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<h1>Multi-Headed Attention (MHA)</h1>
<p>This is a tutorial/implementation of multi-headed attention from paper <a href="https://papers.labml.ai/paper/1706.03762">Attention Is All You Need</a> in <a href="https://pytorch.org/">PyTorch</a>. The implementation is inspired from <a href="https://nlp.seas.harvard.edu/2018/04/03/attention.html">Annotated Transformer</a>.</p>
<p>Here is the <a href="basic/autoregressive_experiment.html">training code</a> that uses a basic transformer with MHA for NLP auto-regression.</p>
<p><a href="basic/autoregressive_experiment.html">Here is an experiment implementation</a> that trains a simple transformer.</p>
<p><a href="https://colab.research.google.com/github/labmlai/annotated_deep_learning_paper_implementations/blob/master/labml_nn/transformers/basic/autoregressive_experiment.ipynb"><img alt="Open In Colab" src="https://colab.research.google.com/assets/colab-badge.svg"></a></p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">24</span><span></span><span class="kn">import</span> <span class="nn">math</span>
<span class="lineno">25</span><span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Optional</span><span class="p">,</span> <span class="n">List</span>
<span class="lineno">26</span>
<span class="lineno">27</span><span class="kn">import</span> <span class="nn">torch</span>
<span class="lineno">28</span><span class="kn">from</span> <span class="nn">torch</span> <span class="kn">import</span> <span class="n">nn</span> <span class="k">as</span> <span class="n">nn</span>
<span class="lineno">29</span>
<span class="lineno">30</span><span class="kn">from</span> <span class="nn">labml</span> <span class="kn">import</span> <span class="n">tracker</span>
<span class="lineno">31</span><span class="kn">from</span> <span class="nn">labml_helpers.module</span> <span class="kn">import</span> <span class="n">Module</span></pre></div>
</div>
</div>
<div class='section' id='section-1'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-1'>#</a>
</div>
<p> <a id="PrepareMHA"></a></p>
<h2>Prepare for multi-head attention</h2>
<p>This module does a linear transformation and splits the vector into given number of heads for multi-head attention. This is used to transform <strong>key</strong>, <strong>query</strong>, and <strong>value</strong> vectors.</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">34</span><span class="k">class</span> <span class="nc">PrepareForMultiHeadAttention</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-2'>
<div class='docs'>
<div class='section-link'>
<a href='#section-2'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">45</span> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">d_model</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">heads</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">d_k</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">bias</span><span class="p">:</span> <span class="nb">bool</span><span class="p">):</span>
<span class="lineno">46</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span></pre></div>
</div>
</div>
<div class='section' id='section-3'>
<div class='docs'>
<div class='section-link'>
<a href='#section-3'>#</a>
</div>
<p>Linear layer for linear transform </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">48</span> <span class="bp">self</span><span class="o">.</span><span class="n">linear</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">d_model</span><span class="p">,</span> <span class="n">heads</span> <span class="o">*</span> <span class="n">d_k</span><span class="p">,</span> <span class="n">bias</span><span class="o">=</span><span class="n">bias</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-4'>
<div class='docs'>
<div class='section-link'>
<a href='#section-4'>#</a>
</div>
<p>Number of heads </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">50</span> <span class="bp">self</span><span class="o">.</span><span class="n">heads</span> <span class="o">=</span> <span class="n">heads</span></pre></div>
</div>
</div>
<div class='section' id='section-5'>
<div class='docs'>
<div class='section-link'>
<a href='#section-5'>#</a>
</div>
<p>Number of dimensions in vectors in each head </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">52</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_k</span> <span class="o">=</span> <span class="n">d_k</span></pre></div>
</div>
</div>
<div class='section' id='section-6'>
<div class='docs'>
<div class='section-link'>
<a href='#section-6'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">54</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">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-7'>
<div class='docs'>
<div class='section-link'>
<a href='#section-7'>#</a>
</div>
<p>Input has shape <code class="highlight"><span></span><span class="p">[</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">d_model</span><span class="p">]</span></code>
or <code class="highlight"><span></span><span class="p">[</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">d_model</span><span class="p">]</span></code>
. We apply the linear transformation to the last dimension and split that into the heads. </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">58</span> <span class="n">head_shape</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span></pre></div>
</div>
</div>
<div class='section' id='section-8'>
<div class='docs'>
<div class='section-link'>
<a href='#section-8'>#</a>
</div>
<p>Linear transform </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">61</span> <span class="n">x</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">linear</span><span class="p">(</span><span class="n">x</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-9'>
<div class='docs'>
<div class='section-link'>
<a href='#section-9'>#</a>
</div>
