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Varuna Jayasiri
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<h2>Paper Implementations</h2>
<h4>✨ <a href="transformers/index.html">Transformers</a></h4>
<ul><li><a href="transformers/mha.html">Multi-headed attention</a> </li>
<li><a href="transformers/flash/index.html">Triton Flash Attention</a> </li>
<li><a href="transformers/models.html">Transformer building blocks</a> </li>
<li><a href="transformers/xl/index.html">Transformer XL</a> </li>
<li><a href="transformers/xl/relative_mha.html">Relative multi-headed attention</a> </li>

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</div>
</div>
<div class='section' id='section-0'>
<div class='docs'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-0'>#</a>
</div>
<h3>Test Flash Attention Implementation</h3>
<p>This is the code to test and measure performance of our flash attention implementation</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">1</span><span></span><span class="kn">import</span> <span class="nn">triton</span>
<span class="lineno">2</span>
<span class="lineno">3</span><span class="kn">import</span> <span class="nn">torch</span>
<span class="lineno">4</span><span class="kn">from</span> <span class="nn">labml</span> <span class="kn">import</span> <span class="n">logger</span><span class="p">,</span> <span class="n">monit</span>
<span class="lineno">5</span><span class="kn">from</span> <span class="nn">labml_nn.transformers.flash</span> <span class="kn">import</span> <span class="n">attention</span>
<span class="lineno">6</span>
<span class="lineno">7</span><span class="n">HI_PRES_TORCH</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">float32</span></pre></div>
<div class="highlight"><pre><span class="lineno">7</span><span></span><span class="kn">import</span> <span class="nn">torch</span>
<span class="lineno">8</span><span class="kn">import</span> <span class="nn">triton</span>
<span class="lineno">9</span>
<span class="lineno">10</span><span class="kn">from</span> <span class="nn">labml</span> <span class="kn">import</span> <span class="n">logger</span><span class="p">,</span> <span class="n">monit</span>
<span class="lineno">11</span><span class="kn">from</span> <span class="nn">labml_nn.transformers.flash</span> <span class="kn">import</span> <span class="n">attention</span>
<span class="lineno">12</span>
<span class="lineno">13</span><span class="n">HI_PRES_TORCH</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">float32</span></pre></div>
</div>
</div>
<div class='section' id='section-1'>
<div class='docs'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-1'>#</a>
</div>
<h4>Calculate absolute and relative error for reporting</h4>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">10</span><span class="nd">@torch</span><span class="o">.</span><span class="n">no_grad</span><span class="p">()</span>
<span class="lineno">11</span><span class="k">def</span> <span class="nf">_calc_abs_rel_error</span><span class="p">(</span><span class="n">a</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">b</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">atol</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">):</span>
<span class="lineno">12</span> <span class="n">d</span> <span class="o">=</span> <span class="p">(</span><span class="n">a</span> <span class="o">-</span> <span class="n">b</span><span class="p">)</span><span class="o">.</span><span class="n">abs</span><span class="p">()</span>
<span class="lineno">13</span> <span class="n">max_abs</span> <span class="o">=</span> <span class="n">d</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
<span class="lineno">14</span> <span class="n">d</span> <span class="o">=</span> <span class="p">(</span><span class="n">d</span> <span class="o">-</span> <span class="n">atol</span><span class="p">)</span><span class="o">.</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="lineno">15</span> <span class="n">d</span> <span class="o">=</span> <span class="n">d</span> <span class="o">/</span> <span class="n">b</span><span class="o">.</span><span class="n">abs</span><span class="p">()</span>
<span class="lineno">16</span> <span class="n">max_rel</span> <span class="o">=</span> <span class="n">d</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
<span class="lineno">17</span>
<span class="lineno">18</span> <span class="k">return</span> <span class="n">max_abs</span><span class="o">.</span><span class="n">cpu</span><span class="p">()</span><span class="o">.</span><span class="n">item</span><span class="p">(),</span> <span class="n">max_rel</span><span class="o">.</span><span class="n">cpu</span><span class="p">()</span><span class="o">.</span><span class="n">item</span><span class="p">()</span>
<span class="lineno">19</span>
<span class="lineno">20</span>
<span class="lineno">21</span><span class="k">def</span> <span class="nf">_test_op</span><span class="p">(</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">n_heads</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">q_seq_len</span><span class="p">,</span> <span class="n">kv_seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">,</span> <span class="n">causal</span><span class="p">,</span> <span class="n">dtype</span><span class="p">,</span> <span class="n">device</span><span class="p">):</span>
<span class="lineno">22</span> <span class="k">with</span> <span class="n">monit</span><span class="o">.</span><span class="n">section</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Init </span><span class="si">{</span><span class="n">q_seq_len</span><span class="si">}</span><span class="s1"> </span><span class="si">{</span><span class="n">kv_seq_len</span><span class="si">}</span><span class="s1"> </span><span class="si">{</span><span class="n">d_head</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">):</span>
<span class="lineno">23</span> <span class="n">torch</span><span class="o">.</span><span class="n">manual_seed</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span>
<span class="lineno">24</span> <span class="n">q</span> <span class="o">=</span> <span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">n_heads</span><span class="p">,</span> <span class="n">q_seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span>
<span class="lineno">25</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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="o">.</span><span class="n">normal_</span><span class="p">(</span><span class="n">mean</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">std</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span><span class="o">.</span><span class="n">requires_grad_</span><span class="p">())</span>
<span class="lineno">26</span> <span class="n">k</span> <span class="o">=</span> <span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">kv_seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span>
<span class="lineno">27</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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="o">.</span><span class="n">normal_</span><span class="p">(</span><span class="n">mean</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">std</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span><span class="o">.</span><span class="n">requires_grad_</span><span class="p">())</span>
<span class="lineno">28</span> <span class="n">v</span> <span class="o">=</span> <span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">kv_seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span>
<span class="lineno">29</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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="o">.</span><span class="n">normal_</span><span class="p">(</span><span class="n">mean</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">std</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span><span class="o">.</span><span class="n">requires_grad_</span><span class="p">())</span>
<span class="lineno">30</span> <span class="n">sm_scale</span> <span class="o">=</span> <span class="n">d_head</span> <span class="o">**</span> <span class="o">-</span><span class="mf">0.5</span>
<span class="lineno">31</span> <span class="n">d_out</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn_like</span><span class="p">(</span><span class="n">q</span><span class="p">)</span></pre></div>
<div class="highlight"><pre><span class="lineno">16</span><span class="nd">@torch</span><span class="o">.</span><span class="n">no_grad</span><span class="p">()</span>
<span class="lineno">17</span><span class="k">def</span> <span class="nf">_calc_abs_rel_error</span><span class="p">(</span><span class="n">a</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">b</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">atol</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-2'>
@ -120,76 +103,28 @@
<div class='section-link'>
<a href='#section-2'>#</a>
</div>
<p>reference implementation </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">33</span> <span class="n">mask</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">tril</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">q_seq_len</span><span class="p">,</span> <span class="n">kv_seq_len</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">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">bool</span><span class="p">))</span>
<span class="lineno">34</span> <span class="n">torch</span><span class="o">.</span><span class="n">cuda</span><span class="o">.</span><span class="n">synchronize</span><span class="p">()</span>
<span class="lineno">35</span>
<span class="lineno">36</span> <span class="k">with</span> <span class="n">monit</span><span class="o">.</span><span class="n">section</span><span class="p">(</span><span class="s1">&#39;Pytorch&#39;</span><span class="p">):</span>
<span class="lineno">37</span> <span class="n">p</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">q</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">q_seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span>
<span class="lineno">38</span> <span class="n">k</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)[:,</span> <span class="p">:,</span> <span class="kc">None</span><span class="p">,</span> <span class="p">:,</span> <span class="p">:])</span> <span class="o">*</span> <span class="n">sm_scale</span>
<span class="lineno">39</span> <span class="k">if</span> <span class="n">causal</span><span class="p">:</span>
<span class="lineno">40</span> <span class="n">p</span><span class="p">[:,</span> <span class="p">:,</span> <span class="p">:,</span> <span class="o">~</span><span class="n">mask</span><span class="p">]</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="s2">&quot;-inf&quot;</span><span class="p">)</span>
<span class="lineno">41</span> <span class="n">p</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">softmax</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">HI_PRES_TORCH</span><span class="p">),</span> <span class="n">dim</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">dtype</span><span class="p">)</span>
<span class="lineno">42</span> <span class="n">ref_out</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">v</span><span class="p">[:,</span> <span class="p">:,</span> <span class="kc">None</span><span class="p">,</span> <span class="p">:,</span> <span class="p">:])</span>
<span class="lineno">43</span> <span class="n">ref_out</span> <span class="o">=</span> <span class="n">ref_out</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">q</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="lineno">44</span> <span class="n">ref_out</span><span class="o">.</span><span class="n">backward</span><span class="p">(</span><span class="n">d_out</span><span class="p">)</span>
