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</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="linalg.html">Linear Algebra</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="_autosummary/mlx.core.linalg.inv.html">mlx.core.linalg.inv</a></li>
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</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="metal.html">Metal</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
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</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="nn.html">Neural Networks</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="_autosummary/mlx.nn.value_and_grad.html">mlx.nn.value_and_grad</a></li>
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<li class="toctree-l2 has-children"><a class="reference internal" href="nn/module.html">Module</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
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</details></li>
<li class="toctree-l2 has-children"><a class="reference internal" href="nn/layers.html">Layers</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.ALiBi.html">mlx.nn.ALiBi</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.AvgPool1d.html">mlx.nn.AvgPool1d</a></li>
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<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.BatchNorm.html">mlx.nn.BatchNorm</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.CELU.html">mlx.nn.CELU</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.Conv1d.html">mlx.nn.Conv1d</a></li>
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<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.Conv3d.html">mlx.nn.Conv3d</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.ConvTranspose1d.html">mlx.nn.ConvTranspose1d</a></li>
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<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.Dropout.html">mlx.nn.Dropout</a></li>
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<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.GELU.html">mlx.nn.GELU</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.GLU.html">mlx.nn.GLU</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.GroupNorm.html">mlx.nn.GroupNorm</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.GRU.html">mlx.nn.GRU</a></li>
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<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.HardTanh.html">mlx.nn.HardTanh</a></li>
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<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.LayerNorm.html">mlx.nn.LayerNorm</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.LeakyReLU.html">mlx.nn.LeakyReLU</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.Linear.html">mlx.nn.Linear</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.LogSigmoid.html">mlx.nn.LogSigmoid</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.LogSoftmax.html">mlx.nn.LogSoftmax</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.LSTM.html">mlx.nn.LSTM</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.MaxPool1d.html">mlx.nn.MaxPool1d</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.MaxPool2d.html">mlx.nn.MaxPool2d</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.Mish.html">mlx.nn.Mish</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.MultiHeadAttention.html">mlx.nn.MultiHeadAttention</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.PReLU.html">mlx.nn.PReLU</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.QuantizedEmbedding.html">mlx.nn.QuantizedEmbedding</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.QuantizedLinear.html">mlx.nn.QuantizedLinear</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.RMSNorm.html">mlx.nn.RMSNorm</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.ReLU.html">mlx.nn.ReLU</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.ReLU6.html">mlx.nn.ReLU6</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.RNN.html">mlx.nn.RNN</a></li>
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<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.SinusoidalPositionalEncoding.html">mlx.nn.SinusoidalPositionalEncoding</a></li>
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<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.Softshrink.html">mlx.nn.Softshrink</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.Softsign.html">mlx.nn.Softsign</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.Softmax.html">mlx.nn.Softmax</a></li>
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<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary/mlx.nn.Tanh.html">mlx.nn.Tanh</a></li>
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<li class="toctree-l2 has-children"><a class="reference internal" href="nn/functions.html">Functions</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.elu.html">mlx.nn.elu</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.celu.html">mlx.nn.celu</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.gelu.html">mlx.nn.gelu</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.gelu_approx.html">mlx.nn.gelu_approx</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.gelu_fast_approx.html">mlx.nn.gelu_fast_approx</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.glu.html">mlx.nn.glu</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.hard_shrink.html">mlx.nn.hard_shrink</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.hard_tanh.html">mlx.nn.hard_tanh</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.hardswish.html">mlx.nn.hardswish</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.leaky_relu.html">mlx.nn.leaky_relu</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.log_sigmoid.html">mlx.nn.log_sigmoid</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.log_softmax.html">mlx.nn.log_softmax</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.mish.html">mlx.nn.mish</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.prelu.html">mlx.nn.prelu</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.relu.html">mlx.nn.relu</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.relu6.html">mlx.nn.relu6</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.selu.html">mlx.nn.selu</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.sigmoid.html">mlx.nn.sigmoid</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.silu.html">mlx.nn.silu</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.softmax.html">mlx.nn.softmax</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.softmin.html">mlx.nn.softmin</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.softplus.html">mlx.nn.softplus</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.softshrink.html">mlx.nn.softshrink</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.step.html">mlx.nn.step</a></li>
<li class="toctree-l3"><a class="reference internal" href="nn/_autosummary_functions/mlx.nn.tanh.html">mlx.nn.tanh</a></li>
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</details></li>
<li class="toctree-l2 has-children"><a class="reference internal" href="nn/losses.html">Loss Functions</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
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<h1>Optimizers</h1>
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<h2> Contents </h2>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#saving-and-loading">Saving and Loading</a><ul class="visible nav section-nav flex-column">
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<section id="optimizers">
