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<li class="toctree-l1"><a class="reference internal" href="amp_examples.html">CUDA Automatic Mixed Precision examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="autograd.html">Autograd mechanics</a></li>
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<section id="extending-pytorch">
<h1>Extending PyTorch<a class="headerlink" href="#extending-pytorch" title="Permalink to this heading">¶</a></h1>
<p>In this note we’ll cover ways of extending <a class="reference internal" href="../nn.html#module-torch.nn" title="torch.nn"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.nn</span></code></a>,
<a class="reference internal" href="../torch.html#module-torch.autograd" title="torch.autograd"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.autograd</span></code></a>, <a class="reference internal" href="../torch.html#module-torch" title="torch"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch</span></code></a>, and writing custom C extensions utilizing our C
libraries.</p>
<section id="extending-torch-autograd">
<span id="extending-autograd"></span><h2>Extending <a class="reference internal" href="../torch.html#module-torch.autograd" title="torch.autograd"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.autograd</span></code></a><a class="headerlink" href="#extending-torch-autograd" title="Permalink to this heading">¶</a></h2>
<p>Adding operations to <a class="reference internal" href="../torch.html#module-torch.autograd" title="torch.autograd"><code class="xref py py-mod docutils literal notranslate"><span class="pre">autograd</span></code></a> requires implementing a new
<a class="reference internal" href="../autograd.html#torch.autograd.Function" title="torch.autograd.Function"><code class="xref py py-class docutils literal notranslate"><span class="pre">Function</span></code></a> subclass for each operation. Recall that Functions
are what <a class="reference internal" href="../torch.html#module-torch.autograd" title="torch.autograd"><code class="xref py py-mod docutils literal notranslate"><span class="pre">autograd</span></code></a> uses to encode the operation history and compute
gradients.</p>
<p>The first part of this doc is focused on backward mode AD as it is the most widely used
feature. A section at the end discusses the extensions for forward mode AD.</p>
<section id="when-to-use">
<h3>When to use<a class="headerlink" href="#when-to-use" title="Permalink to this heading">¶</a></h3>
<p>In general, implement a custom function if you want to perform computations in your model
that are not differentiable or rely on non-PyTorch libraries (e.g., NumPy), but
still wish for your operation to chain with other ops and work with the autograd engine.</p>
<p>In some situations, custom functions can also be used to improve performance and
memory usage: If you implemented your forward and backward passes using a
<a class="reference external" href="https://pytorch.org/tutorials/advanced/cpp_extension.html">C++ extension</a>,
you can wrap them in <a class="reference internal" href="../autograd.html#torch.autograd.Function" title="torch.autograd.Function"><code class="xref py py-class docutils literal notranslate"><span class="pre">Function</span></code></a> to interface with the autograd
engine. If you’d like to reduce the number of buffers saved for the backward pass,
custom functions can be used to combine ops together.</p>
</section>
<section id="when-not-to-use">
<h3>When not to use<a class="headerlink" href="#when-not-to-use" title="Permalink to this heading">¶</a></h3>
<p>If you can already write your function in terms of PyTorch’s built-in ops, its
backward graph is (most likely) already able to be recorded by autograd. In this case, you do
not need to implement the backward function yourself. Consider using a plain
old Python function.</p>
<p>If you need to maintain state, i.e., trainable parameters, you should (also) use a
custom module. See the section below for more information on extending <a class="reference internal" href="../nn.html#module-torch.nn" title="torch.nn"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.nn</span></code></a>.</p>
<p>If you’d like to alter the gradients during the backward pass or perform a side
effect, consider registering a
<a class="reference external" href="https://pytorch.org/docs/stable/generated/torch.Tensor.register_hook.html#torch.Tensor.register_hook">tensor</a> or
<a class="reference external" href="https://pytorch.org/docs/stable/notes/modules.html#module-hooks">Module</a> hook.</p>
</section>
<section id="how-to-use">
<h3>How to use<a class="headerlink" href="#how-to-use" title="Permalink to this heading">¶</a></h3>
<p>Take the following steps:
1. Subclass <a class="reference internal" href="../autograd.html#torch.autograd.Function" title="torch.autograd.Function"><code class="xref py py-class docutils literal notranslate"><span class="pre">Function</span></code></a> and implement the <a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a>,
(optional) <code class="xref py py-meth docutils literal notranslate"><span class="pre">setup_context()</span></code> and
<a class="reference internal" href="../generated/torch.autograd.Function.backward.html#torch.autograd.Function.backward" title="torch.autograd.Function.backward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">backward()</span></code></a> methods.
2. Call the proper methods on the <cite>ctx</cite> argument.
3. Declare whether your function supports
<a class="reference external" href="https://pytorch.org/tutorials/intermediate/custom_function_double_backward_tutorial.html">double backward</a>.
4. Validate whether your gradients are correct using gradcheck.</p>
<p><strong>Step 1:</strong> After subclassing <a class="reference internal" href="../autograd.html#torch.autograd.Function" title="torch.autograd.Function"><code class="xref py py-class docutils literal notranslate"><span class="pre">Function</span></code></a>, you’ll need to define 3 methods:</p>
<ul class="simple">
<li><p><a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a> is the code that performs the operation. It can take
as many arguments as you want, with some of them being optional, if you
specify the default values. All kinds of Python objects are accepted here.
