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    <li>RNNOp design</li>
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  <div class="section" id="rnnop-design">
<span id="rnnop-design"></span><h1>RNNOp design<a class="headerlink" href="#rnnop-design" title="Permalink to this headline"></a></h1>
<p>This document is about an RNN operator which requires that instances in a mini-batch have the same length.  We will have a more flexible RNN operator.</p>
<div class="section" id="rnn-algorithm-implementation">
<span id="rnn-algorithm-implementation"></span><h2>RNN Algorithm Implementation<a class="headerlink" href="#rnn-algorithm-implementation" title="Permalink to this headline"></a></h2>
<p aligh="center">
<img src="./images/rnn.jpg"/>
</p><p>The above diagram shows an RNN unrolled into a full network.</p>
<p>There are several important concepts:</p>
<ul class="simple">
<li><em>step-net</em>: the sub-graph to run at each step,</li>
<li><em>memory</em>, $h_t$, the state of the current step,</li>
<li><em>ex-memory</em>, $h_{t-1}$, the state of the previous step,</li>
<li><em>initial memory value</em>, the ex-memory of the first step.</li>
</ul>
<div class="section" id="step-scope">
<span id="step-scope"></span><h3>Step-scope<a class="headerlink" href="#step-scope" title="Permalink to this headline"></a></h3>
<p>There could be local variables defined in step-nets.  PaddlePaddle runtime realizes these variables in <em>step-scopes</em> &#8211; scopes created for each step.</p>
<p aligh="center">
<img src="./images/rnn.png"/><br/>
Figure 2 the RNN's data flow
</p><p>Please be aware that all steps run the same step-net.  Each step</p>
<ol class="simple">
<li>creates the step-scope,</li>
<li>realizes local variables, including step-outputs, in the step-scope, and</li>
<li>runs the step-net, which could use these variables.</li>
</ol>
<p>The RNN operator will compose its output from step outputs in step scopes.</p>
</div>
<div class="section" id="memory-and-ex-memory">
<span id="memory-and-ex-memory"></span><h3>Memory and Ex-memory<a class="headerlink" href="#memory-and-ex-memory" title="Permalink to this headline"></a></h3>
<p>Let&#8217;s give more details about memory and ex-memory via a simply example:</p>
<p>$$
h_t = U h_{t-1} + W x_t
$$,</p>
<p>where $h_t$ and $h_{t-1}$ are the memory and ex-memory of step $t$&#8217;s respectively.</p>
<p>In the implementation, we can make an ex-memory variable either &#8220;refers to&#8221; the memory variable of the previous step,
or copy the value of the previous memory value to the current ex-memory variable.</p>
</div>
<div class="section" id="usage-in-python">
<span id="usage-in-python"></span><h3>Usage in Python<a class="headerlink" href="#usage-in-python" title="Permalink to this headline"></a></h3>
<p>For more information on Block, please refer to the <a class="reference external" href="https://github.com/PaddlePaddle/Paddle/blob/develop/doc/design/block.md">design doc</a>.</p>
<p>We can define an RNN&#8217;s step-net using Block:</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">paddle</span> <span class="kn">as</span> <span class="nn">pd</span>

<span class="n">X</span> <span class="o">=</span> <span class="n">some_op</span><span class="p">()</span> <span class="c1"># x is some operator&#39;s output, and is a LoDTensor</span>
<span class="n">a</span> <span class="o">=</span> <span class="n">some_op</span><span class="p">()</span>

<span class="c1"># declare parameters</span>
<span class="n">W</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">[</span><span class="mi">20</span><span class="p">,</span> <span class="mi">30</span><span class="p">])</span>
<span class="n">U</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">[</span><span class="mi">20</span><span class="p">,</span> <span class="mi">30</span><span class="p">])</span>