<span class="lineno">45</span> <span class="n">ref_dv</span><span class="p">,</span> <span class="n">v</span><span class="o">.</span><span class="n">grad</span> <span class="o">=</span> <span class="n">v</span><span class="o">.</span><span class="n">grad</span><span class="o">.</span><span class="n">clone</span><span class="p">(),</span> <span class="kc">None</span>
<span class="lineno">46</span> <span class="n">ref_dk</span><span class="p">,</span> <span class="n">k</span><span class="o">.</span><span class="n">grad</span> <span class="o">=</span> <span class="n">k</span><span class="o">.</span><span class="n">grad</span><span class="o">.</span><span class="n">clone</span><span class="p">(),</span> <span class="kc">None</span>
<span class="lineno">47</span> <span class="n">ref_dq</span><span class="p">,</span> <span class="n">q</span><span class="o">.</span><span class="n">grad</span> <span class="o">=</span> <span class="n">q</span><span class="o">.</span><span class="n">grad</span><span class="o">.</span><span class="n">clone</span><span class="p">(),</span> <span class="kc">None</span>
<span class="lineno">48</span> <span class="n">torch</span><span class="o">.</span><span class="n">cuda</span><span class="o">.</span><span class="n">synchronize</span><span class="p">()</span>
<span class="lineno">49</span>
<span class="lineno">50</span> <span class="k">with</span> <span class="n">monit</span><span class="o">.</span><span class="n">section</span><span class="p">(</span><span class="s1">&#39;Triton&#39;</span><span class="p">):</span>
<span class="lineno">51</span> <span class="k">assert</span> <span class="n">q</span><span class="o">.</span><span class="n">dtype</span> <span class="o">==</span> <span class="n">dtype</span>
<span class="lineno">52</span> <span class="n">tri_out</span> <span class="o">=</span> <span class="n">attention</span><span class="p">(</span><span class="n">q</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">causal</span><span class="p">,</span> <span class="n">sm_scale</span><span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">dtype</span><span class="p">)</span>
<span class="lineno">53</span> <span class="n">monit</span><span class="o">.</span><span class="n">progress</span><span class="p">(</span><span class="mf">0.5</span><span class="p">)</span>
<span class="lineno">54</span>
<span class="lineno">55</span> <span class="n">tri_out</span><span class="o">.</span><span class="n">backward</span><span class="p">(</span><span class="n">d_out</span><span class="p">)</span>
<span class="lineno">56</span> <span class="n">monit</span><span class="o">.</span><span class="n">progress</span><span class="p">(</span><span class="mf">0.9</span><span class="p">)</span>
<span class="lineno">57</span> <span class="n">tri_dv</span><span class="p">,</span> <span class="n">v</span><span class="o">.</span><span class="n">grad</span> <span class="o">=</span> <span class="n">v</span><span class="o">.</span><span class="n">grad</span><span class="o">.</span><span class="n">clone</span><span class="p">(),</span> <span class="kc">None</span> <span class="c1"># type: ignore</span>
<span class="lineno">58</span> <span class="n">tri_dk</span><span class="p">,</span> <span class="n">k</span><span class="o">.</span><span class="n">grad</span> <span class="o">=</span> <span class="n">k</span><span class="o">.</span><span class="n">grad</span><span class="o">.</span><span class="n">clone</span><span class="p">(),</span> <span class="kc">None</span> <span class="c1"># type: ignore</span>
<span class="lineno">59</span> <span class="n">tri_dq</span><span class="p">,</span> <span class="n">q</span><span class="o">.</span><span class="n">grad</span> <span class="o">=</span> <span class="n">q</span><span class="o">.</span><span class="n">grad</span><span class="o">.</span><span class="n">clone</span><span class="p">(),</span> <span class="kc">None</span> <span class="c1"># type: ignore</span>
<span class="lineno">60</span> <span class="n">torch</span><span class="o">.</span><span class="n">cuda</span><span class="o">.</span><span class="n">synchronize</span><span class="p">()</span>
<span class="lineno">61</span>
<span class="lineno">62</span> <span class="k">with</span> <span class="n">monit</span><span class="o">.</span><span class="n">section</span><span class="p">(</span><span class="s1">&#39;Test&#39;</span><span class="p">)</span> <span class="k">as</span> <span class="n">s</span><span class="p">:</span></pre></div>
<div class="highlight"><pre><span class="lineno">21</span> <span class="n">d</span> <span class="o">=</span> <span class="p">(</span><span class="n">a</span> <span class="o">-</span> <span class="n">b</span><span class="p">)</span><span class="o">.</span><span class="n">abs</span><span class="p">()</span>
<span class="lineno">22</span> <span class="n">max_abs</span> <span class="o">=</span> <span class="n">d</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
<span class="lineno">23</span> <span class="n">d</span> <span class="o">=</span> <span class="p">(</span><span class="n">d</span> <span class="o">-</span> <span class="n">atol</span><span class="p">)</span><span class="o">.</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="lineno">24</span> <span class="n">d</span> <span class="o">=</span> <span class="n">d</span> <span class="o">/</span> <span class="n">b</span><span class="o">.</span><span class="n">abs</span><span class="p">()</span>
<span class="lineno">25</span> <span class="n">max_rel</span> <span class="o">=</span> <span class="n">d</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
<span class="lineno">26</span>
<span class="lineno">27</span> <span class="k">return</span> <span class="n">max_abs</span><span class="o">.</span><span class="n">cpu</span><span class="p">()</span><span class="o">.</span><span class="n">item</span><span class="p">(),</span> <span class="n">max_rel</span><span class="o">.</span><span class="n">cpu</span><span class="p">()</span><span class="o">.</span><span class="n">item</span><span class="p">()</span></pre></div>
</div>
</div>
<div class='section' id='section-3'>
<div class='docs'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-3'>#</a>
</div>
<p>compare </p>
<h4>Compare our implementation with naive PyTorch attention</h4>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">64</span> <span class="n">passed</span> <span class="o">=</span> <span class="kc">True</span>
<span class="lineno">65</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">tri_out</span><span class="p">,</span> <span class="n">ref_out</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">,</span> <span class="n">rtol</span><span class="o">=</span><span class="mf">0.</span><span class="p">):</span>
<span class="lineno">66</span> <span class="n">abs_err</span><span class="p">,</span> <span class="n">rel_err</span> <span class="o">=</span> <span class="n">_calc_abs_rel_error</span><span class="p">(</span><span class="n">ref_out</span><span class="p">,</span> <span class="n">tri_out</span><span class="p">)</span>
<span class="lineno">67</span> <span class="n">logger</span><span class="o">.</span><span class="n">log</span><span class="p">((</span><span class="s1">&#39;[FAILED]&#39;</span><span class="p">,</span> <span class="n">logger</span><span class="o">.</span><span class="n">Text</span><span class="o">.</span><span class="n">danger</span><span class="p">),</span> <span class="sa">f</span><span class="s1">&#39; Out mismatch </span><span class="si">{</span><span class="n">abs_err</span><span class="si">}</span><span class="s1"> </span><span class="si">{</span><span class="n">rel_err</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
<span class="lineno">68</span> <span class="n">passed</span> <span class="o">=</span> <span class="kc">False</span>
<span class="lineno">69</span> <span class="n">rtol</span> <span class="o">=</span> <span class="mf">1e-1</span>
<span class="lineno">70</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">tri_dq</span><span class="p">,</span> <span class="n">ref_dq</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">,</span> <span class="n">rtol</span><span class="o">=</span><span class="n">rtol</span><span class="p">):</span>
<span class="lineno">71</span> <span class="n">abs_err</span><span class="p">,</span> <span class="n">rel_err</span> <span class="o">=</span> <span class="n">_calc_abs_rel_error</span><span class="p">(</span><span class="n">ref_dq</span><span class="p">,</span> <span class="n">tri_dq</span><span class="p">)</span>
<span class="lineno">72</span> <span class="n">logger</span><span class="o">.</span><span class="n">log</span><span class="p">((</span><span class="s1">&#39;[FAILED]&#39;</span><span class="p">,</span> <span class="n">logger</span><span class="o">.</span><span class="n">Text</span><span class="o">.</span><span class="n">danger</span><span class="p">),</span> <span class="sa">f</span><span class="s1">&#39; dQ mismatch </span><span class="si">{</span><span class="n">abs_err</span><span class="si">}</span><span class="s1"> </span><span class="si">{</span><span class="n">rel_err</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
<span class="lineno">73</span> <span class="n">passed</span> <span class="o">=</span> <span class="kc">False</span>
<span class="lineno">74</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">tri_dv</span><span class="p">,</span> <span class="n">ref_dv</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">,</span> <span class="n">rtol</span><span class="o">=</span><span class="n">rtol</span><span class="p">):</span>
<span class="lineno">75</span> <span class="n">abs_err</span><span class="p">,</span> <span class="n">rel_err</span> <span class="o">=</span> <span class="n">_calc_abs_rel_error</span><span class="p">(</span><span class="n">ref_dv</span><span class="p">,</span> <span class="n">tri_dv</span><span class="p">)</span>
<span class="lineno">76</span> <span class="n">logger</span><span class="o">.</span><span class="n">log</span><span class="p">((</span><span class="s1">&#39;[FAILED]&#39;</span><span class="p">,</span> <span class="n">logger</span><span class="o">.</span><span class="n">Text</span><span class="o">.</span><span class="n">danger</span><span class="p">),</span> <span class="sa">f</span><span class="s1">&#39; dV mismatch </span><span class="si">{</span><span class="n">abs_err</span><span class="si">}</span><span class="s1"> </span><span class="si">{</span><span class="n">rel_err</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
<span class="lineno">77</span> <span class="n">passed</span> <span class="o">=</span> <span class="kc">False</span>
<span class="lineno">78</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">tri_dk</span><span class="p">,</span> <span class="n">ref_dk</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">,</span> <span class="n">rtol</span><span class="o">=</span><span class="n">rtol</span><span class="p">):</span>
<span class="lineno">79</span> <span class="n">abs_err</span><span class="p">,</span> <span class="n">rel_err</span> <span class="o">=</span> <span class="n">_calc_abs_rel_error</span><span class="p">(</span><span class="n">ref_dk</span><span class="p">,</span> <span class="n">tri_dk</span><span class="p">)</span>