<code class="xref py py-class docutils literal notranslate"><span class="pre">Tensor</span></code> arguments that track history (i.e., with
<code class="docutils literal notranslate"><span class="pre">requires_grad=True</span></code>) will be converted to ones that don’t track history
before the call, and their use will be registered in the graph. Note that this
logic won’t traverse lists/dicts/any other data structures and will only
consider tensors that are direct arguments to the call. You can
return either a single <code class="xref py py-class docutils literal notranslate"><span class="pre">Tensor</span></code> output, or a <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a> of
tensors if there are multiple outputs. Also, please refer to the
docs of <a class="reference internal" href="../autograd.html#torch.autograd.Function" title="torch.autograd.Function"><code class="xref py py-class docutils literal notranslate"><span class="pre">Function</span></code></a> to find descriptions of useful methods that can be
called only from <a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a>.</p></li>
<li><p><code class="xref py py-meth docutils literal notranslate"><span class="pre">setup_context()</span></code> (optional). One can either write a “combined” <a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a> that
accepts a <code class="docutils literal notranslate"><span class="pre">ctx</span></code> object or (as of PyTorch 2.0) a separate <a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a> that does
not accept <code class="docutils literal notranslate"><span class="pre">ctx</span></code> and a <code class="xref py py-meth docutils literal notranslate"><span class="pre">setup_context()</span></code> method where the <code class="docutils literal notranslate"><span class="pre">ctx</span></code> modification happens.
The <a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a> should have the compute and <code class="xref py py-meth docutils literal notranslate"><span class="pre">setup_context()</span></code> should
only be responsible for the <code class="docutils literal notranslate"><span class="pre">ctx</span></code> modification (and not have any compute).
In general the separate <a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a> and <code class="xref py py-meth docutils literal notranslate"><span class="pre">setup_context()</span></code> is closer to how
PyTorch native operations work and therefore more composable with various PyTorch subsystems.
See <a class="reference internal" href="#combining-forward-context"><span class="std std-ref">Combined or separate forward() and setup_context()</span></a> for more details.</p></li>
<li><p><a class="reference internal" href="../generated/torch.autograd.Function.backward.html#torch.autograd.Function.backward" title="torch.autograd.Function.backward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">backward()</span></code></a> (or <code class="xref py py-meth docutils literal notranslate"><span class="pre">vjp()</span></code>) defines the gradient formula.
It will be given as many <code class="xref py py-class docutils literal notranslate"><span class="pre">Tensor</span></code> arguments as there were outputs, with each
of them representing gradient w.r.t. that output. It is important NEVER to modify
these in-place. It should return as many tensors as there
were inputs, with each of them containing the gradient w.r.t. its
corresponding input. If your inputs didn’t require gradient
(<code class="xref py py-attr docutils literal notranslate"><span class="pre">needs_input_grad</span></code> is a tuple of booleans indicating
whether each input needs gradient computation), or were non-<code class="xref py py-class docutils literal notranslate"><span class="pre">Tensor</span></code>
objects, you can return <code class="xref py py-class docutils literal notranslate"><span class="pre">python:None</span></code>. Also, if you have optional
arguments to <a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a> you can return more gradients than there
were inputs, as long as they’re all <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="docutils literal notranslate"><span class="pre">None</span></code></a>.</p></li>
</ul>
<p><strong>Step 2:</strong> It is your responsibility to use the functions in <code class="docutils literal notranslate"><span class="pre">ctx</span></code>
properly in order to ensure that the new <a class="reference internal" href="../autograd.html#torch.autograd.Function" title="torch.autograd.Function"><code class="xref py py-class docutils literal notranslate"><span class="pre">Function</span></code></a> works properly with
the autograd engine.</p>
<ul class="simple">
<li><p><a class="reference internal" href="../generated/torch.autograd.function.FunctionCtx.save_for_backward.html#torch.autograd.function.FunctionCtx.save_for_backward" title="torch.autograd.function.FunctionCtx.save_for_backward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">save_for_backward()</span></code></a> must be
used to save any tensors to be used in the backward pass. Non-tensors should
be stored directly on <cite>ctx</cite>. If tensors that are neither input nor output
are saved for backward your <a class="reference internal" href="../autograd.html#torch.autograd.Function" title="torch.autograd.Function"><code class="xref py py-class docutils literal notranslate"><span class="pre">Function</span></code></a> may not support double backward
(see step 3).</p></li>
<li><p><a class="reference internal" href="../generated/torch.autograd.function.FunctionCtx.mark_dirty.html#torch.autograd.function.FunctionCtx.mark_dirty" title="torch.autograd.function.FunctionCtx.mark_dirty"><code class="xref py py-meth docutils literal notranslate"><span class="pre">mark_dirty()</span></code></a> must be used to
mark any input that is modified inplace by the forward function.</p></li>
<li><p><a class="reference internal" href="../generated/torch.autograd.function.FunctionCtx.mark_non_differentiable.html#torch.autograd.function.FunctionCtx.mark_non_differentiable" title="torch.autograd.function.FunctionCtx.mark_non_differentiable"><code class="xref py py-meth docutils literal notranslate"><span class="pre">mark_non_differentiable()</span></code></a> must
be used to tell the engine if an output is not differentiable. By
default all output tensors that are of differentiable type will be set
to require gradient. Tensors of non-differentiable type (i.e., integral types)
are never marked as requiring gradients.</p></li>
<li><p><a class="reference internal" href="../generated/torch.autograd.function.FunctionCtx.set_materialize_grads.html#torch.autograd.function.FunctionCtx.set_materialize_grads" title="torch.autograd.function.FunctionCtx.set_materialize_grads"><code class="xref py py-meth docutils literal notranslate"><span class="pre">set_materialize_grads()</span></code></a> can be
used to tell the autograd engine to optimize gradient computations in the cases where
the output does not depend on the input by not materializing grad tensors given to backward
function. That is, if set to False, None object in python or “undefined tensor” (tensor x for
which x.defined() is False) in C++ will not be converted to a tensor filled with zeros prior
to calling backward, and so your code will need to handle such objects as if they were
tensors filled with zeros. The default value of this setting is True.</p></li>
</ul>
<p><strong>Step 3:</strong> If your <a class="reference internal" href="../autograd.html#torch.autograd.Function" title="torch.autograd.Function"><code class="xref py py-class docutils literal notranslate"><span class="pre">Function</span></code></a> does not support double backward
you should explicitly declare this by decorating backward with the
<code class="xref py py-func docutils literal notranslate"><span class="pre">once_differentiable()</span></code>. With this decorator, attempts to
perform double backward through your function will produce an error.