<p>Split last dimension into heads </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">64</span> <span class="n">x</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="o">*</span><span class="n">head_shape</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">heads</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_k</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-10'>
<div class='docs'>
<div class='section-link'>
<a href='#section-10'>#</a>
</div>
<p>Output has shape <code class="highlight"><span></span><span class="p">[</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">heads</span><span class="p">,</span> <span class="n">d_k</span><span class="p">]</span></code>
or <code class="highlight"><span></span><span class="p">[</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">d_model</span><span class="p">]</span></code>
</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">67</span> <span class="k">return</span> <span class="n">x</span></pre></div>
</div>
</div>
<div class='section' id='section-11'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-11'>#</a>
</div>
<p> <a id="MHA"></a></p>
<h2>Multi-Head Attention Module</h2>
<p>This computes scaled multi-headed attention for given <code class="highlight"><span></span><span class="n">query</span></code>
, <code class="highlight"><span></span><span class="n">key</span></code>
and <code class="highlight"><span></span><span class="n">value</span></code>
vectors.</p>
<p><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop"><span class="mord mathnormal">A</span><span class="mord mathnormal">tt</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">o</span><span class="mord mathnormal">n</span></span><span class="mopen">(</span><span class="mord mathnormal">Q</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">K</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em;"></span><span class="mord"><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6944399999999998em;"><span style="top:-2.20556em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">se</span><span class="mord mathnormal mtight" style="margin-right:0.03588em;">q</span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop"><span class="mop"><span class="mord coloredeq eqh" style=""><span class="mord mathnormal" style="">so</span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mord mathnormal" style="">t</span><span class="mord mathnormal" style="">ma</span><span class="mord mathnormal" style="">x</span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.030548em;"><span></span></span></span></span></span></span><span class="mord"><span class="delimsizing size4">(</span></span><span class="mord coloredeq eqe" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5261079999999998em;"><span style="top:-2.25278em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord sqrt" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.85722em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em"><span class="mord coloredeq eqi" style=""><span class="mord" style=""><span class="mord mathnormal" style="">d</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-2.81722em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
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<p>In simple terms, it finds keys that matches the query, and gets the values of those keys.</p>
<p>It uses dot-product of query and key as the indicator of how matching they are. Before taking the <span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqh" style=""><span class="mord mathnormal" style="">so</span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mord mathnormal" style="">t</span><span class="mord mathnormal" style="">ma</span><span class="mord mathnormal" style="">x</span></span></span></span></span> the dot-products are scaled by <span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.383108em;vertical-align:-0.538em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.5864385em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8622307142857143em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight coloredeq eqi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="">d</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-2.8222307142857144em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
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s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.17776928571428574em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqj" style=""><span class="mord mtight" style="">1</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.538em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>. This is done to avoid large dot-product values causing softmax to give very small gradients when <span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqi" style=""><span class="mord" style=""><span class="mord mathnormal" style="">d</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span> is large.</p>
<p>Softmax is calculated along the axis of of the sequence (or time).</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">70</span><span class="k">class</span> <span class="nc">MultiHeadAttention</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-12'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-12'>#</a>
</div>
<ul><li><code class="highlight"><span></span><span class="n">heads</span></code>
is the number of heads. </li>
<li><code class="highlight"><span></span><span class="n">d_model</span></code>
is the number of features in the <code class="highlight"><span></span><span class="n">query</span></code>
, <code class="highlight"><span></span><span class="n">key</span></code>
and <code class="highlight"><span></span><span class="n">value</span></code>
vectors.</li></ul>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">91</span> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">heads</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">d_model</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">dropout_prob</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.1</span><span class="p">,</span> <span class="n">bias</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-13'>
<div class='docs'>
<div class='section-link'>