<span class="lineno">80</span> <span class="n">logger</span><span class="o">.</span><span class="n">log</span><span class="p">((</span><span class="s1">&#39;[FAILED]&#39;</span><span class="p">,</span> <span class="n">logger</span><span class="o">.</span><span class="n">Text</span><span class="o">.</span><span class="n">danger</span><span class="p">),</span> <span class="sa">f</span><span class="s1">&#39; dK mismatch </span><span class="si">{</span><span class="n">abs_err</span><span class="si">}</span><span class="s1"> </span><span class="si">{</span><span class="n">rel_err</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
<span class="lineno">81</span> <span class="n">passed</span> <span class="o">=</span> <span class="kc">False</span>
<span class="lineno">82</span>
<span class="lineno">83</span> <span class="k">if</span> <span class="n">passed</span><span class="p">:</span>
<span class="lineno">84</span> <span class="n">logger</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="s1">&#39;[PASSED]&#39;</span><span class="p">,</span> <span class="n">logger</span><span class="o">.</span><span class="n">Text</span><span class="o">.</span><span class="n">success</span><span class="p">)</span>
<span class="lineno">85</span> <span class="n">s</span><span class="o">.</span><span class="n">success</span> <span class="o">=</span> <span class="kc">True</span>
<span class="lineno">86</span> <span class="k">else</span><span class="p">:</span>
<span class="lineno">87</span> <span class="n">s</span><span class="o">.</span><span class="n">success</span> <span class="o">=</span> <span class="kc">False</span>
<span class="lineno">88</span> <span class="n">torch</span><span class="o">.</span><span class="n">cuda</span><span class="o">.</span><span class="n">synchronize</span><span class="p">()</span></pre></div>
<div class="highlight"><pre><span class="lineno">30</span><span class="k">def</span> <span class="nf">test_fwd_bwd</span><span class="p">(</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">n_heads</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">q_seq_len</span><span class="p">,</span> <span class="n">kv_seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">,</span> <span class="n">causal</span><span class="p">,</span> <span class="n">dtype</span><span class="p">,</span> <span class="n">device</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-4'>
@ -200,12 +135,16 @@
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">91</span><span class="k">def</span> <span class="nf">_perf_triton_fn</span><span class="p">(</span><span class="o">*</span><span class="p">,</span> <span class="n">device</span><span class="p">,</span> <span class="n">dtype</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">n_groups</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">,</span> <span class="n">causal</span><span class="p">):</span>
<span class="lineno">92</span> <span class="n">q</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span> <span class="o">*</span> <span class="n">n_groups</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="lineno">93</span> <span class="n">k</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="lineno">94</span> <span class="n">v</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="lineno">95</span> <span class="n">sm_scale</span> <span class="o">=</span> <span class="n">d_head</span> <span class="o">**</span> <span class="o">-</span><span class="mf">0.5</span>
<span class="lineno">96</span> <span class="k">return</span> <span class="k">lambda</span><span class="p">:</span> <span class="n">attention</span><span class="p">(</span><span class="n">q</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">causal</span><span class="p">,</span> <span class="n">sm_scale</span><span class="p">)</span></pre></div>
<div class="highlight"><pre><span class="lineno">35</span> <span class="k">with</span> <span class="n">monit</span><span class="o">.</span><span class="n">section</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Init </span><span class="si">{</span><span class="n">q_seq_len</span><span class="si">}</span><span class="s1"> </span><span class="si">{</span><span class="n">kv_seq_len</span><span class="si">}</span><span class="s1"> </span><span class="si">{</span><span class="n">d_head</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">):</span>
<span class="lineno">36</span> <span class="n">torch</span><span class="o">.</span><span class="n">manual_seed</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span>
<span class="lineno">37</span> <span class="n">q</span> <span class="o">=</span> <span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">n_heads</span><span class="p">,</span> <span class="n">q_seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span>
<span class="lineno">38</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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="o">.</span><span class="n">normal_</span><span class="p">(</span><span class="n">mean</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">std</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span><span class="o">.</span><span class="n">requires_grad_</span><span class="p">())</span>
<span class="lineno">39</span> <span class="n">k</span> <span class="o">=</span> <span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">kv_seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span>
<span class="lineno">40</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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="o">.</span><span class="n">normal_</span><span class="p">(</span><span class="n">mean</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">std</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span><span class="o">.</span><span class="n">requires_grad_</span><span class="p">())</span>
<span class="lineno">41</span> <span class="n">v</span> <span class="o">=</span> <span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">kv_seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span>
<span class="lineno">42</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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="o">.</span><span class="n">normal_</span><span class="p">(</span><span class="n">mean</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">std</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span><span class="o">.</span><span class="n">requires_grad_</span><span class="p">())</span>
<span class="lineno">43</span> <span class="n">sm_scale</span> <span class="o">=</span> <span class="n">d_head</span> <span class="o">**</span> <span class="o">-</span><span class="mf">0.5</span>
<span class="lineno">44</span> <span class="n">d_out</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn_like</span><span class="p">(</span><span class="n">q</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-5'>
@ -213,15 +152,40 @@
<div class='section-link'>
<a href='#section-5'>#</a>
</div>
<p>reference implementation </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">99</span><span class="k">def</span> <span class="nf">_perf_flash</span><span class="p">(</span><span class="o">*</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">n_groups</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">,</span> <span class="n">causal</span><span class="p">,</span> <span class="n">device</span><span class="p">,</span> <span class="n">dtype</span><span class="p">):</span>
<span class="lineno">100</span> <span class="n">q</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">k_heads</span> <span class="o">*</span> <span class="n">n_groups</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="lineno">101</span> <span class="n">k</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="lineno">102</span> <span class="n">v</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="lineno">103</span> <span class="kn">from</span> <span class="nn">flash_attn</span> <span class="kn">import</span> <span class="n">flash_attn_func</span>
<span class="lineno">104</span> <span class="k">return</span> <span class="k">lambda</span><span class="p">:</span> <span class="n">flash_attn_func</span><span class="p">(</span><span class="n">q</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">causal</span><span class="o">=</span><span class="n">causal</span><span class="p">)</span></pre></div>
<div class="highlight"><pre><span class="lineno">46</span> <span class="n">mask</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">tril</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">q_seq_len</span><span class="p">,</span> <span class="n">kv_seq_len</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">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">bool</span><span class="p">))</span>
<span class="lineno">47</span> <span class="n">torch</span><span class="o">.</span><span class="n">cuda</span><span class="o">.</span><span class="n">synchronize</span><span class="p">()</span>
<span class="lineno">48</span>
<span class="lineno">49</span> <span class="k">with</span> <span class="n">monit</span><span class="o">.</span><span class="n">section</span><span class="p">(</span><span class="s1">&#39;Pytorch&#39;</span><span class="p">):</span>
<span class="lineno">50</span> <span class="n">p</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">q</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">q_seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span>
<span class="lineno">51</span> <span class="n">k</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)[:,</span> <span class="p">:,</span> <span class="kc">None</span><span class="p">,</span> <span class="p">:,</span> <span class="p">:])</span> <span class="o">*</span> <span class="n">sm_scale</span>
<span class="lineno">52</span> <span class="k">if</span> <span class="n">causal</span><span class="p">:</span>
<span class="lineno">53</span> <span class="n">p</span><span class="p">[:,</span> <span class="p">:,</span> <span class="p">:,</span> <span class="o">~</span><span class="n">mask</span><span class="p">]</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="s2">&quot;-inf&quot;</span><span class="p">)</span>
<span class="lineno">54</span> <span class="n">p</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">softmax</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">HI_PRES_TORCH</span><span class="p">),</span> <span class="n">dim</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">dtype</span><span class="p">)</span>
<span class="lineno">55</span> <span class="n">ref_out</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">v</span><span class="p">[:,</span> <span class="p">:,</span> <span class="kc">None</span><span class="p">,</span> <span class="p">:,</span> <span class="p">:])</span>
<span class="lineno">56</span> <span class="n">ref_out</span> <span class="o">=</span> <span class="n">ref_out</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">q</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="lineno">57</span> <span class="n">ref_out</span><span class="o">.</span><span class="n">backward</span><span class="p">(</span><span class="n">d_out</span><span class="p">)</span>
<span class="lineno">58</span> <span class="n">ref_dv</span><span class="p">,</span> <span class="n">v</span><span class="o">.</span><span class="n">grad</span> <span class="o">=</span> <span class="n">v</span><span class="o">.</span><span class="n">grad</span><span class="o">.</span><span class="n">clone</span><span class="p">(),</span> <span class="kc">None</span>
<span class="lineno">59</span> <span class="n">ref_dk</span><span class="p">,</span> <span class="n">k</span><span class="o">.</span><span class="n">grad</span> <span class="o">=</span> <span class="n">k</span><span class="o">.</span><span class="n">grad</span><span class="o">.</span><span class="n">clone</span><span class="p">(),</span> <span class="kc">None</span>