See our double backward tutorial for more information on double backward.</p>
<p><strong>Step 4:</strong> It is recommended that you use <a class="reference internal" href="../generated/torch.autograd.gradcheck.html#torch.autograd.gradcheck" title="torch.autograd.gradcheck"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.autograd.gradcheck()</span></code></a>
to check whether your backward function correctly computes gradients of the
forward by computing the Jacobian matrix using your backward function and
comparing the value element-wise with the Jacobian computed numerically using
finite-differencing.</p>
</section>
<section id="example">
<h3>Example<a class="headerlink" href="#example" title="Permalink to this heading">¶</a></h3>
<p>Below you can find code for a <code class="docutils literal notranslate"><span class="pre">Linear</span></code> function, with
additional comments:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Inherit from Function</span>
<span class="k">class</span> <span class="nc">LinearFunction</span><span class="p">(</span><span class="n">Function</span><span class="p">):</span>
<span class="c1"># Note that forward, setup_context, and backward are @staticmethods</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="n">weight</span><span class="p">,</span> <span class="n">bias</span><span class="p">):</span>
<span class="n">output</span> <span class="o">=</span> <span class="nb">input</span><span class="o">.</span><span class="n">mm</span><span class="p">(</span><span class="n">weight</span><span class="o">.</span><span class="n">t</span><span class="p">())</span>
<span class="k">if</span> <span class="n">bias</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">output</span> <span class="o">+=</span> <span class="n">bias</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">expand_as</span><span class="p">(</span><span class="n">output</span><span class="p">)</span>
<span class="k">return</span> <span class="n">output</span>
<span class="nd">@staticmethod</span>
<span class="c1"># inputs is a Tuple of all of the inputs passed to forward.</span>
<span class="c1"># output is the output of the forward().</span>
<span class="k">def</span> <span class="nf">setup_context</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">inputs</span><span class="p">,</span> <span class="n">output</span><span class="p">):</span>
<span class="nb">input</span><span class="p">,</span> <span class="n">weight</span><span class="p">,</span> <span class="n">bias</span> <span class="o">=</span> <span class="n">inputs</span>
<span class="n">ctx</span><span class="o">.</span><span class="n">save_for_backward</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="n">weight</span><span class="p">,</span> <span class="n">bias</span><span class="p">)</span>
<span class="c1"># This function has only a single output, so it gets only one gradient</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">backward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">grad_output</span><span class="p">):</span>
<span class="c1"># This is a pattern that is very convenient - at the top of backward</span>
<span class="c1"># unpack saved_tensors and initialize all gradients w.r.t. inputs to</span>
<span class="c1"># None. Thanks to the fact that additional trailing Nones are</span>
<span class="c1"># ignored, the return statement is simple even when the function has</span>
<span class="c1"># optional inputs.</span>
<span class="nb">input</span><span class="p">,</span> <span class="n">weight</span><span class="p">,</span> <span class="n">bias</span> <span class="o">=</span> <span class="n">ctx</span><span class="o">.</span><span class="n">saved_tensors</span>
<span class="n">grad_input</span> <span class="o">=</span> <span class="n">grad_weight</span> <span class="o">=</span> <span class="n">grad_bias</span> <span class="o">=</span> <span class="kc">None</span>
<span class="c1"># These needs_input_grad checks are optional and there only to</span>
<span class="c1"># improve efficiency. If you want to make your code simpler, you can</span>
<span class="c1"># skip them. Returning gradients for inputs that don't require it is</span>
<span class="c1"># not an error.</span>
<span class="k">if</span> <span class="n">ctx</span><span class="o">.</span><span class="n">needs_input_grad</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
<span class="n">grad_input</span> <span class="o">=</span> <span class="n">grad_output</span><span class="o">.</span><span class="n">mm</span><span class="p">(</span><span class="n">weight</span><span class="p">)</span>
<span class="k">if</span> <span class="n">ctx</span><span class="o">.</span><span class="n">needs_input_grad</span><span class="p">[</span><span class="mi">1</span><span class="p">]:</span>
<span class="n">grad_weight</span> <span class="o">=</span> <span class="n">grad_output</span><span class="o">.</span><span class="n">t</span><span class="p">()</span><span class="o">.</span><span class="n">mm</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
<span class="k">if</span> <span class="n">bias</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">ctx</span><span class="o">.</span><span class="n">needs_input_grad</span><span class="p">[</span><span class="mi">2</span><span class="p">]:</span>
<span class="n">grad_bias</span> <span class="o">=</span> <span class="n">grad_output</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="k">return</span> <span class="n">grad_input</span><span class="p">,</span> <span class="n">grad_weight</span><span class="p">,</span> <span class="n">grad_bias</span>
</pre></div>
</div>
<p>Now, to make it easier to use these custom ops, we recommend either aliasing
them or wrapping them in a function. Wrapping in a function lets us support
default arguments and keyword arguments:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Option 1: alias</span>
<span class="n">linear</span> <span class="o">=</span> <span class="n">LinearFunction</span><span class="o">.</span><span class="n">apply</span>
<span class="c1"># Option 2: wrap in a function, to support default args and keyword args.</span>
<span class="k">def</span> <span class="nf">linear</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="n">weight</span><span class="p">,</span> <span class="n">bias</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="k">return</span> <span class="n">LinearFunction</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="n">weight</span><span class="p">,</span> <span class="n">bias</span><span class="p">)</span>
</pre></div>
</div>
<p>Here, we give an additional example of a function that is parametrized by
non-Tensor arguments:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">MulConstant</span><span class="p">(</span><span class="n">Function</span><span class="p">):</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="n">tensor</span><span class="p">,</span> <span class="n">constant</span><span class="p">):</span>
<span class="k">return</span> <span class="n">tensor</span> <span class="o">*</span> <span class="n">constant</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">setup_context</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">inputs</span><span class="p">,</span> <span class="n">output</span><span class="p">):</span>
