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<title>mlx.optimizers.Adam &#8212; MLX 0.21.0 documentation</title>
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<h1>mlx.optimizers.Adam<a class="headerlink" href="#mlx-optimizers-adam" title="Link to this heading">#</a></h1>
<dl class="py class">
<dt class="sig sig-object py" id="mlx.optimizers.Adam">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><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 v3.13)"><span class="pre">float</span></a><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Callable" title="(in Python v3.13)"><span class="pre">Callable</span></a><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="../../_autosummary/mlx.core.array.html#mlx.core.array" title="mlx.core.array"><span class="pre">array</span></a><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference internal" href="../../_autosummary/mlx.core.array.html#mlx.core.array" title="mlx.core.array"><span class="pre">array</span></a><span class="p"><span class="pre">]</span></span></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 v3.13)"><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 v3.13)"><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 v3.13)"><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="Link to this definition">#</a></dt>
<dd><p>The Adam optimizer [1].</p>
<p>Our Adam implementation follows the original paper and omits the bias
correction in the first and second moment estimates. In detail,</p>
<em class="property"><span class="pre">class</span><span class="w"> </span></em><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 v3.13)"><span class="pre">float</span></a><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Callable" title="(in Python v3.13)"><span class="pre">Callable</span></a><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="../../_autosummary/mlx.core.array.html#mlx.core.array" title="mlx.core.array"><span class="pre">array</span></a><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference internal" href="../../_autosummary/mlx.core.array.html#mlx.core.array" title="mlx.core.array"><span class="pre">array</span></a><span class="p"><span class="pre">]</span></span></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 v3.13)"><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 v3.13)"><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 v3.13)"><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>, <em class="sig-param"><span class="n"><span class="pre">bias_correction</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#bool" title="(in Python v3.13)"><span class="pre">bool</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">False</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx.optimizers.Adam" title="Link to this definition">#</a></dt>
<dd><p>The Adam optimizer [1]. In detail,</p>
<p>[1]: Kingma, D.P. and Ba, J., 2015. Adam: A method for stochastic
optimization. ICLR 2015.</p>
<div class="math notranslate nohighlight">
@@ -886,13 +884,15 @@ w_{t+1} &amp;= w_t - \lambda \frac{m_{t+1}}{\sqrt{v_{t+1} + \epsilon}}\end{split
gradient and its square. Default: <code class="docutils literal notranslate"><span class="pre">(0.9,</span> <span class="pre">0.999)</span></code></p></li>
<li><p><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)"><em>float</em></a><em>, </em><em>optional</em>) – The term <span class="math notranslate nohighlight">\(\epsilon\)</span> added to the
denominator to improve numerical stability. Default: <code class="docutils literal notranslate"><span class="pre">1e-8</span></code></p></li>
<li><p><strong>bias_correction</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.13)"><em>bool</em></a><em>, </em><em>optional</em>) – If set to <code class="docutils literal notranslate"><span class="pre">True</span></code>, bias correction
is applied. Default: <code class="docutils literal notranslate"><span class="pre">False</span></code></p></li>
</ul>
</dd>
</dl>
<p class="rubric">Methods</p>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<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>
<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>
<td><p></p></td>
</tr>
<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>