<span class="lineno">60</span> <span class="n">ref_dq</span><span class="p">,</span> <span class="n">q</span><span class="o">.</span><span class="n">grad</span> <span class="o">=</span> <span class="n">q</span><span class="o">.</span><span class="n">grad</span><span class="o">.</span><span class="n">clone</span><span class="p">(),</span> <span class="kc">None</span>
<span class="lineno">61</span> <span class="n">torch</span><span class="o">.</span><span class="n">cuda</span><span class="o">.</span><span class="n">synchronize</span><span class="p">()</span>
<span class="lineno">62</span>
<span class="lineno">63</span> <span class="k">with</span> <span class="n">monit</span><span class="o">.</span><span class="n">section</span><span class="p">(</span><span class="s1">&#39;Triton&#39;</span><span class="p">):</span>
<span class="lineno">64</span> <span class="k">assert</span> <span class="n">q</span><span class="o">.</span><span class="n">dtype</span> <span class="o">==</span> <span class="n">dtype</span>
<span class="lineno">65</span> <span class="n">tri_out</span> <span class="o">=</span> <span class="n">attention</span><span class="p">(</span><span class="n">q</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">causal</span><span class="p">,</span> <span class="n">sm_scale</span><span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">dtype</span><span class="p">)</span>
<span class="lineno">66</span> <span class="n">monit</span><span class="o">.</span><span class="n">progress</span><span class="p">(</span><span class="mf">0.5</span><span class="p">)</span>
<span class="lineno">67</span>
<span class="lineno">68</span> <span class="n">tri_out</span><span class="o">.</span><span class="n">backward</span><span class="p">(</span><span class="n">d_out</span><span class="p">)</span>
<span class="lineno">69</span> <span class="n">monit</span><span class="o">.</span><span class="n">progress</span><span class="p">(</span><span class="mf">0.9</span><span class="p">)</span>
<span class="lineno">70</span> <span class="n">tri_dv</span><span class="p">,</span> <span class="n">v</span><span class="o">.</span><span class="n">grad</span> <span class="o">=</span> <span class="n">v</span><span class="o">.</span><span class="n">grad</span><span class="o">.</span><span class="n">clone</span><span class="p">(),</span> <span class="kc">None</span> <span class="c1"># type: ignore</span>
<span class="lineno">71</span> <span class="n">tri_dk</span><span class="p">,</span> <span class="n">k</span><span class="o">.</span><span class="n">grad</span> <span class="o">=</span> <span class="n">k</span><span class="o">.</span><span class="n">grad</span><span class="o">.</span><span class="n">clone</span><span class="p">(),</span> <span class="kc">None</span> <span class="c1"># type: ignore</span>
<span class="lineno">72</span> <span class="n">tri_dq</span><span class="p">,</span> <span class="n">q</span><span class="o">.</span><span class="n">grad</span> <span class="o">=</span> <span class="n">q</span><span class="o">.</span><span class="n">grad</span><span class="o">.</span><span class="n">clone</span><span class="p">(),</span> <span class="kc">None</span> <span class="c1"># type: ignore</span>
<span class="lineno">73</span> <span class="n">torch</span><span class="o">.</span><span class="n">cuda</span><span class="o">.</span><span class="n">synchronize</span><span class="p">()</span>
<span class="lineno">74</span>
<span class="lineno">75</span> <span class="k">with</span> <span class="n">monit</span><span class="o">.</span><span class="n">section</span><span class="p">(</span><span class="s1">&#39;Test&#39;</span><span class="p">)</span> <span class="k">as</span> <span class="n">s</span><span class="p">:</span></pre></div>
</div>
</div>
<div class='section' id='section-6'>
@ -229,40 +193,47 @@
<div class='section-link'>
<a href='#section-6'>#</a>
</div>
<p>compare </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">107</span><span class="k">def</span> <span class="nf">_perf_fn</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">fn</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">n_groups</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">,</span> <span class="n">causal</span><span class="p">,</span> <span class="n">is_bwd</span><span class="p">:</span> <span class="nb">bool</span><span class="p">):</span>
<span class="lineno">108</span> <span class="k">if</span> <span class="n">is_bwd</span><span class="p">:</span>
<span class="lineno">109</span> <span class="n">o</span> <span class="o">=</span> <span class="n">fn</span><span class="p">()</span>
<span class="lineno">110</span> <span class="n">do</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn_like</span><span class="p">(</span><span class="n">o</span><span class="p">)</span>
<span class="lineno">111</span> <span class="n">fn</span> <span class="o">=</span> <span class="k">lambda</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">backward</span><span class="p">(</span><span class="n">do</span><span class="p">,</span> <span class="n">retain_graph</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="lineno">112</span> <span class="n">ms</span> <span class="o">=</span> <span class="n">triton</span><span class="o">.</span><span class="n">testing</span><span class="o">.</span><span class="n">do_bench</span><span class="p">(</span><span class="n">fn</span><span class="p">)</span>
<span class="lineno">113</span>
<span class="lineno">114</span> <span class="n">flops_per_matmul</span> <span class="o">=</span> <span class="mf">2.0</span> <span class="o">*</span> <span class="n">batch_size</span> <span class="o">*</span> <span class="n">k_heads</span> <span class="o">*</span> <span class="n">n_groups</span> <span class="o">*</span> <span class="n">seq_len</span> <span class="o">*</span> <span class="n">seq_len</span> <span class="o">*</span> <span class="n">d_head</span>
<span class="lineno">115</span> <span class="n">total_flops</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">flops_per_matmul</span>
<span class="lineno">116</span> <span class="k">if</span> <span class="n">causal</span><span class="p">:</span>
<span class="lineno">117</span> <span class="n">total_flops</span> <span class="o">*=</span> <span class="mf">0.5</span>
<span class="lineno">118</span> <span class="k">if</span> <span class="n">is_bwd</span><span class="p">:</span>
<span class="lineno">119</span> <span class="n">total_flops</span> <span class="o">*=</span> <span class="mf">2.5</span> <span class="c1"># 2.0(bwd) + 0.5(recompute)</span>
<span class="lineno">120</span>
<span class="lineno">121</span> <span class="n">tf_ps</span> <span class="o">=</span> <span class="n">total_flops</span> <span class="o">*</span> <span class="mf">1e-12</span> <span class="o">/</span> <span class="p">(</span><span class="n">ms</span> <span class="o">*</span> <span class="mf">1e-3</span><span class="p">)</span>
<span class="lineno">122</span> <span class="n">logger</span><span class="o">.</span><span class="n">log</span><span class="p">((</span><span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">name</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">,</span> <span class="n">logger</span><span class="o">.</span><span class="n">Text</span><span class="o">.</span><span class="n">key</span><span class="p">),</span> <span class="s1">&#39;: &#39;</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">ms</span><span class="w"> </span><span class="si">:</span><span class="s1">,.1f</span><span class="si">}</span><span class="s1">ms&#39;</span><span class="p">,</span> <span class="s1">&#39; &#39;</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">tf_ps</span><span class="w"> </span><span class="si">:</span><span class="s1">,.2f</span><span class="si">}</span><span class="s1">TFps&#39;</span><span class="p">)</span></pre></div>
<div class="highlight"><pre><span class="lineno">77</span> <span class="n">passed</span> <span class="o">=</span> <span class="kc">True</span>
<span class="lineno">78</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">tri_out</span><span class="p">,</span> <span class="n">ref_out</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">,</span> <span class="n">rtol</span><span class="o">=</span><span class="mf">0.</span><span class="p">):</span>
<span class="lineno">79</span> <span class="n">abs_err</span><span class="p">,</span> <span class="n">rel_err</span> <span class="o">=</span> <span class="n">_calc_abs_rel_error</span><span class="p">(</span><span class="n">ref_out</span><span class="p">,</span> <span class="n">tri_out</span><span class="p">)</span>
<span class="lineno">80</span> <span class="n">logger</span><span class="o">.</span><span class="n">log</span><span class="p">((</span><span class="s1">&#39;[FAILED]&#39;</span><span class="p">,</span> <span class="n">logger</span><span class="o">.</span><span class="n">Text</span><span class="o">.</span><span class="n">danger</span><span class="p">),</span> <span class="sa">f</span><span class="s1">&#39; Out mismatch </span><span class="si">{</span><span class="n">abs_err</span><span class="si">}</span><span class="s1"> </span><span class="si">{</span><span class="n">rel_err</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
<span class="lineno">81</span> <span class="n">passed</span> <span class="o">=</span> <span class="kc">False</span>
<span class="lineno">82</span> <span class="n">rtol</span> <span class="o">=</span> <span class="mf">1e-1</span>
<span class="lineno">83</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">tri_dq</span><span class="p">,</span> <span class="n">ref_dq</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">,</span> <span class="n">rtol</span><span class="o">=</span><span class="n">rtol</span><span class="p">):</span>
<span class="lineno">84</span> <span class="n">abs_err</span><span class="p">,</span> <span class="n">rel_err</span> <span class="o">=</span> <span class="n">_calc_abs_rel_error</span><span class="p">(</span><span class="n">ref_dq</span><span class="p">,</span> <span class="n">tri_dq</span><span class="p">)</span>
<span class="lineno">85</span> <span class="n">logger</span><span class="o">.</span><span class="n">log</span><span class="p">((</span><span class="s1">&#39;[FAILED]&#39;</span><span class="p">,</span> <span class="n">logger</span><span class="o">.</span><span class="n">Text</span><span class="o">.</span><span class="n">danger</span><span class="p">),</span> <span class="sa">f</span><span class="s1">&#39; dQ mismatch </span><span class="si">{</span><span class="n">abs_err</span><span class="si">}</span><span class="s1"> </span><span class="si">{</span><span class="n">rel_err</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
<span class="lineno">86</span> <span class="n">passed</span> <span class="o">=</span> <span class="kc">False</span>
<span class="lineno">87</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">tri_dv</span><span class="p">,</span> <span class="n">ref_dv</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">,</span> <span class="n">rtol</span><span class="o">=</span><span class="n">rtol</span><span class="p">):</span>
<span class="lineno">88</span> <span class="n">abs_err</span><span class="p">,</span> <span class="n">rel_err</span> <span class="o">=</span> <span class="n">_calc_abs_rel_error</span><span class="p">(</span><span class="n">ref_dv</span><span class="p">,</span> <span class="n">tri_dv</span><span class="p">)</span>