<span class="c1"># ctx is a context object that can be used to stash information</span>
<span class="c1"># for backward computation</span>
<span class="n">tensor</span><span class="p">,</span> <span class="n">constant</span> <span class="o">=</span> <span class="n">inputs</span>
<span class="n">ctx</span><span class="o">.</span><span class="n">constant</span> <span class="o">=</span> <span class="n">constant</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">backward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">grad_output</span><span class="p">):</span>
<span class="c1"># We return as many input gradients as there were arguments.</span>
<span class="c1"># Gradients of non-Tensor arguments to forward must be None.</span>
<span class="k">return</span> <span class="n">grad_output</span> <span class="o">*</span> <span class="n">ctx</span><span class="o">.</span><span class="n">constant</span><span class="p">,</span> <span class="kc">None</span>
</pre></div>
</div>
<p>And here, we optimize the above example by calling set_materialize_grads(False):</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">MulConstant</span><span class="p">(</span><span class="n">Function</span><span class="p">):</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="n">tensor</span><span class="p">,</span> <span class="n">constant</span><span class="p">):</span>
<span class="k">return</span> <span class="n">tensor</span> <span class="o">*</span> <span class="n">constant</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">setup_context</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">inputs</span><span class="p">,</span> <span class="n">output</span><span class="p">):</span>
<span class="n">tensor</span><span class="p">,</span> <span class="n">constant</span> <span class="o">=</span> <span class="n">inputs</span>
<span class="n">ctx</span><span class="o">.</span><span class="n">set_materialize_grads</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
<span class="n">ctx</span><span class="o">.</span><span class="n">constant</span> <span class="o">=</span> <span class="n">constant</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">backward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">grad_output</span><span class="p">):</span>
<span class="c1"># Here we must handle None grad_output tensor. In this case we</span>
<span class="c1"># can skip unnecessary computations and just return None.</span>
<span class="k">if</span> <span class="n">grad_output</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">return</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span>
<span class="c1"># We return as many input gradients as there were arguments.</span>
<span class="c1"># Gradients of non-Tensor arguments to forward must be None.</span>
<span class="k">return</span> <span class="n">grad_output</span> <span class="o">*</span> <span class="n">ctx</span><span class="o">.</span><span class="n">constant</span><span class="p">,</span> <span class="kc">None</span>
</pre></div>
</div>
<p>If you need any “intermediate” Tensors computed in <a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a> to be saved,
either they must be returned as outputs, or combine <code class="docutils literal notranslate"><span class="pre">forward</span></code> and <code class="xref py py-meth docutils literal notranslate"><span class="pre">setup_context()</span></code>
(see <a class="reference internal" href="#combining-forward-context"><span class="std std-ref">Combined or separate forward() and setup_context()</span></a>).
Note that this means if you want gradients to flow through those intermediate values, you
need to define the gradient formula for them (see also
<a class="reference external" href="https://pytorch.org/tutorials/intermediate/custom_function_double_backward_tutorial.html">the double backward tutorial</a>
):</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">MyCube</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">autograd</span><span class="o">.</span><span class="n">Function</span><span class="p">):</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="c1"># We wish to save dx for backward. In order to do so, it must</span>
<span class="c1"># be returned as an output.</span>
<span class="n">dx</span> <span class="o">=</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">x</span> <span class="o">**</span> <span class="mi">2</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">x</span> <span class="o">**</span> <span class="mi">3</span>
<span class="k">return</span> <span class="n">result</span><span class="p">,</span> <span class="n">dx</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">setup_context</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">inputs</span><span class="p">,</span> <span class="n">output</span><span class="p">):</span>
<span class="n">x</span><span class="p">,</span> <span class="o">=</span> <span class="n">inputs</span>
<span class="n">result</span><span class="p">,</span> <span class="n">dx</span> <span class="o">=</span> <span class="n">output</span>
<span class="n">ctx</span><span class="o">.</span><span class="n">save_for_backward</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dx</span><span class="p">)</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">backward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">grad_output</span><span class="p">,</span> <span class="n">grad_dx</span><span class="p">):</span>
<span class="n">x</span><span class="p">,</span> <span class="n">dx</span> <span class="o">=</span> <span class="n">ctx</span><span class="o">.</span><span class="n">saved_tensors</span>
<span class="c1"># In order for the autograd.Function to work with higher-order</span>
<span class="c1"># gradients, we must add the gradient contribution of `dx`,</span>
<span class="c1"># which is grad_dx * 6 * x.</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">grad_output</span> <span class="o">*</span> <span class="n">dx</span> <span class="o">+</span> <span class="n">grad_dx</span> <span class="o">*</span> <span class="mi">6</span> <span class="o">*</span> <span class="n">x</span>
<span class="k">return</span> <span class="n">result</span>
<span class="c1"># Wrap MyCube in a function so that it is clearer what the output is</span>
<span class="k">def</span> <span class="nf">my_cube</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="n">result</span><span class="p">,</span> <span class="n">dx</span> <span class="o">=</span> <span class="n">MyCube</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="k">return</span> <span class="n">result</span>
</pre></div>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Inputs to <code class="docutils literal notranslate"><span class="pre">backward</span></code>, i.e., <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_output</span></code>, can also be tensors that
track history. So if <code class="docutils literal notranslate"><span class="pre">backward</span></code> is implemented with differentiable
operations, (e.g., invocation of another custom
<a class="reference internal" href="../autograd.html#torch.autograd.Function" title="torch.autograd.Function"><code class="xref py py-class docutils literal notranslate"><span class="pre">Function</span></code></a>), higher order derivatives will work.