<span class="n">rnn</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">create_rnn_op</span><span class="p">(</span><span class="n">output_num</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="k">with</span> <span class="n">rnn</span><span class="o">.</span><span class="n">stepnet</span><span class="p">():</span>
    <span class="n">x</span> <span class="o">=</span> <span class="n">rnn</span><span class="o">.</span><span class="n">add_input</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
    <span class="c1"># declare a memory (rnn&#39;s step)</span>
    <span class="n">h</span> <span class="o">=</span> <span class="n">rnn</span><span class="o">.</span><span class="n">add_memory</span><span class="p">(</span><span class="n">init</span><span class="o">=</span><span class="n">a</span><span class="p">)</span>
    <span class="c1"># h.pre_state() means previous memory of rnn</span>
    <span class="n">new_state</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">add_two</span><span class="p">(</span> <span class="n">pd</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">W</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="o">+</span> <span class="n">pd</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">U</span><span class="p">,</span> <span class="n">h</span><span class="o">.</span><span class="n">pre_state</span><span class="p">()))</span>
    <span class="c1"># update current memory</span>
    <span class="n">h</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">new_state</span><span class="p">)</span>
    <span class="c1"># indicate that h variables in all step scopes should be merged</span>
    <span class="n">rnn</span><span class="o">.</span><span class="n">add_outputs</span><span class="p">(</span><span class="n">h</span><span class="p">)</span>

<span class="n">out</span> <span class="o">=</span> <span class="n">rnn</span><span class="p">()</span>
</pre></div>
</div>
<p>Python API functions in above example:</p>
<ul class="simple">
<li><code class="docutils literal"><span class="pre">rnn.add_input</span></code> indicates the parameter is a variable that will be segmented into step-inputs.</li>
<li><code class="docutils literal"><span class="pre">rnn.add_memory</span></code> creates a variable used as the memory.</li>
<li><code class="docutils literal"><span class="pre">rnn.add_outputs</span></code> mark the variables that will be concatenated across steps into the RNN output.</li>
</ul>
</div>
<div class="section" id="nested-rnn-and-lodtensor">
<span id="nested-rnn-and-lodtensor"></span><h3>Nested RNN and LoDTensor<a class="headerlink" href="#nested-rnn-and-lodtensor" title="Permalink to this headline"></a></h3>
<p>An RNN whose step-net includes other RNN operators is known as an <em>nested RNN</em>.</p>
<p>For example, we could have a 2-level RNN, where the top level corresponds to paragraphs, and the lower level corresponds to sentences.</p>
<p>The following figure illustrates the feeding of text into the lower level, one sentence each step, and the feeding of step outputs to the top level. The final top level output is about the whole text.</p>
<p aligh="center">
<img src="./images/2_level_rnn.png"/>
</p><div class="highlight-python"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">paddle</span> <span class="kn">as</span> <span class="nn">pd</span>

<span class="n">W</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">[</span><span class="mi">20</span><span class="p">,</span> <span class="mi">30</span><span class="p">])</span>
<span class="n">U</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">[</span><span class="mi">20</span><span class="p">,</span> <span class="mi">30</span><span class="p">])</span>

<span class="n">W0</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">[</span><span class="mi">20</span><span class="p">,</span> <span class="mi">30</span><span class="p">])</span>
<span class="n">U0</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">[</span><span class="mi">20</span><span class="p">,</span> <span class="mi">30</span><span class="p">])</span>

<span class="c1"># a is output of some op</span>
<span class="n">a</span> <span class="o">=</span> <span class="n">some_op</span><span class="p">()</span>

<span class="c1"># chapter_data is a set of 128-dim word vectors</span>
<span class="c1"># the first level of LoD is sentence</span>
<span class="c1"># the second level of LoD is chapter</span>
<span class="n">chapter_data</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">[</span><span class="bp">None</span><span class="p">,</span> <span class="mi">128</span><span class="p">],</span> <span class="nb">type</span><span class="o">=</span><span class="n">pd</span><span class="o">.</span><span class="n">lod_tensor</span><span class="p">,</span> <span class="n">level</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>