<span class="lineno">89</span> <span class="n">logger</span><span class="o">.</span><span class="n">log</span><span class="p">((</span><span class="s1">&#39;[FAILED]&#39;</span><span class="p">,</span> <span class="n">logger</span><span class="o">.</span><span class="n">Text</span><span class="o">.</span><span class="n">danger</span><span class="p">),</span> <span class="sa">f</span><span class="s1">&#39; dV mismatch </span><span class="si">{</span><span class="n">abs_err</span><span class="si">}</span><span class="s1"> </span><span class="si">{</span><span class="n">rel_err</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
<span class="lineno">90</span> <span class="n">passed</span> <span class="o">=</span> <span class="kc">False</span>
<span class="lineno">91</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">tri_dk</span><span class="p">,</span> <span class="n">ref_dk</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">,</span> <span class="n">rtol</span><span class="o">=</span><span class="n">rtol</span><span class="p">):</span>
<span class="lineno">92</span> <span class="n">abs_err</span><span class="p">,</span> <span class="n">rel_err</span> <span class="o">=</span> <span class="n">_calc_abs_rel_error</span><span class="p">(</span><span class="n">ref_dk</span><span class="p">,</span> <span class="n">tri_dk</span><span class="p">)</span>
<span class="lineno">93</span> <span class="n">logger</span><span class="o">.</span><span class="n">log</span><span class="p">((</span><span class="s1">&#39;[FAILED]&#39;</span><span class="p">,</span> <span class="n">logger</span><span class="o">.</span><span class="n">Text</span><span class="o">.</span><span class="n">danger</span><span class="p">),</span> <span class="sa">f</span><span class="s1">&#39; dK mismatch </span><span class="si">{</span><span class="n">abs_err</span><span class="si">}</span><span class="s1"> </span><span class="si">{</span><span class="n">rel_err</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
<span class="lineno">94</span> <span class="n">passed</span> <span class="o">=</span> <span class="kc">False</span>
<span class="lineno">95</span>
<span class="lineno">96</span> <span class="k">if</span> <span class="n">passed</span><span class="p">:</span>
<span class="lineno">97</span> <span class="n">logger</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="s1">&#39;[PASSED]&#39;</span><span class="p">,</span> <span class="n">logger</span><span class="o">.</span><span class="n">Text</span><span class="o">.</span><span class="n">success</span><span class="p">)</span>
<span class="lineno">98</span> <span class="n">s</span><span class="o">.</span><span class="n">success</span> <span class="o">=</span> <span class="kc">True</span>
<span class="lineno">99</span> <span class="k">else</span><span class="p">:</span>
<span class="lineno">100</span> <span class="n">s</span><span class="o">.</span><span class="n">success</span> <span class="o">=</span> <span class="kc">False</span>
<span class="lineno">101</span> <span class="n">torch</span><span class="o">.</span><span class="n">cuda</span><span class="o">.</span><span class="n">synchronize</span><span class="p">()</span></pre></div>
</div>
</div>
<div class='section' id='section-7'>
<div class='docs'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-7'>#</a>
</div>
<p> Get a partial function to test performance of our implementation</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">125</span><span class="k">def</span> <span class="nf">_test</span><span class="p">():</span>
<span class="lineno">126</span> <span class="n">device</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">device</span><span class="p">(</span><span class="s1">&#39;cuda:0&#39;</span><span class="p">)</span>
<span class="lineno">127</span> <span class="n">torch</span><span class="o">.</span><span class="n">cuda</span><span class="o">.</span><span class="n">set_device</span><span class="p">(</span><span class="n">device</span><span class="p">)</span>
<span class="lineno">128</span>
<span class="lineno">129</span> <span class="n">dtype</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">float16</span></pre></div>
<div class="highlight"><pre><span class="lineno">104</span><span class="k">def</span> <span class="nf">_perf_triton_fn</span><span class="p">(</span><span class="o">*</span><span class="p">,</span> <span class="n">device</span><span class="p">,</span> <span class="n">dtype</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">n_groups</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">,</span> <span class="n">causal</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-8'>
@ -270,36 +241,130 @@
<div class='section-link'>
<a href='#section-8'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">108</span> <span class="n">q</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span> <span class="o">*</span> <span class="n">n_groups</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="lineno">109</span> <span class="n">k</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="lineno">110</span> <span class="n">v</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="lineno">111</span> <span class="n">sm_scale</span> <span class="o">=</span> <span class="n">d_head</span> <span class="o">**</span> <span class="o">-</span><span class="mf">0.5</span>
<span class="lineno">112</span> <span class="k">return</span> <span class="k">lambda</span><span class="p">:</span> <span class="n">attention</span><span class="p">(</span><span class="n">q</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">causal</span><span class="p">,</span> <span class="n">sm_scale</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-9'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-9'>#</a>
</div>
<p> Get a partial function to test performance of original flash implementation</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">115</span><span class="k">def</span> <span class="nf">_perf_flash</span><span class="p">(</span><span class="o">*</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">n_groups</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">,</span> <span class="n">causal</span><span class="p">,</span> <span class="n">device</span><span class="p">,</span> <span class="n">dtype</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>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">119</span> <span class="n">q</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">k_heads</span> <span class="o">*</span> <span class="n">n_groups</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="lineno">120</span> <span class="n">k</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="lineno">121</span> <span class="n">v</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">((</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">d_head</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="lineno">122</span> <span class="kn">from</span> <span class="nn">flash_attn</span> <span class="kn">import</span> <span class="n">flash_attn_func</span>
<span class="lineno">123</span> <span class="k">return</span> <span class="k">lambda</span><span class="p">:</span> <span class="n">flash_attn_func</span><span class="p">(</span><span class="n">q</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">causal</span><span class="o">=</span><span class="n">causal</span><span class="p">)</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>
<h3>Measure the speed</h3>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">126</span><span class="k">def</span> <span class="nf">measure_performance</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">fn</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">k_heads</span><span class="p">,</span> <span class="n">n_groups</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">d_head</span><span class="p">,</span> <span class="n">causal</span><span class="p">,</span> <span class="n">is_bwd</span><span class="p">:</span> <span class="nb">bool</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-12'>
<div class='docs'>
<div class='section-link'>
<a href='#section-12'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">130</span> <span class="k">if</span> <span class="n">is_bwd</span><span class="p">:</span>
<span class="lineno">131</span> <span class="n">o</span> <span class="o">=</span> <span class="n">fn</span><span class="p">()</span>
<span class="lineno">132</span> <span class="n">do</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn_like</span><span class="p">(</span><span class="n">o</span><span class="p">)</span>
<span class="lineno">133</span> <span class="n">fn</span> <span class="o">=</span> <span class="k">lambda</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">backward</span><span class="p">(</span><span class="n">do</span><span class="p">,</span> <span class="n">retain_graph</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="lineno">134</span> <span class="n">ms</span> <span class="o">=</span> <span class="n">triton</span><span class="o">.</span><span class="n">testing</span><span class="o">.</span><span class="n">do_bench</span><span class="p">(</span><span class="n">fn</span><span class="p">)</span>
<span class="lineno">135</span>
<span class="lineno">136</span> <span class="n">flops_per_matmul</span> <span class="o">=</span> <span class="mf">2.0</span> <span class="o">*</span> <span class="n">batch_size</span> <span class="o">*</span> <span class="n">k_heads</span> <span class="o">*</span> <span class="n">n_groups</span> <span class="o">*</span> <span class="n">seq_len</span> <span class="o">*</span> <span class="n">seq_len</span> <span class="o">*</span> <span class="n">d_head</span>
<span class="lineno">137</span> <span class="n">total_flops</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">flops_per_matmul</span>
<span class="lineno">138</span> <span class="k">if</span> <span class="n">causal</span><span class="p">:</span>
<span class="lineno">139</span> <span class="n">total_flops</span> <span class="o">*=</span> <span class="mf">0.5</span>
<span class="lineno">140</span> <span class="k">if</span> <span class="n">is_bwd</span><span class="p">:</span>
<span class="lineno">141</span> <span class="n">total_flops</span> <span class="o">*=</span> <span class="mf">2.5</span> <span class="c1"># 2.0(bwd) + 0.5(recompute)</span>
<span class="lineno">142</span>
<span class="lineno">143</span> <span class="n">tf_ps</span> <span class="o">=</span> <span class="n">total_flops</span> <span class="o">*</span> <span class="mf">1e-12</span> <span class="o">/</span> <span class="p">(</span><span class="n">ms</span> <span class="o">*</span> <span class="mf">1e-3</span><span class="p">)</span>
<span class="lineno">144</span> <span class="n">logger</span><span class="o">.</span><span class="n">log</span><span class="p">((</span><span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">name</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">,</span> <span class="n">logger</span><span class="o">.</span><span class="n">Text</span><span class="o">.</span><span class="n">key</span><span class="p">),</span> <span class="s1">&#39;: &#39;</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">ms</span><span class="w"> </span><span class="si">:</span><span class="s1">,.1f</span><span class="si">}</span><span class="s1">ms&#39;</span><span class="p">,</span> <span class="s1">&#39; &#39;</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">tf_ps</span><span class="w"> </span><span class="si">:</span><span class="s1">,.2f</span><span class="si">}</span><span class="s1">TFps&#39;</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">147</span><span class="k">def</span> <span class="nf">main</span><span class="p">():</span>
<span class="lineno">148</span> <span class="n">device</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">device</span><span class="p">(</span><span class="s1">&#39;cuda:0&#39;</span><span class="p">)</span>