In this case, the tensors saved with <code class="docutils literal notranslate"><span class="pre">save_for_backward</span></code> can also be used
in the backward and have gradients flowing back but tensors saved in the <code class="docutils literal notranslate"><span class="pre">ctx</span></code>
won’t have gradients flowing back for them.
If you need gradients to flow back for a Tensor saved in the <code class="docutils literal notranslate"><span class="pre">ctx</span></code>, you should
make it an output of the custom <code class="docutils literal notranslate"><span class="pre">Function</span></code> and save it with <code class="docutils literal notranslate"><span class="pre">save_for_backward</span></code>.</p>
</div>
<p>You probably want to check if the backward method you implemented actually
computes the derivatives of your function. It is possible by comparing with
numerical approximations using small finite differences:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">torch.autograd</span> <span class="kn">import</span> <span class="n">gradcheck</span>
<span class="c1"># gradcheck takes a tuple of tensors as input, check if your gradient</span>
<span class="c1"># evaluated with these tensors are close enough to numerical</span>
<span class="c1"># approximations and returns True if they all verify this condition.</span>
<span class="nb">input</span> <span class="o">=</span> <span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span><span class="mi">20</span><span class="p">,</span><span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">double</span><span class="p">,</span><span class="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">),</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">30</span><span class="p">,</span><span class="mi">20</span><span class="p">,</span><span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">double</span><span class="p">,</span><span class="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">))</span>
<span class="n">test</span> <span class="o">=</span> <span class="n">gradcheck</span><span class="p">(</span><span class="n">linear</span><span class="p">,</span> <span class="nb">input</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-6</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1e-4</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">test</span><span class="p">)</span>
</pre></div>
</div>
<p>See <a class="reference internal" href="../autograd.html#grad-check"><span class="std std-ref">Numerical gradient checking</span></a> for more details on finite-difference gradient comparisons.
If your function is used in higher order derivatives (differentiating the backward pass) you
can use the <code class="docutils literal notranslate"><span class="pre">gradgradcheck</span></code> function from the same package to check higher order derivatives.</p>
</section>
<section id="combined-or-separate-forward-and-setup-context">
<span id="combining-forward-context"></span><h3>Combined or separate <a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a> and <code class="xref py py-meth docutils literal notranslate"><span class="pre">setup_context()</span></code><a class="headerlink" href="#combined-or-separate-forward-and-setup-context" title="Permalink to this heading">¶</a></h3>
<p>There are two main ways to define <a class="reference internal" href="../autograd.html#torch.autograd.Function" title="torch.autograd.Function"><code class="xref py py-class docutils literal notranslate"><span class="pre">Function</span></code></a>. Either:</p>
<ul class="simple">
<li><p>define a <a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a> that combines the forward compute logic with <code class="xref py py-meth docutils literal notranslate"><span class="pre">setup_context()</span></code></p></li>
<li><p>(as of PyTorch 2.0) define a separate <a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a> and <code class="xref py py-meth docutils literal notranslate"><span class="pre">setup_context()</span></code></p></li>
</ul>
<p>We recommend the second option (separate <a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a> and <code class="xref py py-meth docutils literal notranslate"><span class="pre">setup_context()</span></code>)
because that is closer to how PyTorch native operations are implemented and it composes
with <a class="reference internal" href="../func.api.html#module-torch.func" title="torch.func"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.func</span></code></a> transforms. However, we plan to support both approaches going forward;
combining <a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a> with <code class="xref py py-meth docutils literal notranslate"><span class="pre">setup_context()</span></code>: leads to more flexibility since
you are able to save intermediates without returning them as output.</p>
<p>Please see the previous section for how to define <a class="reference internal" href="../autograd.html#torch.autograd.Function" title="torch.autograd.Function"><code class="xref py py-class docutils literal notranslate"><span class="pre">Function</span></code></a> with separate
<a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a> and <code class="xref py py-meth docutils literal notranslate"><span class="pre">setup_context()</span></code>.</p>
<p>Here is an example of how to define a <a class="reference internal" href="../autograd.html#torch.autograd.Function" title="torch.autograd.Function"><code class="xref py py-class docutils literal notranslate"><span class="pre">Function</span></code></a> with combined <a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a> and
<code class="xref py py-meth docutils literal notranslate"><span class="pre">setup_context()</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">LinearFunction</span><span class="p">(</span><span class="n">Function</span><span class="p">):</span>
<span class="nd">@staticmethod</span>
<span class="c1"># ctx is the first argument to forward</span>
<span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="nb">input</span><span class="p">,</span> <span class="n">weight</span><span class="p">,</span> <span class="n">bias</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="c1"># The forward pass can use ctx.</span>
<span class="n">ctx</span><span class="o">.</span><span class="n">save_for_backward</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="n">weight</span><span class="p">,</span> <span class="n">bias</span><span class="p">)</span>
