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            <h1>Noam Optimizer</h1>
<p>This is the <a href="https://pytorch.org">PyTorch</a> implementation of optimizer introduced in the paper <a href="https://papers.labml.ai/paper/1706.03762">Attention Is All You Need</a>.</p>

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        <div class='code'>
            <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>
<span class="lineno">15</span>
<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>
<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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            <h2>Noam Optimizer</h2>
<p>This class extends from Adam optimizer defined in <a href="adam.html"><code class="highlight"><span></span><span class="n">adam</span><span class="o">.</span><span class="n">py</span></code>
</a>.</p>

        </div>
        <div class='code'>
            <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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            <h3>Initialize the optimizer</h3>
<ul><li><code class="highlight"><span></span><span class="n">params</span></code>
 is the list of parameters </li>
<li><code class="highlight"><span></span><span class="n">lr</span></code>
 is the learning rate <span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqg" style=""><span class="mord mathnormal" style="margin-right:0.0037em">α</span></span></span></span></span> </li>
<li><code class="highlight"><span></span><span class="n">betas</span></code>
 is a tuple of (<span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05278em;">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>, <span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05278em;">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>) </li>
<li><code class="highlight"><span></span><span class="n">eps</span></code>
 is <span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord coloredeq eqd" style=""><span class="mord mathnormal" style="">ϵ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.19444em;"><span class="mord">^</span></span></span></span></span></span></span></span></span></span> or <span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqd" style=""><span class="mord mathnormal" style="">ϵ</span></span></span></span></span> based on <code class="highlight"><span></span><span class="n">optimized_update</span></code>
 </li>
<li><code class="highlight"><span></span><span class="n">weight_decay</span></code>
 is an instance of class <code class="highlight"><span></span><span class="n">WeightDecay</span></code>
 defined in <a href="index.html"><code class="highlight"><span></span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span></code>
</a> </li>
<li>&#x27;optimized_update&#x27; is a flag whether to optimize the bias correction of the second moment  by doing it after adding <span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqd" style=""><span class="mord mathnormal" style="">ϵ</span></span></span></span></span> </li>
<li><code class="highlight"><span></span><span class="n">amsgrad</span></code>
 is a flag indicating whether to use AMSGrad or fallback to plain Adam </li>
<li><code class="highlight"><span></span><span class="n">warmup</span></code>
 number of warmup steps </li>
<li><code class="highlight"><span></span><span class="n">d_model</span></code>
 model size; i.e. number of dimensions in the transformer </li>
<li><code class="highlight"><span></span><span class="n">defaults</span></code>
 is a dictionary of default for group values.  This is useful when you want to extend the class <code class="highlight"><span></span><span class="n">AdamWarmup</span></code>
.</li></ul>

        </div>
        <div class='code'>
            <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>
<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>
<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>
<span class="lineno">30</span>                 <span class="n">amsgrad</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
<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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                <a href='#section-3'>#</a>
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        </div>
        <div class='code'>
            <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>
<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>
<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>
<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 class='section' id='section-4'>
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            <div class='section-link'>
                <a href='#section-4'>#</a>
            </div>
            <h3>Get learning-rate</h3>
<p><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="mord coloredeq eqg" style=""><span class="mord mathnormal" style="margin-right:0.0037em">α</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.25278em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.85722em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord"><span class="mord mathnormal">d</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">o</span><span class="mord mathnormal mtight">d</span><span class="mord mathnormal mtight">e</span><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.81722em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.18278000000000005em;"><span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.93em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord coloredeq eqb" style=""><span class="mop" style=""><span style="">m</span><span style="">i</span><span style="">n</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="delimsizing size3" style=""><span style="">(</span></span></span><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.21746em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord sqrt" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.89254em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em"><span class="mord mathnormal" style="">t</span></span></span><span style="top:-2.85254em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
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c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.14746000000000004em;"><span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style="">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.93em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.29208em;"><span style="top:-2.2960000000000003em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqh" style=""><span class="mord mathnormal" style="margin-right:0.02691em">w</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.814em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">3/2</span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord mathnormal" style="">t</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.704em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord" style=""><span class="delimsizing size3" style=""><span style="">)</span></span></span></span></span></span></span></span> where <span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqh" style=""><span class="mord mathnormal" style="margin-right:0.02691em">w</span></span></span></span></span> is the number of warmup steps.</p>

        </div>
        <div class='code'>
            <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>
        </div>
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        <div class='docs'>
            <div class='section-link'>
                <a href='#section-5'>#</a>
            </div>
            <p><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="mord coloredeq eqb" style=""><span class="mop" style=""><span style="">m</span><span style="">i</span><span style="">n</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="delimsizing size3" style=""><span style="">(</span></span></span><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.21746em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord sqrt" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.89254em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em"><span class="mord mathnormal" style="">t</span></span></span><span style="top:-2.85254em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
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        </div>
        <div class='code'>
            <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">&#39;step&#39;</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">&#39;step&#39;</span><span class="p">]</span> <span class="o">*</span> <span class="n">group</span><span class="p">[</span><span class="s1">&#39;warmup&#39;</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>
        </div>
    </div>
    <div class='section' id='section-6'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-6'>#</a>
            </div>
            <p><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="mord coloredeq eqg" style=""><span class="mord mathnormal" style="margin-right:0.0037em">α</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.25278em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.85722em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord"><span class="mord mathnormal">d</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">o</span><span class="mord mathnormal mtight">d</span><span class="mord mathnormal mtight">e</span><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.81722em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
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        </div>
        <div class='code'>
            <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">&#39;lr&#39;</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>
        </div>
    </div>
    <div class='section' id='section-7'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-7'>#</a>
            </div>
            <h3>Plot learning rate for different warmups and model sizes</h3>
<p><img alt="Plot of learning rate" src="noam_lr.png"></p>

        </div>
        <div class='code'>
            <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>
        </div>
    </div>
    <div class='section' id='section-8'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-8'>#</a>
            </div>

        </div>
        <div class='code'>
            <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>
<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>
<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>
<span class="lineno">76</span>
<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>
<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>
<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>
<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>
<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">&#39;step&#39;</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>
<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">&quot;512:4000&quot;</span><span class="p">,</span> <span class="s2">&quot;512:8000&quot;</span><span class="p">,</span> <span class="s2">&quot;2048:2000&quot;</span><span class="p">])</span>
<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">&quot;Learning Rate&quot;</span><span class="p">)</span>
<span class="lineno">84</span>    <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="lineno">85</span>
<span class="lineno">86</span>
<span class="lineno">87</span><span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">&#39;__main__&#39;</span><span class="p">:</span>
<span class="lineno">88</span>    <span class="n">_test_noam_lr</span><span class="p">()</span></pre></div>
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