<span class="lineno">149</span> <span class="n">torch</span><span class="o">.</span><span class="n">cuda</span><span class="o">.</span><span class="n">set_device</span><span class="p">(</span><span class="n">device</span><span class="p">)</span>
<span class="lineno">150</span>
<span class="lineno">151</span> <span class="n">dtype</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">float16</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>only works on post-Ampere GPUs right now </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">132</span> <span class="n">_test_op</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2048</span><span class="p">,</span> <span class="mi">2048</span><span class="p">,</span> <span class="mi">128</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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="lineno">133</span> <span class="n">_test_op</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">32</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">2001</span><span class="p">,</span> <span class="mi">4001</span><span class="p">,</span> <span class="mi">128</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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="lineno">134</span> <span class="n">_test_op</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">32</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">2048</span><span class="p">,</span> <span class="mi">1024</span><span class="p">,</span> <span class="mi">128</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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="lineno">135</span> <span class="n">_test_op</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">32</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">2001</span><span class="p">,</span> <span class="mi">4001</span><span class="p">,</span> <span class="mi">128</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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="lineno">136</span>
<span class="lineno">137</span> <span class="n">_conf</span> <span class="o">=</span> <span class="p">{</span>
<span class="lineno">138</span> <span class="s1">&#39;batch_size&#39;</span><span class="p">:</span> <span class="mi">16</span><span class="p">,</span>
<span class="lineno">139</span> <span class="s1">&#39;k_heads&#39;</span><span class="p">:</span> <span class="mi">8</span><span class="p">,</span>
<span class="lineno">140</span> <span class="s1">&#39;n_groups&#39;</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span>
<span class="lineno">141</span> <span class="s1">&#39;seq_len&#39;</span><span class="p">:</span> <span class="mi">2048</span><span class="p">,</span>
<span class="lineno">142</span> <span class="s1">&#39;d_head&#39;</span><span class="p">:</span> <span class="mi">128</span><span class="p">,</span>
<span class="lineno">143</span> <span class="p">}</span>
<span class="lineno">144</span>
<span class="lineno">145</span> <span class="k">for</span> <span class="n">_causal</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">]:</span>
<span class="lineno">146</span> <span class="k">for</span> <span class="n">is_bwd</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">]:</span>
<span class="lineno">147</span> <span class="n">logger</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="s2">&quot;Causal&quot;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">_causal</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s2">&quot;Non-causal&quot;</span><span class="si">}</span><span class="s1"> </span><span class="si">{</span><span class="s2">&quot; Backward&quot;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_bwd</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s2">&quot;&quot;</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">,</span> <span class="n">logger</span><span class="o">.</span><span class="n">Text</span><span class="o">.</span><span class="n">title</span><span class="p">)</span>
<span class="lineno">148</span> <span class="n">_perf_fn</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;flash&#39;</span><span class="p">,</span> <span class="n">_perf_flash</span><span class="p">(</span><span class="n">causal</span><span class="o">=</span><span class="n">_causal</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">dtype</span><span class="o">=</span><span class="n">dtype</span><span class="p">,</span> <span class="o">**</span><span class="n">_conf</span><span class="p">),</span>
<span class="lineno">149</span> <span class="n">is_bwd</span><span class="o">=</span><span class="n">is_bwd</span><span class="p">,</span>
<span class="lineno">150</span> <span class="n">causal</span><span class="o">=</span><span class="n">_causal</span><span class="p">,</span> <span class="o">**</span><span class="n">_conf</span><span class="p">)</span>
<span class="lineno">151</span> <span class="n">_perf_fn</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;triton&#39;</span><span class="p">,</span> <span class="n">_perf_triton_fn</span><span class="p">(</span><span class="n">causal</span><span class="o">=</span><span class="n">_causal</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">dtype</span><span class="o">=</span><span class="n">dtype</span><span class="p">,</span> <span class="o">**</span><span class="n">_conf</span><span class="p">),</span>
<span class="lineno">152</span> <span class="n">is_bwd</span><span class="o">=</span><span class="n">is_bwd</span><span class="p">,</span>
<span class="lineno">153</span> <span class="n">causal</span><span class="o">=</span><span class="n">_causal</span><span class="p">,</span> <span class="o">**</span><span class="n">_conf</span><span class="p">)</span>
<span class="lineno">154</span>
<span class="lineno">155</span>
<span class="lineno">156</span><span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s2">&quot;__main__&quot;</span><span class="p">:</span>
<span class="lineno">157</span> <span class="n">_test</span><span class="p">()</span></pre></div>
<div class="highlight"><pre><span class="lineno">154</span> <span class="n">test_fwd_bwd</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2048</span><span class="p">,</span> <span class="mi">2048</span><span class="p">,</span> <span class="mi">128</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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="lineno">155</span> <span class="n">test_fwd_bwd</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">32</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">2001</span><span class="p">,</span> <span class="mi">4001</span><span class="p">,</span> <span class="mi">128</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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="lineno">156</span> <span class="n">test_fwd_bwd</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">32</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">2048</span><span class="p">,</span> <span class="mi">1024</span><span class="p">,</span> <span class="mi">128</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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="lineno">157</span> <span class="n">test_fwd_bwd</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">32</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">2001</span><span class="p">,</span> <span class="mi">4001</span><span class="p">,</span> <span class="mi">128</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</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="lineno">158</span>
<span class="lineno">159</span> <span class="n">_conf</span> <span class="o">=</span> <span class="p">{</span>
<span class="lineno">160</span> <span class="s1">&#39;batch_size&#39;</span><span class="p">:</span> <span class="mi">16</span><span class="p">,</span>
<span class="lineno">161</span> <span class="s1">&#39;k_heads&#39;</span><span class="p">:</span> <span class="mi">8</span><span class="p">,</span>
<span class="lineno">162</span> <span class="s1">&#39;n_groups&#39;</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span>
<span class="lineno">163</span> <span class="s1">&#39;seq_len&#39;</span><span class="p">:</span> <span class="mi">2048</span><span class="p">,</span>
<span class="lineno">164</span> <span class="s1">&#39;d_head&#39;</span><span class="p">:</span> <span class="mi">128</span><span class="p">,</span>
<span class="lineno">165</span> <span class="p">}</span>
<span class="lineno">166</span>
<span class="lineno">167</span> <span class="k">for</span> <span class="n">_causal</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">]:</span>
<span class="lineno">168</span> <span class="k">for</span> <span class="n">is_bwd</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">]:</span>
<span class="lineno">169</span> <span class="n">logger</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="s2">&quot;Causal&quot;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">_causal</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s2">&quot;Non-causal&quot;</span><span class="si">}</span><span class="s1"> </span><span class="si">{</span><span class="s2">&quot; Backward&quot;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_bwd</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s2">&quot;&quot;</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">,</span> <span class="n">logger</span><span class="o">.</span><span class="n">Text</span><span class="o">.</span><span class="n">title</span><span class="p">)</span>
<span class="lineno">170</span> <span class="n">measure_performance</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;flash&#39;</span><span class="p">,</span> <span class="n">_perf_flash</span><span class="p">(</span><span class="n">causal</span><span class="o">=</span><span class="n">_causal</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">dtype</span><span class="o">=</span><span class="n">dtype</span><span class="p">,</span> <span class="o">**</span><span class="n">_conf</span><span class="p">),</span>
<span class="lineno">171</span> <span class="n">is_bwd</span><span class="o">=</span><span class="n">is_bwd</span><span class="p">,</span>
<span class="lineno">172</span> <span class="n">causal</span><span class="o">=</span><span class="n">_causal</span><span class="p">,</span> <span class="o">**</span><span class="n">_conf</span><span class="p">)</span>
<span class="lineno">173</span> <span class="n">measure_performance</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;triton&#39;</span><span class="p">,</span> <span class="n">_perf_triton_fn</span><span class="p">(</span><span class="n">causal</span><span class="o">=</span><span class="n">_causal</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">dtype</span><span class="o">=</span><span class="n">dtype</span><span class="p">,</span> <span class="o">**</span><span class="n">_conf</span><span class="p">),</span>
<span class="lineno">174</span> <span class="n">is_bwd</span><span class="o">=</span><span class="n">is_bwd</span><span class="p">,</span>
<span class="lineno">175</span> <span class="n">causal</span><span class="o">=</span><span class="n">_causal</span><span class="p">,</span> <span class="o">**</span><span class="n">_conf</span><span class="p">)</span>
<span class="lineno">176</span>
<span class="lineno">177</span>
<span class="lineno">178</span><span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s2">&quot;__main__&quot;</span><span class="p">:</span>
<span class="lineno">179</span> <span class="n">main</span><span class="p">()</span></pre></div>
</div>
</div>
<div class='footer'>

1
labml_nn/__init__.py
View File

@ -25,6 +25,7 @@ implementations.