<span class="n">output</span> <span class="o">=</span> <span class="nb">input</span><span class="o">.</span><span class="n">mm</span><span class="p">(</span><span class="n">weight</span><span class="o">.</span><span class="n">t</span><span class="p">())</span>
<span class="k">if</span> <span class="n">bias</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">output</span> <span class="o">+=</span> <span class="n">bias</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">expand_as</span><span class="p">(</span><span class="n">output</span><span class="p">)</span>
<span class="k">return</span> <span class="n">output</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">backward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">grad_output</span><span class="p">):</span>
<span class="nb">input</span><span class="p">,</span> <span class="n">weight</span><span class="p">,</span> <span class="n">bias</span> <span class="o">=</span> <span class="n">ctx</span><span class="o">.</span><span class="n">saved_tensors</span>
<span class="n">grad_input</span> <span class="o">=</span> <span class="n">grad_weight</span> <span class="o">=</span> <span class="n">grad_bias</span> <span class="o">=</span> <span class="kc">None</span>
<span class="k">if</span> <span class="n">ctx</span><span class="o">.</span><span class="n">needs_input_grad</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
<span class="n">grad_input</span> <span class="o">=</span> <span class="n">grad_output</span><span class="o">.</span><span class="n">mm</span><span class="p">(</span><span class="n">weight</span><span class="p">)</span>
<span class="k">if</span> <span class="n">ctx</span><span class="o">.</span><span class="n">needs_input_grad</span><span class="p">[</span><span class="mi">1</span><span class="p">]:</span>
<span class="n">grad_weight</span> <span class="o">=</span> <span class="n">grad_output</span><span class="o">.</span><span class="n">t</span><span class="p">()</span><span class="o">.</span><span class="n">mm</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
<span class="k">if</span> <span class="n">bias</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">ctx</span><span class="o">.</span><span class="n">needs_input_grad</span><span class="p">[</span><span class="mi">2</span><span class="p">]:</span>
<span class="n">grad_bias</span> <span class="o">=</span> <span class="n">grad_output</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="k">return</span> <span class="n">grad_input</span><span class="p">,</span> <span class="n">grad_weight</span><span class="p">,</span> <span class="n">grad_bias</span>
</pre></div>
</div>
</section>
<section id="forward-mode-ad">
<span id="forward-ad-autograd-function"></span><h3>Forward mode AD<a class="headerlink" href="#forward-mode-ad" title="Permalink to this heading">¶</a></h3>
<p>Overriding the forward mode AD formula has a very similar API with some different subtleties.
You can implement the <a class="reference internal" href="../generated/torch.autograd.Function.jvp.html#torch.autograd.Function.jvp" title="torch.autograd.Function.jvp"><code class="xref py py-meth docutils literal notranslate"><span class="pre">jvp()</span></code></a> function.</p>
<p>It will be given as many <code class="xref py py-class docutils literal notranslate"><span class="pre">Tensor</span></code> arguments as there were inputs, with each
of them representing gradient w.r.t. that input. It should return as many tensors as there
were outputs, with each of them containing the gradient w.r.t. its corresponding output.
The <a class="reference internal" href="../generated/torch.autograd.Function.jvp.html#torch.autograd.Function.jvp" title="torch.autograd.Function.jvp"><code class="xref py py-meth docutils literal notranslate"><span class="pre">jvp()</span></code></a> will be called just after the <a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a>
method, before the <code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code> returns.</p>
<p><a class="reference internal" href="../generated/torch.autograd.Function.jvp.html#torch.autograd.Function.jvp" title="torch.autograd.Function.jvp"><code class="xref py py-meth docutils literal notranslate"><span class="pre">jvp()</span></code></a> has a few subtle differences with the <a class="reference internal" href="../generated/torch.autograd.Function.backward.html#torch.autograd.Function.backward" title="torch.autograd.Function.backward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">backward()</span></code></a> function:</p>
<ul class="simple">
<li><p>You can use the <cite>ctx</cite> to pass any data from the <a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a> to the <a class="reference internal" href="../generated/torch.autograd.Function.jvp.html#torch.autograd.Function.jvp" title="torch.autograd.Function.jvp"><code class="xref py py-meth docutils literal notranslate"><span class="pre">jvp()</span></code></a> function.
If that state will not be needed for the <a class="reference internal" href="../generated/torch.autograd.Function.backward.html#torch.autograd.Function.backward" title="torch.autograd.Function.backward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">backward()</span></code></a>,
you can explicitly free it by doing <code class="docutils literal notranslate"><span class="pre">del</span> <span class="pre">ctx.foo</span></code> at the end of the <a class="reference internal" href="../generated/torch.autograd.Function.jvp.html#torch.autograd.Function.jvp" title="torch.autograd.Function.jvp"><code class="xref py py-meth docutils literal notranslate"><span class="pre">jvp()</span></code></a> function.</p></li>
<li><p>The implementation of <a class="reference internal" href="../generated/torch.autograd.Function.jvp.html#torch.autograd.Function.jvp" title="torch.autograd.Function.jvp"><code class="xref py py-meth docutils literal notranslate"><span class="pre">jvp()</span></code></a> must be backward differentiable or explicitly check that
none of the given forward mode gradient has <code class="docutils literal notranslate"><span class="pre">requires_grad</span></code> set.</p></li>
<li><p>The <a class="reference internal" href="../generated/torch.autograd.Function.jvp.html#torch.autograd.Function.jvp" title="torch.autograd.Function.jvp"><code class="xref py py-meth docutils literal notranslate"><span class="pre">jvp()</span></code></a> function must match the view/inplace behavior of <a class="reference internal" href="../generated/torch.autograd.Function.forward.html#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a>.