<span id="id1"></span><h1>Optimizers<a class="headerlink" href="#optimizers" title="Link to this heading">#</a></h1>
<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
<code class="xref py py-mod docutils literal notranslate"><span class="pre">mlx.core</span></code> functions. A typical example involves calling
<a class="reference internal" href="optimizers/_autosummary/mlx.optimizers.Optimizer.update.html#mlx.optimizers.Optimizer.update" title="mlx.optimizers.Optimizer.update"><code class="xref py py-meth docutils literal notranslate"><span class="pre">Optimizer.update()</span></code></a> to update a model’s parameters based on the loss
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
model’s parameters and the <strong>optimizer state</strong>.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Create a model</span>
<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>
<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="c1"># Create the gradient function and the optimizer</span>
<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>
<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>
<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>
<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>
<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>
<span class="c1"># Update the model with the gradients. So far no computation has happened.</span>
<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>
<span class="c1"># Compute the new parameters but also the optimizer state.</span>
<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>
</pre></div>
</div>
<section id="saving-and-loading">
<h2>Saving and Loading<a class="headerlink" href="#saving-and-loading" title="Link to this heading">#</a></h2>
<p>To serialize an optimizer, save its state. To load an optimizer, load and set
the saved state. Here’s a simple example:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">mlx.core</span> <span class="k">as</span> <span class="nn">mx</span>
<span class="kn">from</span> <span class="nn">mlx.utils</span> <span class="kn">import</span> <span class="n">tree_flatten</span><span class="p">,</span> <span class="n">tree_unflatten</span>
<span class="kn">import</span> <span class="nn">mlx.optimizers</span> <span class="k">as</span> <span class="nn">optim</span>
<span class="n">optimizer</span> <span class="o">=</span> <span class="n">optim</span><span class="o">.</span><span class="n">Adam</span><span class="p">(</span><span class="n">learning_rate</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">)</span>
<span class="c1"># Perform some updates with the optimizer</span>
<span class="n">model</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;w&quot;</span> <span class="p">:</span> <span class="n">mx</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">))}</span>
<span class="n">grads</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;w&quot;</span> <span class="p">:</span> <span class="n">mx</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">))}</span>
<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>
<span class="c1"># Save the state</span>
<span class="n">state</span> <span class="o">=</span> <span class="n">tree_flatten</span><span class="p">(</span><span class="n">optimizer</span><span class="o">.</span><span class="n">state</span><span class="p">)</span>
<span class="n">mx</span><span class="o">.</span><span class="n">save_safetensors</span><span class="p">(</span><span class="s2">&quot;optimizer.safetensors&quot;</span><span class="p">,</span> <span class="nb">dict</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
<span class="c1"># Later on, for example when loading from a checkpoint,</span>
<span class="c1"># recreate the optimizer and load the state</span>
<span class="n">optimizer</span> <span class="o">=</span> <span class="n">optim</span><span class="o">.</span><span class="n">Adam</span><span class="p">(</span><span class="n">learning_rate</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">)</span>
<span class="n">state</span> <span class="o">=</span> <span class="n">tree_unflatten</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">mx</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="s2">&quot;optimizer.safetensors&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">items</span><span class="p">()))</span>
<span class="n">optimizer</span><span class="o">.</span><span class="n">state</span> <span class="o">=</span> <span class="n">state</span>
</pre></div>
</div>
<p>Note, not every optimizer configuation parameter is saved in the state. For
example, for Adam the learning rate is saved but the <code class="docutils literal notranslate"><span class="pre">betas</span></code> and <code class="docutils literal notranslate"><span class="pre">eps</span></code>
parameters are not. A good rule of thumb is if the parameter can be scheduled
then it will be included in the optimizer state.</p>
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<li class="toctree-l1"><a class="reference internal" href="optimizers/schedulers.html">Schedulers</a><ul>
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<li class="toctree-l3"><a class="reference internal" href="optimizers/_autosummary/mlx.optimizers.cosine_decay.html#mlx.optimizers.cosine_decay"><code class="docutils literal notranslate"><span class="pre">cosine_decay()</span></code></a></li>
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<li class="toctree-l3"><a class="reference internal" href="optimizers/_autosummary/mlx.optimizers.exponential_decay.html#mlx.optimizers.exponential_decay"><code class="docutils literal notranslate"><span class="pre">exponential_decay()</span></code></a></li>
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<li class="toctree-l2"><a class="reference internal" href="optimizers/_autosummary/mlx.optimizers.join_schedules.html">mlx.optimizers.join_schedules</a><ul>
<li class="toctree-l3"><a class="reference internal" href="optimizers/_autosummary/mlx.optimizers.join_schedules.html#mlx.optimizers.join_schedules"><code class="docutils literal notranslate"><span class="pre">join_schedules()</span></code></a></li>
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<li class="toctree-l2"><a class="reference internal" href="optimizers/_autosummary/mlx.optimizers.linear_schedule.html">mlx.optimizers.linear_schedule</a><ul>
<li class="toctree-l3"><a class="reference internal" href="optimizers/_autosummary/mlx.optimizers.linear_schedule.html#mlx.optimizers.linear_schedule"><code class="docutils literal notranslate"><span class="pre">linear_schedule()</span></code></a></li>
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<li class="toctree-l2"><a class="reference internal" href="optimizers/_autosummary/mlx.optimizers.step_decay.html">mlx.optimizers.step_decay</a><ul>
<li class="toctree-l3"><a class="reference internal" href="optimizers/_autosummary/mlx.optimizers.step_decay.html#mlx.optimizers.step_decay"><code class="docutils literal notranslate"><span class="pre">step_decay()</span></code></a></li>
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<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary/mlx.optimizers.clip_grad_norm.html#mlx.optimizers.clip_grad_norm" title="mlx.optimizers.clip_grad_norm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">clip_grad_norm</span></code></a>(grads, max_norm)</p></td>
<td><p>Clips the global norm of the gradients.</p></td>
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