanSquaredError</span><span class="p">(),</span>
<span class="n">optimizer</span><span class="o">=</span><span class="n">optimizer</span><span class="p">)</span>
<span class="n">history</span> <span class="o">=</span> <span class="n">model</span><span class="p">.</span><span class="n">fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">epochs</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">batch_size</span><span class="o">=</span><span class="n">N</span><span class="p">)</span>
</code></pre></div></div>
<h3 id="tensorflow-compile-static-graph">TensorFlow: compile static graph</h3>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="p">...</span>
<span class="n">model</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">tf</span><span class="p">.</span><span class="n">keras</span><span class="p">.</span><span class="n">layers</span><span class="p">.</span><span class="n">Dense</span><span class="p">(</span><span class="n">D</span><span class="p">))</span>
<span class="n">optimizer</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">optimizers</span><span class="p">.</span><span class="n">SGD</span><span class="p">(</span><span class="mf">1e-1</span><span class="p">)</span>
<span class="o">@</span><span class="n">tf</span><span class="p">.</span><span class="n">function</span>
<span class="k">def</span> <span class="nf">model_func</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">model</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">loss</span> <span class="o">=</span> <span class="n">tf</span><span class="p">.</span><span class="n">losses</span><span class="p">.</span><span class="n">MeanSquaredError</span><span class="p">()(</span><span class="n">y_pred</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="k">return</span> <span class="n">y_pred</span><span class="p">,</span> <span class="n">loss</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">50</span><span class="p">):</span>
<span class="p">...</span>
</code></pre></div></div>
<ul>
<li><code class="language-plaintext highlighter-rouge">@tf.function</code> decorator (implicitly) compiles python functions to static graph for better performance.</li>
</ul>
<h3 id="dynamic-vs-static">Dynamic vs. Static</h3>
<ul>
<li>
<p>Dynamic Computation Graphs:
Building the graph and computing the graph happen at the same time.<br />
Graph building and execution are intertwined, so always need to keep code around<br />
Inefficient, especially if we are building the same graph over and over again.</p>
</li>
<li>
<p>Static Computation Graphs:<br />
Build computational graph describing our computation(including finding paths for backprop)<br />
Reuse the same graph on every iteration<br />
Once graph is built, can serialize it and run it without the code that built the graph<br />
Framework can optimize the graph before it runs</p>
</li>
</ul>
<h3 id="pytorch-vs-tensorflow">PyTorch vs. TensorFlow</h3>
<ul>
<li>
<p>PyTorch<br />
Dynamic Graphs as default set<br />
Static: ONNX, TorchScript</p>
</li>
<li>
<p>TensorFlow<br />
Dynamic: Eager set<br />
Static: <code class="language-plaintext highlighter-rouge">@tf.function</code></p>
</li>
</ul>
<h3 id="model-parallel-vs-data-parallel">Model Parallel vs. Data Parallel</h3>
<ul>
<li>
<p>Model parallelism:<br />
split computation graph into parts and distribute to GPUs/nodes</p>
</li>
<li>
<p>Data parallelism:<br />
split minibatch into chunks and distribute to GPUs/ nodes<br />
PyTorch: <code class="language-plaintext highlighter-rouge">nn.DataParallel</code>, <code class="language-plaintext highlighter-rouge">nn.DistributedDataParallel</code><br />
TensorFlow: <code class="language-plaintext highlighter-rouge">tf.distributed.Strategy</code></p>
</li>
</ul>
</div>
</section>
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<div class="floating-header-title">cs231n - Lecture 6. Hardware and Software</div>
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