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<h1>Noam Optimizer</h1>
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<p>This is the <a href="https://pytorch.org">PyTorch</a> implementation of optimizer introduced in the paper
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<a href="https://arxiv.org/abs/1706.03762">Attention Is All You Need</a>.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">14</span><span></span><span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Dict</span>
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<span class="lineno">15</span>
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<span class="lineno">16</span><span class="kn">from</span> <span class="nn">labml_nn.optimizers</span> <span class="kn">import</span> <span class="n">WeightDecay</span>
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<span class="lineno">17</span><span class="kn">from</span> <span class="nn">labml_nn.optimizers.amsgrad</span> <span class="kn">import</span> <span class="n">AMSGrad</span></pre></div>
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<a href='#section-1'>#</a>
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<h2>Noam Optimizer</h2>
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<p>This class extends from Adam optimizer defined in <a href="adam.html"><code>adam.py</code></a>.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">20</span><span class="k">class</span> <span class="nc">Noam</span><span class="p">(</span><span class="n">AMSGrad</span><span class="p">):</span></pre></div>
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<div class='docs doc-strings'>
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</div>
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<h3>Initialize the optimizer</h3>
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<ul>
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<li><code>params</code> is the list of parameters</li>
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<li><code>lr</code> is the learning rate $\alpha$</li>
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<li><code>betas</code> is a tuple of ($\beta_1$, $\beta_2$)</li>
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<li><code>eps</code> is $\hat{\epsilon}$ or $\epsilon$ based on <code>optimized_update</code></li>
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<li><code>weight_decay</code> is an instance of class <code>WeightDecay</code> defined in <a href="index.html"><code>__init__.py</code></a></li>
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<li>‘optimized_update’ is a flag whether to optimize the bias correction of the second moment
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by doing it after adding $\epsilon$</li>
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<li><code>amsgrad</code> is a flag indicating whether to use AMSGrad or fallback to plain Adam</li>
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<li><code>warmup</code> number of warmup steps</li>
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<li><code>d_model</code> model size; i.e. number of dimensions in the transformer</li>
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<li><code>defaults</code> is a dictionary of default for group values.
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This is useful when you want to extend the class <code>AdamWarmup</code>.</li>
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</ul>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">27</span> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span> <span class="n">lr</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">,</span> <span class="n">betas</span><span class="o">=</span><span class="p">(</span><span class="mf">0.9</span><span class="p">,</span> <span class="mf">0.999</span><span class="p">),</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-16</span><span class="p">,</span>
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<span class="lineno">28</span> <span class="n">weight_decay</span><span class="p">:</span> <span class="n">WeightDecay</span> <span class="o">=</span> <span class="n">WeightDecay</span><span class="p">(),</span>
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<span class="lineno">29</span> <span class="n">optimized_update</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">,</span>
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<span class="lineno">30</span> <span class="n">amsgrad</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
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<span class="lineno">31</span> <span class="n">warmup</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">d_model</span><span class="o">=</span><span class="mi">512</span><span class="p">,</span> <span class="n">defaults</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span></pre></div>
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<div class='docs'>
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<a href='#section-3'>#</a>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">49</span> <span class="n">defaults</span> <span class="o">=</span> <span class="p">{}</span> <span class="k">if</span> <span class="n">defaults</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">defaults</span>
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<span class="lineno">50</span> <span class="n">defaults</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="nb">dict</span><span class="p">(</span><span class="n">warmup</span><span class="o">=</span><span class="n">warmup</span><span class="p">))</span>
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<span class="lineno">51</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="n">lr</span><span class="p">,</span> <span class="n">betas</span><span class="p">,</span> <span class="n">eps</span><span class="p">,</span> <span class="n">weight_decay</span><span class="p">,</span> <span class="n">optimized_update</span><span class="p">,</span> <span class="n">amsgrad</span><span class="p">,</span> <span class="n">defaults</span><span class="p">)</span>
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<span class="lineno">52</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_model</span> <span class="o">=</span> <span class="n">d_model</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-4'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-4'>#</a>
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</div>
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<h3>Get learning-rate</h3>
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<p>
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<script type="math/tex; mode=display">\alpha \frac{1}{\sqrt{d_{model}}} \min \bigg(\frac{1}{\sqrt{t}}, \frac{t}{w^{3/2}}\bigg)</script>
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where $w$ is the number of warmup steps.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">54</span> <span class="k">def</span> <span class="nf">get_lr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">state</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="nb">any</span><span class="p">],</span> <span class="n">group</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="nb">any</span><span class="p">]):</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-5'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-5'>#</a>