<span class="k">def</span> <span class="nf">lower_level_rnn</span><span class="p">(</span><span class="n">paragraph</span><span class="p">):</span>
    <span class="sd">&#39;&#39;&#39;</span>
<span class="sd">    x: the input</span>
<span class="sd">    &#39;&#39;&#39;</span>
    <span class="n">rnn</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">create_rnn_op</span><span class="p">(</span><span class="n">output_num</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
    <span class="k">with</span> <span class="n">rnn</span><span class="o">.</span><span class="n">stepnet</span><span class="p">():</span>
        <span class="n">sentence</span> <span class="o">=</span> <span class="n">rnn</span><span class="o">.</span><span class="n">add_input</span><span class="p">(</span><span class="n">paragraph</span><span class="p">,</span> <span class="n">level</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
        <span class="n">h</span> <span class="o">=</span> <span class="n">rnn</span><span class="o">.</span><span class="n">add_memory</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">[</span><span class="mi">20</span><span class="p">,</span> <span class="mi">30</span><span class="p">])</span>
        <span class="n">h</span><span class="o">.</span><span class="n">update</span><span class="p">(</span>
            <span class="n">pd</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">W</span><span class="p">,</span> <span class="n">sentence</span><span class="p">)</span> <span class="o">+</span> <span class="n">pd</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">U</span><span class="p">,</span> <span class="n">h</span><span class="o">.</span><span class="n">pre_state</span><span class="p">()))</span>
        <span class="c1"># get the last state as sentence&#39;s info</span>
        <span class="n">rnn</span><span class="o">.</span><span class="n">add_outputs</span><span class="p">(</span><span class="n">h</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">rnn</span>

<span class="n">top_level_rnn</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">create_rnn_op</span><span class="p">(</span><span class="n">output_num</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="k">with</span> <span class="n">top_level_rnn</span><span class="o">.</span><span class="n">stepnet</span><span class="p">():</span>
    <span class="n">paragraph_data</span> <span class="o">=</span> <span class="n">rnn</span><span class="o">.</span><span class="n">add_input</span><span class="p">(</span><span class="n">chapter_data</span><span class="p">,</span> <span class="n">level</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
    <span class="n">low_rnn</span> <span class="o">=</span> <span class="n">lower_level_rnn</span><span class="p">(</span><span class="n">paragraph_data</span><span class="p">)</span>
    <span class="n">paragraph_out</span> <span class="o">=</span> <span class="n">low_rnn</span><span class="p">()</span>

    <span class="n">h</span> <span class="o">=</span> <span class="n">rnn</span><span class="o">.</span><span class="n">add_memory</span><span class="p">(</span><span class="n">init</span><span class="o">=</span><span class="n">a</span><span class="p">)</span>
    <span class="n">h</span><span class="o">.</span><span class="n">update</span><span class="p">(</span>
        <span class="n">pd</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">W0</span><span class="p">,</span> <span class="n">paragraph_data</span><span class="p">)</span> <span class="o">+</span> <span class="n">pd</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">U0</span><span class="p">,</span> <span class="n">h</span><span class="o">.</span><span class="n">pre_state</span><span class="p">()))</span>
    <span class="n">top_level_rnn</span><span class="o">.</span><span class="n">add_outputs</span><span class="p">(</span><span class="n">h</span><span class="p">)</span>

<span class="c1"># just output the last step</span>
<span class="n">chapter_out</span> <span class="o">=</span> <span class="n">top_level_rnn</span><span class="p">(</span><span class="n">output_all_steps</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
</pre></div>
</div>
<p>in above example, the construction of the <code class="docutils literal"><span class="pre">top_level_rnn</span></code> calls  <code class="docutils literal"><span class="pre">lower_level_rnn</span></code>.  The input is a LoD Tensor. The top level RNN segments input text data into paragraphs, and the lower level RNN segments each paragraph into sentences.</p>
<p>By default, the <code class="docutils literal"><span class="pre">RNNOp</span></code> will concatenate the outputs from all the time steps,
if the <code class="docutils literal"><span class="pre">output_all_steps</span></code> set to False, it will only output the final time step.</p>
<p align="center">
<img src="images/rnn_2level_data.png"/>
</p></div>
</div>
</div>


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