#### ✨ [Transformers](transformers/index.html)
* [Multi-headed attention](transformers/mha.html)
* [Triton Flash Attention](transformers/flash/index.html)
* [Transformer building blocks](transformers/models.html)
* [Transformer XL](transformers/xl/index.html)
* [Relative multi-headed attention](transformers/xl/relative_mha.html)

135
labml_nn/transformers/flash/__init__.py
View File

@ -1,8 +1,36 @@
"""
---
title: Flash Attention
summary: >
This is a PyTorch/Triton implementation of Flash Attention 2
with explanations.
---
# Flash Attention
Flash attention speeds up transformer attention mechanism by reducing the number of
memory reads/writes between GPU high bandwidth memory (HBM) and GPU on-chip SRAM.
It's introduced in paper
[FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://arxiv.org/abs/2205.14135)
and further optimized in paper
[FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://arxiv.org/abs/2307.08691).
Official CUDA implementation can be found at [Dao-AILab/flash-attention](https://github.com/Dao-AILab/flash-attention).
Our implementation is based on the
[Triton's example implementation](https://triton-lang.org/main/getting-started/tutorials/06-fused-attention.html).
*Note: You can click on the mathematical symbols or identifiers to highlight them*.
You can run [test.py](./test.html) to see correctness and measure performance of this implementation.
## Forward pass
Here's the attention forward pass. The formulas represent a single attention head.
$Q_i$ is query vector (row vector) at position $i$
and $K_j$ and $V_j$ are the key and value row vectors at position $j$.
$O_i$ is the output vector at position $i$.
\begin{align}
S_{ij} &= \sigma Q_i K_j^T
\\
@ -15,6 +43,12 @@ O_i &= \sum_j P_{ij} V_j
&= \frac{1}{L_i} \sum_j e^{S_{ij}} V_j
\end{align}
$S_{ij}$ is the attention score matrix before softmax,
$L_i$ is the softmax denominator,
and $P_{ij}$ is the attention matrix after softmax.
#### Flash Attention Optimization
You can compute $O_i$, instead of doing the full softmax,
by computing the sum of exponents $l_i$ and the unnormalized output $\tilde{O}_i$
while iterating over keys:
@ -57,8 +91,14 @@ Then finally,
$$O_i = \frac{\tilde{O}_i}{l_i}$$
This reduces the memory usage since we don't have to compute full $S_{ij}$ matrix or $P_{ij}$ matrix.
It also speeds up since we don't have to load these large matrices.
Instead it only loads blocks of $K$ and $V$ as it iterates over them.
## Backward pass
Here's the standard backward pass. $dO_i$ is the gradient vector on the output $O_i$
\begin{align}
dV_j &= \sum_i P_{ij} dO_i
\\
@ -95,7 +135,14 @@ Then,
dS_{ij} = P_{ij} dP_{ij} - D_i P_{ij}
\end{align}
*Note: $Q_i$, $K_j$, $dQ_i$, etc are row vectors.*
Flash attention saves $L_i$ from the forward pass since it doesn't take much memory.
So during the backward pass it doesn't have to keep computing $l_i$ or $m_i$.
It first computes $D_i$.
Then it iterates over the queries and compute (accumulate) $dK_j$ and $dV_j$.
Finally it iterates over the keys and compute (accumulate) $dQ_i$.
In both forward and backward pass we calculate logarithms and exponentials of $2$ instead of $e$ for performance.
"""
from typing import Any, Tuple
@ -110,9 +157,12 @@ HI_PRES_TORCH: torch.dtype = torch.float32
class AttentionFunc(torch.autograd.Function):
@staticmethod
def forward(ctx: Any, q: torch.Tensor, k: torch.Tensor, v: torch.Tensor,
def forward(ctx: Any,
q: torch.Tensor, k: torch.Tensor, v: torch.Tensor,
causal: bool, sm_scale: float) -> torch.Tensor:
"""
### Forward pass
Group query attention forward pass. Returns the output in shape `[batch_size, n_heads, q_seq_len, d_head]`.
:param ctx: is the context for torch gradient descent
@ -121,7 +171,7 @@ class AttentionFunc(torch.autograd.Function):
:param k: has shape `[batch_size, k_heads, kv_seq_len, d_head]`
:param v: has shape `[batch_size, k_heads, kv_seq_len, d_head]`
:param causal: whether to apply causal attention mask
:param sm_scale: softmax scale factor
:param sm_scale: softmax scale factor $\sigma$
"""
batch_size, n_heads, q_seq_len, d_head = q.shape
_, k_heads, kv_seq_len, _ = k.shape
@ -171,6 +221,8 @@ class AttentionFunc(torch.autograd.Function):
@staticmethod
def backward(ctx: Any, do: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor, None, None]:
"""
### Backward pass
The backward pass computes the gradients of the input tensors.
:param ctx: is the context for torch gradient descent
@ -264,22 +316,27 @@ def _get_autotune_configs(inner_loop: str) -> list:
"""
configs = []
# List possible BLOCK_Q and BLOCK_K that satisfy BLOCK_Q divisible by BLOCK_K
# and also try to cover a wide range
for bm in [64, 128, 256]:
# We'll try bn in [16, 32, 64, 128] that are divisors and <= bm
for bn in [64, 128, 256]:
if inner_loop == 'key' and bm % bn != 0:
# Possible options for `BLOCK_Q`
for bq in [64, 128, 256]:
# Possible options for `BLOCK_K`
for bk in [64, 128, 256]:
# If the inner loop is along keys the `BLOCK_Q` must be a multiple of `BLOCK_K` for causal masking
if inner_loop == 'key' and bq % bk != 0:
continue
if inner_loop == 'query' and bn % bm != 0:
# Similarly when the inner loop is along queries
if inner_loop == 'query' and bk % bq != 0:
continue
# Number of stages and warps
for s in [2, 3, 4]:
for w in [4, 8]:
if bm * bn < 128 * 128 and w == 8:
if bq * bk < 128 * 128 and w == 8:
continue
configs.append(triton.Config({'BLOCK_Q': bm, 'BLOCK_K': bn}, num_stages=s, num_warps=w))
configs.append(triton.Config({'BLOCK_Q': bq, 'BLOCK_K': bk}, num_stages=s, num_warps=w))
# **Use `return configs` to autotune. Trying all combinations is slow for testing.**
return configs[:1]
@ -292,34 +349,37 @@ def _attn_fwd(t_q, t_k, t_v, sm_scale_log2e, t_lse, t_o,
kv_seq_len: tl.constexpr,
d_head: tl.constexpr,
is_causal: tl.constexpr,
BLOCK_Q: tl.constexpr, # q seq len block
BLOCK_K: tl.constexpr, # k seq len block
BLOCK_Q: tl.constexpr,
BLOCK_K: tl.constexpr,
):
"""
:param t_q: query
:param t_k: keys
:param t_v: values
:param sm_scale: softmax scale
### Triton kernel for Flash attention forward pass
:param t_q: queries $Q_i$
:param t_k: keys $K_j$
:param t_v: values $V_j$
:param sm_scale_log2e: $\sigma \log_2 e$ softmax scale multiplied by $\log_2 e$
:param t_lse: $\log_2 \sum_j e^{S_{ij}}$ (out)
:param t_o: output (out)
:param n_groups: number of groups
:param t_o: $O_i$ output
:param n_groups: number of groups in GQA
:param q_seq_len: query sequence length
:param kv_seq_len: key/value sequence length
:param d_head: size of a head
:param d_head: number of dimensions in a head
:param BLOCK_Q: block size for query sequence length
:param BLOCK_K: block size for key sequence length
:param is_causal: whether causal attention
Strides `z`, `h`, `m` and `d` denote the stride of the corresponding dimensions
(`batch_size`, `n_heads`, `seq_len`, `d_head`) in the query.
Stride `n` denote the stride on `seq_len` of key.
(`batch_size`, `n_heads`, `q_seq_len`, `d_head`) in the query.
Stride `n` denote the stride on `kv_seq_len` of key.
"""
# We are computing the attention for $O_i$ for `i` ... `i + BLOCK_Q' in batch/head combination $z$.
i = tl.program_id(0)
z = tl.program_id(1) // n_groups
g = tl.program_id(1) % n_groups # TODO
g = tl.program_id(1) % n_groups
# Create block pointers
# #### Create block pointers
p_q = tl.make_block_ptr(t_q + z * n_groups * q_seq_len * d_head + g * q_seq_len * d_head,
(q_seq_len, d_head),
(d_head, 1),
@ -354,6 +414,7 @@ def _attn_fwd(t_q, t_k, t_v, sm_scale_log2e, t_lse, t_o,
# Initialize offsets
offs_i = i * BLOCK_Q + tl.arange(0, BLOCK_Q)
offs_j = tl.arange(0, BLOCK_K)
# Mask for $Q$ for the last block
i_mask = offs_i < q_seq_len
@ -427,6 +488,12 @@ def _attn_fwd_inner(b_o, b_l, b_m, b_q,
q_seq_len: tl.constexpr,
kv_seq_len: tl.constexpr
):
"""
#### Inner loop to calculate $O_i$
This iterates through keys and values starting from `j` for `steps` number of steps.