<a href='#section-13'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">97</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span></pre></div>
</div>
</div>
<div class='section' id='section-14'>
<div class='docs'>
<div class='section-link'>
<a href='#section-14'>#</a>
</div>
<p>Number of features per head </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">100</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_k</span> <span class="o">=</span> <span class="n">d_model</span> <span class="o">//</span> <span class="n">heads</span></pre></div>
</div>
</div>
<div class='section' id='section-15'>
<div class='docs'>
<div class='section-link'>
<a href='#section-15'>#</a>
</div>
<p>Number of heads </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">102</span> <span class="bp">self</span><span class="o">.</span><span class="n">heads</span> <span class="o">=</span> <span class="n">heads</span></pre></div>
</div>
</div>
<div class='section' id='section-16'>
<div class='docs'>
<div class='section-link'>
<a href='#section-16'>#</a>
</div>
<p>These transform the <code class="highlight"><span></span><span class="n">query</span></code>
, <code class="highlight"><span></span><span class="n">key</span></code>
and <code class="highlight"><span></span><span class="n">value</span></code>
vectors for multi-headed attention. </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">105</span> <span class="bp">self</span><span class="o">.</span><span class="n">query</span> <span class="o">=</span> <span class="n">PrepareForMultiHeadAttention</span><span class="p">(</span><span class="n">d_model</span><span class="p">,</span> <span class="n">heads</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_k</span><span class="p">,</span> <span class="n">bias</span><span class="o">=</span><span class="n">bias</span><span class="p">)</span>
<span class="lineno">106</span> <span class="bp">self</span><span class="o">.</span><span class="n">key</span> <span class="o">=</span> <span class="n">PrepareForMultiHeadAttention</span><span class="p">(</span><span class="n">d_model</span><span class="p">,</span> <span class="n">heads</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_k</span><span class="p">,</span> <span class="n">bias</span><span class="o">=</span><span class="n">bias</span><span class="p">)</span>
<span class="lineno">107</span> <span class="bp">self</span><span class="o">.</span><span class="n">value</span> <span class="o">=</span> <span class="n">PrepareForMultiHeadAttention</span><span class="p">(</span><span class="n">d_model</span><span class="p">,</span> <span class="n">heads</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_k</span><span class="p">,</span> <span class="n">bias</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-17'>
<div class='docs'>
<div class='section-link'>
<a href='#section-17'>#</a>
</div>
<p>Softmax for attention along the time dimension of <code class="highlight"><span></span><span class="n">key</span></code>
</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">110</span> <span class="bp">self</span><span class="o">.</span><span class="n">softmax</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">dim</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-18'>
<div class='docs'>
<div class='section-link'>
<a href='#section-18'>#</a>
</div>
<p>Output layer </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">113</span> <span class="bp">self</span><span class="o">.</span><span class="n">output</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">d_model</span><span class="p">,</span> <span class="n">d_model</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-19'>
<div class='docs'>
<div class='section-link'>
<a href='#section-19'>#</a>
</div>
<p>Dropout </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">115</span> <span class="bp">self</span><span class="o">.</span><span class="n">dropout</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">dropout_prob</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-20'>
<div class='docs'>
<div class='section-link'>
<a href='#section-20'>#</a>
</div>
<p>Scaling factor before the softmax </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">117</span> <span class="bp">self</span><span class="o">.</span><span class="n">scale</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">d_k</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-21'>
<div class='docs'>
<div class='section-link'>
<a href='#section-21'>#</a>
</div>
<p>We store attentions so that it can be used for logging, or other computations if needed </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">120</span> <span class="bp">self</span><span class="o">.</span><span class="n">attn</span> <span class="o">=</span> <span class="kc">None</span></pre></div>
</div>
</div>
<div class='section' id='section-22'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-22'>#</a>
</div>
<h3>Calculate scores between queries and keys</h3>
<p>This method can be overridden for other variations like relative attention.</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">122</span> <span class="k">def</span> <span class="nf">get_scores</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">query</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-23'>
<div class='docs'>
<div class='section-link'>
<a href='#section-23'>#</a>
</div>
<p>Calculate <span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.043548em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqg" style=""><span class="mord mathnormal" style="">Q</span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">⊤</span></span></span></span></span></span></span></span></span></span></span></span> or <span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.05764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">ijbh</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.0497100000000001em;vertical-align:-0.29971000000000003em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1863979999999999em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">ibh</span><span class="mord mathnormal mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">jbh</span><span class="mord mathnormal mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span> </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">130</span> <span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="s1">&#39;ibhd,jbhd-&gt;ijbh&#39;</span><span class="p">,</span> <span class="n">query</span><span class="p">,</span> <span class="n">key</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-24'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-24'>#</a>
