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Awni Hannun
2024-02-08 12:44:23 -08:00
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@@ -9,7 +9,7 @@
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" />
<title>Function Transforms &#8212; MLX 0.1.0 documentation</title>
<title>Function Transforms &#8212; MLX 0.2.0 documentation</title>
@@ -46,7 +46,7 @@
<script>DOCUMENTATION_OPTIONS.pagename = 'usage/function_transforms';</script>
<link rel="index" title="Index" href="../genindex.html" />
<link rel="search" title="Search" href="../search.html" />
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<meta name="viewport" content="width=device-width, initial-scale=1"/>
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@@ -134,8 +134,8 @@
<img src="../_static/mlx_logo.png" class="logo__image only-light" alt="MLX 0.1.0 documentation - Home"/>
<script>document.write(`<img src="../_static/mlx_logo.png" class="logo__image only-dark" alt="MLX 0.1.0 documentation - Home"/>`);</script>
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<script>document.write(`<img src="../_static/mlx_logo.png" class="logo__image only-dark" alt="MLX 0.2.0 documentation - Home"/>`);</script>
</a></div>
@@ -153,6 +153,7 @@
<li class="toctree-l1"><a class="reference internal" href="indexing.html">Indexing Arrays</a></li>
<li class="toctree-l1"><a class="reference internal" href="saving_and_loading.html">Saving and Loading Arrays</a></li>
<li class="toctree-l1 current active"><a class="current reference internal" href="#">Function Transforms</a></li>
<li class="toctree-l1"><a class="reference internal" href="compile.html">Compilation</a></li>
<li class="toctree-l1"><a class="reference internal" href="numpy.html">Conversion to NumPy and Other Frameworks</a></li>
<li class="toctree-l1"><a class="reference internal" href="using_streams.html">Using Streams</a></li>
</ul>
@@ -348,6 +349,9 @@
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@@ -379,6 +383,7 @@
<li class="toctree-l2"><a class="reference internal" href="../python/_autosummary/mlx.nn.value_and_grad.html">mlx.nn.value_and_grad</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../python/nn/_autosummary/mlx.nn.Module.training.html">mlx.nn.Module.training</a></li>
<li class="toctree-l3"><a class="reference internal" href="../python/nn/_autosummary/mlx.nn.Module.state.html">mlx.nn.Module.state</a></li>
<li class="toctree-l3"><a class="reference internal" href="../python/nn/_autosummary/mlx.nn.Module.apply.html">mlx.nn.Module.apply</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../python/nn/_autosummary/mlx.nn.Module.children.html">mlx.nn.Module.children</a></li>
@@ -451,6 +456,7 @@
<li class="toctree-l3"><a class="reference internal" href="../python/nn/_autosummary_functions/mlx.nn.losses.kl_div_loss.html">mlx.nn.losses.kl_div_loss</a></li>
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@@ -471,8 +477,13 @@
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<li class="toctree-l2"><a class="reference internal" href="../python/_autosummary/mlx.optimizers.Adagrad.html">mlx.optimizers.Adagrad</a></li>
@@ -484,7 +495,7 @@
<li class="toctree-l2"><a class="reference internal" href="../python/_autosummary/mlx.optimizers.Lion.html">mlx.optimizers.Lion</a></li>
</ul>
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<li class="toctree-l1 has-children"><a class="reference internal" href="../python/tree_utils.html">Tree Utils</a><input class="toctree-checkbox" id="toctree-checkbox-15" name="toctree-checkbox-15" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-15"><i class="fa-solid fa-chevron-down"></i></label><ul>
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@@ -676,9 +687,11 @@ document.write(`
<section id="function-transforms">
<span id="id1"></span><h1>Function Transforms<a class="headerlink" href="#function-transforms" title="Permalink to this heading">#</a></h1>
<p>MLX uses composable function transformations for automatic differentiation and
vectorization. The key idea behind composable function transformations is that
every transformation returns a function which can be further transformed.</p>
<p>MLX uses composable function transformations for automatic differentiation,
vectorization, and compute graph optimizations. To see the complete list of
function transformations check-out the <a class="reference internal" href="../python/transforms.html#transforms"><span class="std std-ref">API documentation</span></a>.</p>
<p>The key idea behind composable function transformations is that every
transformation returns a function which can be further transformed.</p>
<p>Here is a simple example:</p>
<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>&gt;&gt;&gt; <span class="nv">dfdx</span> <span class="o">=</span> mx.grad<span class="o">(</span>mx.sin<span class="o">)</span>
&gt;&gt;&gt; dfdx<span class="o">(</span>mx.array<span class="o">(</span>mx.pi<span class="o">))</span>
@@ -700,10 +713,9 @@ array<span class="o">(</span><span class="m">1</span>, <span class="nv">dtype</s
<p>Using <a class="reference internal" href="../python/_autosummary/mlx.core.grad.html#mlx.core.grad" title="mlx.core.grad"><code class="xref py py-func docutils literal notranslate"><span class="pre">grad()</span></code></a> on the output of <a class="reference internal" href="../python/_autosummary/mlx.core.grad.html#mlx.core.grad" title="mlx.core.grad"><code class="xref py py-func docutils literal notranslate"><span class="pre">grad()</span></code></a> is always ok. You keep
getting higher order derivatives.</p>
<p>Any of the MLX function transformations can be composed in any order to any
depth. To see the complete list of function transformations check-out the
<a class="reference internal" href="../python/transforms.html#transforms"><span class="std std-ref">API documentation</span></a>. See the following sections for more
information on <a class="reference internal" href="#auto-diff"><span class="std std-ref">automatic differentiaion</span></a> and
<a class="reference internal" href="#vmap"><span class="std std-ref">automatic vectorization</span></a>.</p>
depth. See the following sections for more information on <a class="reference internal" href="#auto-diff"><span class="std std-ref">automatic
differentiaion</span></a> and <a class="reference internal" href="#vmap"><span class="std std-ref">automatic vectorization</span></a>.
For more information on <a class="reference internal" href="../python/_autosummary/mlx.core.compile.html#mlx.core.compile" title="mlx.core.compile"><code class="xref py py-func docutils literal notranslate"><span class="pre">compile()</span></code></a> see the <a class="reference internal" href="compile.html#compile"><span class="std std-ref">compile documentation</span></a>.</p>
<section id="automatic-differentiation">
<h2>Automatic Differentiation<a class="headerlink" href="#automatic-differentiation" title="Permalink to this heading">#</a></h2>
<p id="auto-diff">Automatic differentiation in MLX works on functions rather than on implicit
@@ -844,11 +856,11 @@ vectorized version takes only <code class="docutils literal notranslate"><span c
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