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<section id="optimizers">
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<span id="id1"></span><h1>Optimizers<a class="headerlink" href="#optimizers" title="Permalink to this heading"></a></h1>
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<p>The optimizers in MLX can be used both with <code class="xref py py-mod docutils literal notranslate"><span class="pre">mlx.nn</span></code> but also with pure
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<code class="xref py py-mod docutils literal notranslate"><span class="pre">mlx.core</span></code> functions. A typical example involves calling
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<code class="xref py py-meth docutils literal notranslate"><span class="pre">Optimizer.update()</span></code> to update a model’s parameters based on the loss
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gradients and subsequently calling <a class="reference internal" href="_autosummary/mlx.core.eval.html#mlx.core.eval" title="mlx.core.eval"><code class="xref py py-func docutils literal notranslate"><span class="pre">mlx.core.eval()</span></code></a> to evaluate both the
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model’s parameters and the <strong>optimizer state</strong>.</p>
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<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Create a model</span>
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<span class="n">model</span> <span class="o">=</span> <span class="n">MLP</span><span class="p">(</span><span class="n">num_layers</span><span class="p">,</span> <span class="n">train_images</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">hidden_dim</span><span class="p">,</span> <span class="n">num_classes</span><span class="p">)</span>
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<span class="n">mx</span><span class="o">.</span><span class="n">eval</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">parameters</span><span class="p">())</span>
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<span class="c1"># Create the gradient function and the optimizer</span>
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<span class="n">loss_and_grad_fn</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">value_and_grad</span><span class="p">(</span><span class="n">model</span><span class="p">,</span> <span class="n">loss_fn</span><span class="p">)</span>
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<span class="n">optimizer</span> <span class="o">=</span> <span class="n">optim</span><span class="o">.</span><span class="n">SGD</span><span class="p">(</span><span class="n">learning_rate</span><span class="o">=</span><span class="n">learning_rate</span><span class="p">)</span>
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<span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">num_epochs</span><span class="p">):</span>
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<span class="k">for</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">batch_iterate</span><span class="p">(</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">train_images</span><span class="p">,</span> <span class="n">train_labels</span><span class="p">):</span>
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<span class="n">loss</span><span class="p">,</span> <span class="n">grads</span> <span class="o">=</span> <span class="n">loss_and_grad_fn</span><span class="p">(</span><span class="n">model</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
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<span class="c1"># Update the model with the gradients. So far no computation has happened.</span>
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<span class="n">optimizer</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">model</span><span class="p">,</span> <span class="n">grads</span><span class="p">)</span>
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<span class="c1"># Compute the new parameters but also the optimizer state.</span>
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<span class="n">mx</span><span class="o">.</span><span class="n">eval</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">optimizer</span><span class="o">.</span><span class="n">state</span><span class="p">)</span>
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</pre></div>
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</div>
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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><a class="reference internal" href="_autosummary/mlx.optimizers.OptimizerState.html#mlx.optimizers.OptimizerState" title="mlx.optimizers.OptimizerState"><code class="xref py py-obj docutils literal notranslate"><span class="pre">OptimizerState</span></code></a></p></td>
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<td><p>The optimizer state implements a recursively defined <a class="reference external" href="https://docs.python.org/3/library/collections.html#collections.defaultdict" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">collections.defaultdict</span></code></a>, namely a missing key in an optimizer state is an <a class="reference internal" href="_autosummary/mlx.optimizers.OptimizerState.html#mlx.optimizers.OptimizerState" title="mlx.optimizers.OptimizerState"><code class="xref py py-class docutils literal notranslate"><span class="pre">OptimizerState</span></code></a>.</p></td>
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</tr>
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<tr class="row-even"><td><p><a class="reference internal" href="_autosummary/mlx.optimizers.Optimizer.html#mlx.optimizers.Optimizer" title="mlx.optimizers.Optimizer"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Optimizer</span></code></a>()</p></td>
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<td><p>The base class for all optimizers.</p></td>
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</tr>
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<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary/mlx.optimizers.SGD.html#mlx.optimizers.SGD" title="mlx.optimizers.SGD"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SGD</span></code></a>(learning_rate[, momentum])</p></td>
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<td><p>Stochastic gradient descent optimizer.</p></td>
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</tr>
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<tr class="row-even"><td><p><a class="reference internal" href="_autosummary/mlx.optimizers.Adam.html#mlx.optimizers.Adam" title="mlx.optimizers.Adam"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Adam</span></code></a>(learning_rate[, betas, eps])</p></td>
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<td><p>Implementation of the Adam optimizer [1].</p></td>
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