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<section id="mlx-optimizers-adam">
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<h1>mlx.optimizers.Adam<a class="headerlink" href="#mlx-optimizers-adam" title="Permalink to this heading"></a></h1>
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<dl class="py class">
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<dt class="sig sig-object py" id="mlx.optimizers.Adam">
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<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mlx.optimizers.</span></span><span class="sig-name descname"><span class="pre">Adam</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">learning_rate</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">betas</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.List" title="(in Python v3.12)"><span class="pre">List</span></a><span class="p"><span class="pre">[</span></span><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">[0.9,</span> <span class="pre">0.999]</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-08</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx.optimizers.Adam" title="Permalink to this definition"></a></dt>
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<dd><p>Implementation of the Adam optimizer [1].</p>
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<p>Our Adam implementation follows the original paper and omits the bias
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correction in the first and second moment estimates. In detail,</p>
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<div class="math notranslate nohighlight">
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\[\begin{split}m_{t+1} &= \beta_1 m_t + (1 - \beta_1) g_t \\
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v_{t+1} &= \beta_2 v_t + (1 - \beta_2) g_t^2 \\
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w_{t+1} &= w_t - \lambda \frac{m_{t+1}}{\sqrt{v_{t+1} + \epsilon}}\end{split}\]</div>
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<p>[1]: Kingma, D.P. and Ba, J., 2015. Adam: A method for stochastic
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optimization. ICLR 2015.</p>
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<p class="rubric">Methods</p>
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<table class="autosummary longtable docutils align-default">
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<tbody>
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<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(learning_rate[, betas, eps])</p></td>
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<td><p></p></td>
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</tr>
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<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">apply_single</span></code>(gradient, parameter, state)</p></td>
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<td><p>Performs the Adam parameter update and stores <span class="math notranslate nohighlight">\(v\)</span> and <span class="math notranslate nohighlight">\(m\)</span> in the optimizer state.</p></td>
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</tr>
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