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</div>
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<p>
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<script type="math/tex; mode=display">\min \bigg(\frac{1}{\sqrt{t}}, \frac{t}{w^{3/2}}\bigg)</script>
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</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">62</span> <span class="n">factor</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">state</span><span class="p">[</span><span class="s1">'step'</span><span class="p">]</span> <span class="o">**</span> <span class="p">(</span><span class="o">-</span><span class="mf">0.5</span><span class="p">),</span> <span class="n">state</span><span class="p">[</span><span class="s1">'step'</span><span class="p">]</span> <span class="o">*</span> <span class="n">group</span><span class="p">[</span><span class="s1">'warmup'</span><span class="p">]</span> <span class="o">**</span> <span class="p">(</span><span class="o">-</span><span class="mf">1.5</span><span class="p">))</span></pre></div>
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</div>
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<div class='section' id='section-6'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-6'>#</a>
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</div>
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<p>
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<script type="math/tex; mode=display">\alpha \frac{1}{\sqrt{d_{model}}} \min \bigg(\frac{1}{\sqrt{t}}, \frac{t}{w^{3/2}}\bigg)</script>
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</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">64</span> <span class="k">return</span> <span class="n">group</span><span class="p">[</span><span class="s1">'lr'</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_model</span> <span class="o">**</span> <span class="p">(</span><span class="o">-</span><span class="mf">0.5</span><span class="p">)</span> <span class="o">*</span> <span class="n">factor</span></pre></div>
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</div>
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<div class='section' id='section-7'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-7'>#</a>
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</div>
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<h3>Plot learning rate for different warmups and model sizes</h3>
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<p><img alt="Plot of learning rate" src="noam_lr.png" /></p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">67</span><span class="k">def</span> <span class="nf">_test_noam_lr</span><span class="p">():</span></pre></div>
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<div class='section' id='section-8'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-8'>#</a>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">73</span> <span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
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<span class="lineno">74</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
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<span class="lineno">75</span> <span class="kn">from</span> <span class="nn">torch</span> <span class="kn">import</span> <span class="n">nn</span>
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<span class="lineno">76</span>
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<span class="lineno">77</span> <span class="n">model</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
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<span class="lineno">78</span> <span class="n">opts</span> <span class="o">=</span> <span class="p">[</span><span class="n">Noam</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">parameters</span><span class="p">(),</span> <span class="n">d_model</span><span class="o">=</span><span class="mi">512</span><span class="p">,</span> <span class="n">warmup</span><span class="o">=</span><span class="mi">4000</span><span class="p">,</span> <span class="n">lr</span><span class="o">=</span><span class="mi">1</span><span class="p">),</span>
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<span class="lineno">79</span> <span class="n">Noam</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">parameters</span><span class="p">(),</span> <span class="n">d_model</span><span class="o">=</span><span class="mi">512</span><span class="p">,</span> <span class="n">warmup</span><span class="o">=</span><span class="mi">8000</span><span class="p">,</span> <span class="n">lr</span><span class="o">=</span><span class="mi">1</span><span class="p">),</span>
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<span class="lineno">80</span> <span class="n">Noam</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">parameters</span><span class="p">(),</span> <span class="n">d_model</span><span class="o">=</span><span class="mi">2048</span><span class="p">,</span> <span class="n">warmup</span><span class="o">=</span><span class="mi">2000</span><span class="p">,</span> <span class="n">lr</span><span class="o">=</span><span class="mi">1</span><span class="p">)]</span>
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<span class="lineno">81</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">20000</span><span class="p">),</span> <span class="p">[[</span><span class="n">opt</span><span class="o">.</span><span class="n">get_lr</span><span class="p">({</span><span class="s1">'step'</span><span class="p">:</span> <span class="n">i</span><span class="p">},</span> <span class="n">opt</span><span class="o">.</span><span class="n">defaults</span><span class="p">)</span> <span class="k">for</span> <span class="n">opt</span> <span class="ow">in</span> <span class="n">opts</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">20000</span><span class="p">)])</span>
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<span class="lineno">82</span> <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">([</span><span class="s2">"512:4000"</span><span class="p">,</span> <span class="s2">"512:8000"</span><span class="p">,</span> <span class="s2">"2048:2000"</span><span class="p">])</span>
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<span class="lineno">83</span> <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Learning Rate"</span><span class="p">)</span>
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<span class="lineno">84</span> <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<span class="lineno">85</span>
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<span class="lineno">86</span>
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<span class="lineno">87</span><span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">'__main__'</span><span class="p">:</span>
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<span class="lineno">88</span> <span class="n">_test_noam_lr</span><span class="p">()</span></pre></div>
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}
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handleImages()
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</script>
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</body>
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</html> |