For example, if the <code class="docutils literal notranslate"><span class="pre">i</span></code> th input is modified inplace, then the <code class="docutils literal notranslate"><span class="pre">i</span></code> th gradient must be updated inplace.
Similarly, if the <code class="docutils literal notranslate"><span class="pre">j</span></code> th output is a view of the <code class="docutils literal notranslate"><span class="pre">k</span></code> th input. Then the returned <code class="docutils literal notranslate"><span class="pre">j</span></code> th output gradient must be
a view of the given <code class="docutils literal notranslate"><span class="pre">k</span></code> th input gradient.</p></li>
<li><p>Because the user cannot specify which gradient needs to be computed, the <a class="reference internal" href="../generated/torch.autograd.Function.jvp.html#torch.autograd.Function.jvp" title="torch.autograd.Function.jvp"><code class="xref py py-meth docutils literal notranslate"><span class="pre">jvp()</span></code></a> function should
always compute gradients for all the outputs.</p></li>
<li><p>The forward mode gradients do respect the flag set by <a class="reference internal" href="../generated/torch.autograd.function.FunctionCtx.set_materialize_grads.html#torch.autograd.function.FunctionCtx.set_materialize_grads" title="torch.autograd.function.FunctionCtx.set_materialize_grads"><code class="xref py py-meth docutils literal notranslate"><span class="pre">set_materialize_grads()</span></code></a>
and you can get <cite>None</cite> input gradients when this is disabled.</p></li>
</ul>
</section>
<section id="torch-func-transforms-and-or-torch-vmap">
<h3><a class="reference internal" href="../func.api.html#module-torch.func" title="torch.func"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.func</span></code></a> transforms and/or <a class="reference internal" href="../generated/torch.vmap.html#torch.vmap" title="torch.vmap"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.vmap()</span></code></a><a class="headerlink" href="#torch-func-transforms-and-or-torch-vmap" title="Permalink to this heading">¶</a></h3>
<p>Please see <a class="reference internal" href="extending.func.html#func-autograd-function"><span class="std std-ref">Extending torch.func with autograd.Function</span></a> for details.</p>
</section>
</section>
<section id="extending-torch-nn">
<h2>Extending <a class="reference internal" href="../nn.html#module-torch.nn" title="torch.nn"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.nn</span></code></a><a class="headerlink" href="#extending-torch-nn" title="Permalink to this heading">¶</a></h2>
<p><a class="reference internal" href="../nn.html#module-torch.nn" title="torch.nn"><code class="xref py py-mod docutils literal notranslate"><span class="pre">nn</span></code></a> exports two kinds of interfaces - modules and their functional
versions. You can extend it in both ways, but we recommend using modules for
all kinds of layers, that hold any parameters or buffers, and recommend using
a functional form parameter-less operations like activation functions, pooling,
etc.</p>
<p>Adding a functional version of an operation is already fully covered in the
section above.</p>
<section id="adding-a-module">
<h3>Adding a <a class="reference internal" href="../generated/torch.nn.Module.html#torch.nn.Module" title="torch.nn.Module"><code class="xref py py-class docutils literal notranslate"><span class="pre">Module</span></code></a><a class="headerlink" href="#adding-a-module" title="Permalink to this heading">¶</a></h3>
<p>Since <a class="reference internal" href="../nn.html#module-torch.nn" title="torch.nn"><code class="xref py py-mod docutils literal notranslate"><span class="pre">nn</span></code></a> heavily utilizes <a class="reference internal" href="../torch.html#module-torch.autograd" title="torch.autograd"><code class="xref py py-mod docutils literal notranslate"><span class="pre">autograd</span></code></a>, adding a new
<a class="reference internal" href="../generated/torch.nn.Module.html#torch.nn.Module" title="torch.nn.Module"><code class="xref py py-class docutils literal notranslate"><span class="pre">Module</span></code></a> requires implementing a <a class="reference internal" href="../autograd.html#torch.autograd.Function" title="torch.autograd.Function"><code class="xref py py-class docutils literal notranslate"><span class="pre">Function</span></code></a>
that performs the operation and can compute the gradient. From now on let’s
assume that we want to implement a <code class="docutils literal notranslate"><span class="pre">Linear</span></code> module and we have the function
implemented as in the listing above. There’s very little code required to
add this. Now, there are two functions that need to be implemented:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">__init__</span></code> (<em>optional</em>) - takes in arguments such as kernel sizes, numbers
of features, etc. and initializes parameters and buffers.</p></li>
<li><p><a class="reference internal" href="../generated/torch.nn.Module.html#torch.nn.Module.forward" title="torch.nn.Module.forward"><code class="xref py py-meth docutils literal notranslate"><span class="pre">forward()</span></code></a> - instantiates a <a class="reference internal" href="../autograd.html#torch.autograd.Function" title="torch.autograd.Function"><code class="xref py py-class docutils literal notranslate"><span class="pre">Function</span></code></a> and
uses it to perform the operation. It’s very similar to a functional wrapper
shown above.</p></li>
</ul>
<p>This is how a <code class="docutils literal notranslate"><span class="pre">Linear</span></code> module can be implemented:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">Linear</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Module</span><span class="p">):</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">input_features</span><span class="p">,</span> <span class="n">output_features</span><span class="p">,</span> <span class="n">bias</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
<span class="bp">self</span><span class="o">.</span><span class="n">input_features</span> <span class="o">=</span> <span class="n">input_features</span>
<span class="bp">self</span><span class="o">.</span><span class="n">output_features</span> <span class="o">=</span> <span class="n">output_features</span>
<span class="c1"># nn.Parameter is a special kind of Tensor, that will get</span>
<span class="c1"># automatically registered as Module's parameter once it's assigned</span>
<span class="c1"># as an attribute. Parameters and buffers need to be registered, or</span>
<span class="c1"># they won't appear in .parameters() (doesn't apply to buffers), and</span>
<span class="c1"># won't be converted when e.g. .cuda() is called. You can use</span>
<span class="c1"># .register_buffer() to register buffers.</span>
<span class="c1"># nn.Parameters require gradients by default.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">weight</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Parameter</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">output_features</span><span class="p">,</span> <span class="n">input_features</span><span class="p">))</span>