</div>
<p> <code class="highlight"><span></span><span class="n">mask</span></code>
has shape <code class="highlight"><span></span><span class="p">[</span><span class="n">seq_len_q</span><span class="p">,</span> <span class="n">seq_len_k</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">]</span></code>
, where first dimension is the query dimension. If the query dimension is equal to <span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord coloredeq eqj" style=""><span class="mord" style="">1</span></span></span></span></span> it will be broadcasted.</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">132</span> <span class="k">def</span> <span class="nf">prepare_mask</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">mask</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span> <span class="n">query_shape</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">key_shape</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span></pre></div>
</div>
</div>
<div class='section' id='section-25'>
<div class='docs'>
<div class='section-link'>
<a href='#section-25'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">138</span> <span class="k">assert</span> <span class="n">mask</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">mask</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="n">query_shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="lineno">139</span> <span class="k">assert</span> <span class="n">mask</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">key_shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="lineno">140</span> <span class="k">assert</span> <span class="n">mask</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">mask</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">==</span> <span class="n">query_shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span></pre></div>
</div>
</div>
<div class='section' id='section-26'>
<div class='docs'>
<div class='section-link'>
<a href='#section-26'>#</a>
</div>
<p>Same mask applied to all heads. </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">143</span> <span class="n">mask</span> <span class="o">=</span> <span class="n">mask</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-27'>
<div class='docs'>
<div class='section-link'>
<a href='#section-27'>#</a>
</div>
<p>resulting mask has shape <code class="highlight"><span></span><span class="p">[</span><span class="n">seq_len_q</span><span class="p">,</span> <span class="n">seq_len_k</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">heads</span><span class="p">]</span></code>
</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">146</span> <span class="k">return</span> <span class="n">mask</span></pre></div>
</div>
</div>
<div class='section' id='section-28'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-28'>#</a>
</div>
<p> <code class="highlight"><span></span><span class="n">query</span></code>
, <code class="highlight"><span></span><span class="n">key</span></code>
and <code class="highlight"><span></span><span class="n">value</span></code>
are the tensors that store collection of <em>query</em>, <em>key</em> and <em>value</em> vectors. They have shape <code class="highlight"><span></span><span class="p">[</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">d_model</span><span class="p">]</span></code>
.</p>
<p><code class="highlight"><span></span><span class="n">mask</span></code>
has shape <code class="highlight"><span></span><span class="p">[</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">]</span></code>
and <code class="highlight"><span></span><span class="n">mask</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">,</span> <span class="n">b</span><span class="p">]</span></code>
indicates whether for batch <code class="highlight"><span></span><span class="n">b</span></code>
, query at position <code class="highlight"><span></span><span class="n">i</span></code>
has access to key-value at position <code class="highlight"><span></span><span class="n">j</span></code>
.</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">148</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="o">*</span><span class="p">,</span>
<span class="lineno">149</span> <span class="n">query</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span>
<span class="lineno">150</span> <span class="n">key</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span>
<span class="lineno">151</span> <span class="n">value</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span>
<span class="lineno">152</span> <span class="n">mask</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-29'>
<div class='docs'>
<div class='section-link'>
<a href='#section-29'>#</a>
</div>
<p><code class="highlight"><span></span><span class="n">query</span></code>
, <code class="highlight"><span></span><span class="n">key</span></code>
and <code class="highlight"><span></span><span class="n">value</span></code>
have shape <code class="highlight"><span></span><span class="p">[</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">d_model</span><span class="p">]</span></code>
</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">164</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">query</span><span class="o">.</span><span class="n">shape</span>
<span class="lineno">165</span>
