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<title>mlx_optimizers.ADOPT &#8212; mlx-optimizers 0.3.0 documentation</title>
<title>mlx_optimizers.ADOPT &#8212; mlx-optimizers 0.4.0 documentation</title>



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<li class="toctree-l2 current active"><a class="current reference internal" href="#">mlx_optimizers.ADOPT</a></li>
<li class="toctree-l2"><a class="reference internal" href="mlx_optimizers.DiffGrad.html">mlx_optimizers.DiffGrad</a></li>
<li class="toctree-l2"><a class="reference internal" href="mlx_optimizers.Muon.html">mlx_optimizers.Muon</a></li>
<li class="toctree-l2"><a class="reference internal" href="mlx_optimizers.MARS.html">mlx_optimizers.MARS</a></li>
<li class="toctree-l2"><a class="reference internal" href="mlx_optimizers.QHAdam.html">mlx_optimizers.QHAdam</a></li>
<li class="toctree-l2"><a class="reference internal" href="mlx_optimizers.MADGRAD.html">mlx_optimizers.MADGRAD</a></li>
<li class="toctree-l2"><a class="reference internal" href="mlx_optimizers.Lamb.html">mlx_optimizers.Lamb</a></li>
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<h1>mlx_optimizers.ADOPT<a class="headerlink" href="#mlx-optimizers-adopt" title="Link to this heading">#</a></h1>
<dl class="py class">
<dt class="sig sig-object py" id="mlx_optimizers.ADOPT">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ADOPT</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><span class="pre">array</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">array</span><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">0.9999]</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-06</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx_optimizers.ADOPT" title="Link to this definition">#</a></dt>
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ADOPT</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><span class="pre">array</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">array</span><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">0.9999]</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weight_decay</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">0.0</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-06</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx_optimizers.ADOPT" title="Link to this definition">#</a></dt>
<dd><p>ADaptive gradient method with the OPTimal convergence rate [1].</p>
<div class="math notranslate nohighlight">
\[\begin{split}v_0 &amp;= g_0^2, m_1 = g_1 / \max{\sqrt{v_0}, \epsilon} \\
Expand All @@ -354,9 +355,10 @@ <h1>mlx_optimizers.ADOPT<a class="headerlink" href="#mlx-optimizers-adopt" title
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>learning_rate</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> or </em><em>callable</em>) – The learning rate <span class="math notranslate nohighlight">\(\eta\)</span>.</p></li>
<li><p><strong>betas</strong> (<em>Tuple</em><em>[</em><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><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>, </em><em>optional</em>) – The coefficients
<li><p><strong>betas</strong> (<em>List</em><em>[</em><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><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>, </em><em>optional</em>) – The coefficients
<span class="math notranslate nohighlight">\((\beta_1, \beta_2)\)</span> used for computing running averages of the
gradient and its square. Default: <code class="docutils literal notranslate"><span class="pre">(0.9,</span> <span class="pre">0.9999)</span></code></p></li>
<li><p><strong>weight_decay</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 weight decay. Default: <code class="docutils literal notranslate"><span class="pre">0.0</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-6</span></code></p></li>
</ul>
Expand All @@ -368,7 +370,7 @@ <h1>mlx_optimizers.ADOPT<a class="headerlink" href="#mlx-optimizers-adopt" title
<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, ...])</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>
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<title>mlx_optimizers.DiffGrad &#8212; mlx-optimizers 0.4.0 documentation</title>



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