In each step it processes `BLOCK_K` entries of keys/values.
"""
tl.static_assert(BLOCK_Q % BLOCK_K == 0)
# Move $K_j$ and $V_j$ pointers
@ -492,6 +559,9 @@ def _attn_bwd_d(t_o, t_do,
q_seq_len: tl.constexpr,
n_groups: tl.constexpr,
):
"""
#### Triton kernel to compute $D_i$
"""
i = tl.program_id(0) * BLOCK_Q
z = tl.program_id(1)
@ -539,9 +609,10 @@ def _attn_bwd_dkdv(t_q, t_k, t_v, sm_scale,
BLOCK_K: tl.constexpr,
):
"""
Compute $dK_j$ and $dV_j$ for $j1 \dots j2$ by iterating over $Q_i$
#### Triton kernel to compute $dK_j$ and $dV_j$
"""
# Compute $dK_j$ and $dV_j$ for `j` ... `j + BLOCK_K` by iterating over $Q_i$
j = tl.program_id(0) * BLOCK_K
z = tl.program_id(1)
@ -671,7 +742,9 @@ def _attn_bwd_dkdv_inner(b_dk, b_dv,
MASK: tl.constexpr,
q_seq_len: tl.constexpr,
kv_seq_len: tl.constexpr):
"""Inner loop along query"""
"""
#### Inner loop to calculate $dK_j$, $dV_j$
"""
# To apply the mask
tl.static_assert(BLOCK_K % BLOCK_Q == 0)
@ -755,6 +828,10 @@ def _attn_bwd_dq(t_q, t_k, t_v, t_do,
BLOCK_Q: tl.constexpr,
BLOCK_K: tl.constexpr,
):
"""
#### Triton kernel to compute $dQ_i$
"""
i = tl.program_id(0) * BLOCK_Q
z = tl.program_id(1) // n_groups
g = tl.program_id(1) % n_groups # TODO
@ -863,7 +940,9 @@ def _attn_bwd_dq_inner(b_dq, b_q, p_kT, p_vT,
MASK: tl.constexpr,
q_seq_len: tl.constexpr,
kv_seq_len: tl.constexpr):
"""Inner loop over key"""
"""
#### Inner loop to calculate $dQ_i$
"""
# Offsets
offs_i = i + tl.arange(0, BLOCK_Q)

44
labml_nn/transformers/flash/test.py
View File

@ -1,6 +1,12 @@
import triton
"""
### Test Flash Attention Implementation
This is the code to test and measure performance of our flash attention implementation
"""
import torch
import triton
from labml import logger, monit
from labml_nn.transformers.flash import attention
@ -9,6 +15,9 @@ HI_PRES_TORCH = torch.float32
@torch.no_grad()
def _calc_abs_rel_error(a: torch.Tensor, b: torch.Tensor, atol=1e-2):
"""
#### Calculate absolute and relative error for reporting
"""
d = (a - b).abs()
max_abs = d.max()
d = (d - atol).clamp(min=0)
@ -18,7 +27,11 @@ def _calc_abs_rel_error(a: torch.Tensor, b: torch.Tensor, atol=1e-2):
return max_abs.cpu().item(), max_rel.cpu().item()
def _test_op(batch_size, n_heads, k_heads, q_seq_len, kv_seq_len, d_head, causal, dtype, device):
def test_fwd_bwd(batch_size, n_heads, k_heads, q_seq_len, kv_seq_len, d_head, causal, dtype, device):
"""
#### Compare our implementation with naive PyTorch attention
"""
with monit.section(f'Init {q_seq_len} {kv_seq_len} {d_head}'):
torch.manual_seed(20)
q = (torch.empty((batch_size, n_heads, q_seq_len, d_head),
@ -89,6 +102,9 @@ def _test_op(batch_size, n_heads, k_heads, q_seq_len, kv_seq_len, d_head, causal
def _perf_triton_fn(*, device, dtype, batch_size, k_heads, n_groups, seq_len, d_head, causal):
"""
Get a partial function to test performance of our implementation
"""
q = torch.randn((batch_size, k_heads * n_groups, seq_len, d_head), dtype=dtype, device=device, requires_grad=True)
k = torch.randn((batch_size, k_heads, seq_len, d_head), dtype=dtype, device=device, requires_grad=True)
v = torch.randn((batch_size, k_heads, seq_len, d_head), dtype=dtype, device=device, requires_grad=True)
@ -97,6 +113,9 @@ def _perf_triton_fn(*, device, dtype, batch_size, k_heads, n_groups, seq_len, d_
def _perf_flash(*, batch_size, k_heads, n_groups, seq_len, d_head, causal, device, dtype):
"""
Get a partial function to test performance of original flash implementation
"""
q = torch.randn((batch_size, seq_len, k_heads * n_groups, d_head), dtype=dtype, device=device, requires_grad=True)
k = torch.randn((batch_size, seq_len, k_heads, d_head), dtype=dtype, device=device, requires_grad=True)
v = torch.randn((batch_size, seq_len, k_heads, d_head), dtype=dtype, device=device, requires_grad=True)
@ -104,7 +123,10 @@ def _perf_flash(*, batch_size, k_heads, n_groups, seq_len, d_head, causal, devic
return lambda: flash_attn_func(q, k, v, causal=causal)
def _perf_fn(name, fn, *, batch_size, k_heads, n_groups, seq_len, d_head, causal, is_bwd: bool):
def measure_performance(name, fn, *, batch_size, k_heads, n_groups, seq_len, d_head, causal, is_bwd: bool):
"""
### Measure the speed
"""
if is_bwd:
o = fn()
do = torch.randn_like(o)
@ -122,17 +144,17 @@ def _perf_fn(name, fn, *, batch_size, k_heads, n_groups, seq_len, d_head, causal
logger.log((f'{name}', logger.Text.key), ': ', f'{ms :,.1f}ms', ' ', f'{tf_ps :,.2f}TFps')
def _test():
def main():
device = torch.device('cuda:0')
torch.cuda.set_device(device)
dtype = torch.float16
# only works on post-Ampere GPUs right now
_test_op(1, 4, 1, 2048, 2048, 128, True, dtype=dtype, device=device)
_test_op(16, 32, 8, 2001, 4001, 128, False, dtype=dtype, device=device)
_test_op(4, 32, 8, 2048, 1024, 128, False, dtype=dtype, device=device)
_test_op(4, 32, 8, 2001, 4001, 128, True, dtype=dtype, device=device)
test_fwd_bwd(1, 4, 1, 2048, 2048, 128, True, dtype=dtype, device=device)
test_fwd_bwd(16, 32, 8, 2001, 4001, 128, False, dtype=dtype, device=device)
test_fwd_bwd(4, 32, 8, 2048, 1024, 128, False, dtype=dtype, device=device)
test_fwd_bwd(4, 32, 8, 2001, 4001, 128, True, dtype=dtype, device=device)
_conf = {
'batch_size': 16,
@ -145,13 +167,13 @@ def _test():
for _causal in [False, True]:
for is_bwd in [False, True]:
logger.log(f'{"Causal" if _causal else "Non-causal"} {" Backward" if is_bwd else ""}', logger.Text.title)
_perf_fn(f'flash', _perf_flash(causal=_causal, device=device, dtype=dtype, **_conf),
measure_performance(f'flash', _perf_flash(causal=_causal, device=device, dtype=dtype, **_conf),
is_bwd=is_bwd,
causal=_causal, **_conf)
_perf_fn(f'triton', _perf_triton_fn(causal=_causal, device=device, dtype=dtype, **_conf),
measure_performance(f'triton', _perf_triton_fn(causal=_causal, device=device, dtype=dtype, **_conf),
is_bwd=is_bwd,
causal=_causal, **_conf)
if __name__ == "__main__":
_test()
main()

1
readme.md
View File

@ -21,6 +21,7 @@ implementations almost weekly.
#### ✨ [Transformers](https://nn.labml.ai/transformers/index.html)
* [Multi-headed attention](https://nn.labml.ai/transformers/mha.html)
* [Triton Flash Attention](https://nn.labml.ai/transformers/flash/index.html)
* [Transformer building blocks](https://nn.labml.ai/transformers/models.html)
* [Transformer XL](https://nn.labml.ai/transformers/xl/index.html)
* [Relative multi-headed attention](https://nn.labml.ai/transformers/xl/relative_mha.html)

4
setup.py
View File

@ -5,7 +5,7 @@ with open("readme.md", "r", encoding="utf-8") as f:
setuptools.setup(
name='labml-nn',
version='0.4.137',
version='0.5.0',
author="Varuna Jayasiri, Nipun Wijerathne",
author_email="vpjayasiri@gmail.com, hnipun@gmail.com",
description="🧑‍🏫 Implementations/tutorials of deep learning papers with side-by-side notes 📝; including transformers (original, xl, switch, feedback, vit), optimizers (adam, radam, adabelief), gans(dcgan, cyclegan, stylegan2), 🎮 reinforcement learning (ppo, dqn), capsnet, distillation, diffusion, etc. 🧠",
@ -20,7 +20,7 @@ setuptools.setup(
'labml_helpers', 'labml_helpers.*',
'test',
'test.*')),
install_requires=['labml==0.4.168',
install_requires=['labml',
'torch',
'torchtext',
'torchvision',