<span class="lineno">166</span> <span class="k">if</span> <span class="n">mask</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="lineno">167</span> <span class="n">mask</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">prepare_mask</span><span class="p">(</span><span class="n">mask</span><span class="p">,</span> <span class="n">query</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">key</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-30'>
<div class='docs'>
<div class='section-link'>
<a href='#section-30'>#</a>
</div>
<p>Prepare <code class="highlight"><span></span><span class="n">query</span></code>
, <code class="highlight"><span></span><span class="n">key</span></code>
and <code class="highlight"><span></span><span class="n">value</span></code>
for attention computation. These will then have shape <code class="highlight"><span></span><span class="p">[</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">heads</span><span class="p">,</span> <span class="n">d_k</span><span class="p">]</span></code>
. </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">171</span> <span class="n">query</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">query</span><span class="p">(</span><span class="n">query</span><span class="p">)</span>
<span class="lineno">172</span> <span class="n">key</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">key</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
<span class="lineno">173</span> <span class="n">value</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">value</span><span class="p">(</span><span class="n">value</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-31'>
<div class='docs'>
<div class='section-link'>
<a href='#section-31'>#</a>
</div>
<p>Compute attention scores <span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.043548em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqg" style=""><span class="mord mathnormal" style="">Q</span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">⊤</span></span></span></span></span></span></span></span></span></span></span></span>. This gives a tensor of shape <code class="highlight"><span></span><span class="p">[</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">heads</span><span class="p">]</span></code>
. </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">177</span> <span class="n">scores</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_scores</span><span class="p">(</span><span class="n">query</span><span class="p">,</span> <span class="n">key</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-32'>
<div class='docs'>
<div class='section-link'>
<a href='#section-32'>#</a>
</div>
<p>Scale scores <span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.633028em;vertical-align:-0.538em;"></span><span class="mord coloredeq eqe" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.095028em;"><span style="top:-2.5864385em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord sqrt mtight" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8622307142857143em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em"><span class="mord mtight coloredeq eqi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="">d</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-2.8222307142857144em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
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c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
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l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.17776928571428574em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.446108em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqg" style=""><span class="mord mathnormal mtight" style="">Q</span><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9270285714285713em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style="">⊤</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.538em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">180</span> <span class="n">scores</span> <span class="o">*=</span> <span class="bp">self</span><span class="o">.</span><span class="n">scale</span></pre></div>
</div>
</div>
<div class='section' id='section-33'>
<div class='docs'>
<div class='section-link'>
<a href='#section-33'>#</a>
</div>
<p>Apply mask </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">183</span> <span class="k">if</span> <span class="n">mask</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="lineno">184</span> <span class="n">scores</span> <span class="o">=</span> <span class="n">scores</span><span class="o">.</span><span class="n">masked_fill</span><span class="p">(</span><span class="n">mask</span> <span class="o">==</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">float</span><span class="p">(</span><span class="s1">&#39;-inf&#39;</span><span class="p">))</span></pre></div>
</div>
</div>
<div class='section' id='section-34'>
<div class='docs'>
<div class='section-link'>
<a href='#section-34'>#</a>
</div>
<p><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqh" style=""><span class="mord mathnormal" style="">so</span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mord mathnormal" style="">t</span><span class="mord mathnormal" style="">ma</span><span class="mord mathnormal" style="">x</span></span></span></span></span> attention along the key sequence dimension <span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em;"></span><span class="mord coloredeq eqc" style=""><span class="mord" style=""><span class="mop op-limits" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6944399999999998em;"><span style="top:-2.20556em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="">se</span><span class="mord mathnormal mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop" style=""><span class="mord coloredeq eqh" style=""><span class="mord mathnormal" style="">so</span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mord mathnormal" style="">t</span><span class="mord mathnormal" style="">ma</span><span class="mord mathnormal" style="">x</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.030548em;"><span></span></span></span></span></span></span><span class="mord" style=""><span class="delimsizing size4" style=""><span style="">(</span></span></span><span class="mord coloredeq eqe" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.095028em;"><span style="top:-2.5864385em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord sqrt mtight" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8622307142857143em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em"><span class="mord mtight coloredeq eqi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="">d</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-2.8222307142857144em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
