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    <li>Design Doc: Computations as Graphs</li>
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  <div class="section" id="design-doc-computations-as-graphs">
<span id="design-doc-computations-as-graphs"></span><h1>Design Doc: Computations as Graphs<a class="headerlink" href="#design-doc-computations-as-graphs" title="Permalink to this headline"></a></h1>
<p>A primary goal of the refactorization of PaddlePaddle is a more flexible representation of deep learning computation, in particular, a graph of operators and variables, instead of sequences of layers as before.</p>
<p>This document explains that the construction of a graph as three steps:</p>
<ul class="simple">
<li>construct the forward part</li>
<li>construct the backward part</li>
<li>construct the optimization part</li>
</ul>
<p>Let us take the problem of image classification as a simple example.  The application program that trains the model looks like:</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">layer</span><span class="o">.</span><span class="n">data</span><span class="p">(</span><span class="s2">&quot;images&quot;</span><span class="p">)</span>
<span class="n">l</span> <span class="o">=</span> <span class="n">layer</span><span class="o">.</span><span class="n">data</span><span class="p">(</span><span class="s2">&quot;label&quot;</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">layer</span><span class="o">.</span><span class="n">fc</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">cost</span> <span class="o">=</span> <span class="n">layer</span><span class="o">.</span><span class="n">mse</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">l</span><span class="p">)</span>
<span class="n">optimize</span><span class="p">(</span><span class="n">cost</span><span class="p">)</span>
<span class="n">train</span><span class="p">(</span><span class="n">cost</span><span class="p">,</span> <span class="n">reader</span><span class="o">=</span><span class="n">mnist</span><span class="o">.</span><span class="n">train</span><span class="p">())</span>
</pre></div>
</div>
<div class="section" id="forward-part">
<span id="forward-part"></span><h2>Forward Part<a class="headerlink" href="#forward-part" title="Permalink to this headline"></a></h2>
<p>The first four lines of above program build the forward part of the graph.</p>
<p><img alt="" src="../_images/graph_construction_example_forward_only.png" /></p>
<p>In particular, the first line <code class="docutils literal"><span class="pre">x</span> <span class="pre">=</span> <span class="pre">layer.data(&quot;images&quot;)</span></code> creates variable x and a Feed operator that copies a column from the minibatch to x.  <code class="docutils literal"><span class="pre">y</span> <span class="pre">=</span> <span class="pre">layer.fc(x)</span></code> creates not only the FC operator and output variable y, but also two parameters, W and b.</p>
<p>In this example, all operators are created as <code class="docutils literal"><span class="pre">OpDesc</span></code> protobuf messages, and all variables are <code class="docutils literal"><span class="pre">VarDesc</span></code>.  These protobuf messages are saved in a <code class="docutils literal"><span class="pre">BlockDesc</span></code> protobuf message.</p>
</div>
<div class="section" id="backward-part">
<span id="backward-part"></span><h2>Backward Part<a class="headerlink" href="#backward-part" title="Permalink to this headline"></a></h2>
<p>The fifth line <code class="docutils literal"><span class="pre">optimize(cost)</span></code> calls two functions, <code class="docutils literal"><span class="pre">ConstructBackwardGraph</span></code> and <code class="docutils literal"><span class="pre">ConstructOptimizationGraph</span></code>.</p>
<p><code class="docutils literal"><span class="pre">ConstructBackwardGraph</span></code> traverses the forward graph in the <code class="docutils literal"><span class="pre">BlockDesc</span></code> protobuf message and builds the backward part.</p>
<p><img alt="" src="../_images/graph_construction_example_forward_backward.png" /></p>
<p>According to the chain rule of gradient computation, <code class="docutils literal"><span class="pre">ConstructBackwardGraph</span></code> would</p>
<ol class="simple">
<li>create a gradient operator G for each operator F,</li>
<li>make all inputs, outputs, and outputs&#8217; gradient of F as inputs of G,</li>
<li>create gradients for all inputs of F, except for those who don&#8217;t have gradients, like x and l, and</li>
<li>make all these gradients as outputs of G.</li>
</ol>
</div>
<div class="section" id="optimization-part">
<span id="optimization-part"></span><h2>Optimization Part<a class="headerlink" href="#optimization-part" title="Permalink to this headline"></a></h2>
<p>For each parameter, like W and b created by <code class="docutils literal"><span class="pre">layer.fc</span></code>, marked as double circles in above graphs, <code class="docutils literal"><span class="pre">ConstructOptimizationGraph</span></code> creates an optimization operator to apply its gradient.  Here results in the complete graph:</p>
<p><img alt="" src="../_images/graph_construction_example_all.png" /></p>
</div>
</div>


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