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c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.17776928571428574em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.446108em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqg" style=""><span class="mord mathnormal mtight" style="">Q</span><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9270285714285713em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style="">⊤</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.538em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mord" style=""><span class="delimsizing size4" style=""><span style="">)</span></span></span></span></span></span></span> </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">188</span> <span class="n">attn</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">softmax</span><span class="p">(</span><span class="n">scores</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-35'>
<div class='docs'>
<div class='section-link'>
<a href='#section-35'>#</a>
</div>
<p>Save attentions if debugging </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">191</span> <span class="n">tracker</span><span class="o">.</span><span class="n">debug</span><span class="p">(</span><span class="s1">&#39;attn&#39;</span><span class="p">,</span> <span class="n">attn</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-36'>
<div class='docs'>
<div class='section-link'>
<a href='#section-36'>#</a>
</div>
<p>Apply dropout </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">194</span> <span class="n">attn</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dropout</span><span class="p">(</span><span class="n">attn</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-37'>
<div class='docs'>
<div class='section-link'>
<a href='#section-37'>#</a>
</div>
<p>Multiply by values <span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em;"></span><span class="mord coloredeq eqc" style=""><span class="mord" style=""><span class="mop op-limits" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6944399999999998em;"><span style="top:-2.20556em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="">se</span><span class="mord mathnormal mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop" style=""><span class="mord coloredeq eqh" style=""><span class="mord mathnormal" style="">so</span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mord mathnormal" style="">t</span><span class="mord mathnormal" style="">ma</span><span class="mord mathnormal" style="">x</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.030548em;"><span></span></span></span></span></span></span><span class="mord" style=""><span class="delimsizing size4" style=""><span style="">(</span></span></span><span class="mord coloredeq eqe" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5261079999999998em;"><span style="top:-2.25278em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord sqrt" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.85722em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em"><span class="mord coloredeq eqi" style=""><span class="mord" style=""><span class="mord mathnormal" style="">d</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-2.81722em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.18278000000000005em;"><span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord coloredeq eqg" style=""><span class="mord mathnormal" style="">Q</span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">⊤</span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.93em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mord" style=""><span class="delimsizing size4" style=""><span style="">)</span></span></span></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span></span></span></span></span> </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">198</span> <span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="s2">&quot;ijbh,jbhd-&gt;ibhd&quot;</span><span class="p">,</span> <span class="n">attn</span><span class="p">,</span> <span class="n">value</span><span class="p">)</span></pre></div>
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</div>
<div class='section' id='section-38'>
<div class='docs'>
<div class='section-link'>
<a href='#section-38'>#</a>
</div>
<p>Save attentions for any other calculations </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">201</span> <span class="bp">self</span><span class="o">.</span><span class="n">attn</span> <span class="o">=</span> <span class="n">attn</span><span class="o">.</span><span class="n">detach</span><span class="p">()</span></pre></div>
</div>
</div>
<div class='section' id='section-39'>
<div class='docs'>
<div class='section-link'>
<a href='#section-39'>#</a>
</div>
<p>Concatenate multiple heads </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">204</span> <span class="n">x</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-40'>
<div class='docs'>
<div class='section-link'>
<a href='#section-40'>#</a>
</div>
<p>Output layer </p>
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<div class='code'>
<div class="highlight"><pre><span class="lineno">207</span> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">output</span><span class="p">(</span><span class="n">x</span><span class="p">)</span></pre></div>
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