<span class="k">if</span> <span class="n">bias</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">bias</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Parameter</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">output_features</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># You should always register all possible parameters, but the</span>
<span class="c1"># optional ones can be None if you want.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">register_parameter</span><span class="p">(</span><span class="s1">'bias'</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
<span class="c1"># Not a very smart way to initialize weights</span>
<span class="n">nn</span><span class="o">.</span><span class="n">init</span><span class="o">.</span><span class="n">uniform_</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">weight</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">bias</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">nn</span><span class="o">.</span><span class="n">init</span><span class="o">.</span><span class="n">uniform_</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">bias</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="nb">input</span><span class="p">):</span>
<span class="c1"># See the autograd section for explanation of what happens here.</span>
<span class="k">return</span> <span class="n">LinearFunction</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">weight</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">bias</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">extra_repr</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="c1"># (Optional)Set the extra information about this module. You can test</span>
<span class="c1"># it by printing an object of this class.</span>
<span class="k">return</span> <span class="s1">'input_features=</span><span class="si">{}</span><span class="s1">, output_features=</span><span class="si">{}</span><span class="s1">, bias=</span><span class="si">{}</span><span class="s1">'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
<span class="bp">self</span><span class="o">.</span><span class="n">input_features</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">output_features</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">bias</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span>
<span class="p">)</span>
</pre></div>
</div>
</section>
</section>
<section id="extending-torch">
<span id="id1"></span><h2>Extending <a class="reference internal" href="../torch.html#module-torch" title="torch"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch</span></code></a><a class="headerlink" href="#extending-torch" title="Permalink to this heading">¶</a></h2>
<p>You can create custom types that emulate <code class="xref py py-class docutils literal notranslate"><span class="pre">Tensor</span></code> by defining a custom
class with methods that match <code class="xref py py-class docutils literal notranslate"><span class="pre">Tensor</span></code>. But what if you want to be able
to pass these types to functions like <a class="reference internal" href="../generated/torch.add.html#torch.add" title="torch.add"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.add()</span></code></a> in the top-level
<a class="reference internal" href="../torch.html#module-torch" title="torch"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch</span></code></a> namespace that accept <code class="xref py py-class docutils literal notranslate"><span class="pre">Tensor</span></code> operands?</p>
<p>If your custom python type defines a method named <code class="docutils literal notranslate"><span class="pre">__torch_function__</span></code>, PyTorch
will invoke your <code class="docutils literal notranslate"><span class="pre">__torch_function__</span></code> implementation when an instance of your
custom class is passed to a function in the <a class="reference internal" href="../torch.html#module-torch" title="torch"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch</span></code></a> namespace. This makes
it possible to define custom implementations for any of the functions in the
<a class="reference internal" href="../torch.html#module-torch" title="torch"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch</span></code></a> namespace which your <code class="docutils literal notranslate"><span class="pre">__torch_function__</span></code> implementation can call,
allowing your users to make use of your custom type with existing PyTorch
workflows that they have already written for <code class="xref py py-class docutils literal notranslate"><span class="pre">Tensor</span></code>. This works with
“duck” types that are unrelated to <code class="xref py py-class docutils literal notranslate"><span class="pre">Tensor</span></code> as well as user-defined
subclasses of <code class="xref py py-class docutils literal notranslate"><span class="pre">Tensor</span></code>.</p>
<section id="extending-torch-with-a-tensor-like-type">
<h3>Extending <a class="reference internal" href="../torch.html#module-torch" title="torch"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch</span></code></a> with a <code class="xref py py-class docutils literal notranslate"><span class="pre">Tensor</span></code>-like type<a class="headerlink" href="#extending-torch-with-a-tensor-like-type" title="Permalink to this heading">¶</a></h3>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This functionality is inspired by the NumPy <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code>
protocol. See <a class="reference external" href="https://numpy.org/doc/stable/user/basics.dispatch.html#basics-dispatch">the NumPy documentation</a>
and <a class="reference external" href="https://numpy.org/neps/nep-0018-array-function-protocol.html">NEP-0018</a> for
more details.</p>
</div>
<p>To make this concrete, let’s begin with a simple example that illustrates the
API dispatch mechanism. We’ll create a custom type that represents a 2D scalar
tensor, parametrized by the order <code class="docutils literal notranslate"><span class="pre">N</span></code> and value along the diagonal entries,
<code class="docutils literal notranslate"><span class="pre">value</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">ScalarTensor</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">N</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_N</span> <span class="o">=</span> <span class="n">N</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_value</span> <span class="o">=</span> <span class="n">value</span>
<span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="s2">"ScalarTensor(N=</span><span class="si">{}</span><span class="s2">, value=</span><span class="si">{}</span><span class="s2">)"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_N</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_value</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">tensor</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_value</span> <span class="o">*</span> <span class="n">torch</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_N</span><span class="p">)</span>
</pre></div>
</div>
<p>This first iteration of the design isn’t very useful. The main functionality of
<code class="docutils literal notranslate"><span class="pre">ScalarTensor</span></code> is to provide a more compact string representation of a scalar
tensor than in the base tensor class:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">d</span> <span class="o">=</span> <span class="n">ScalarTensor</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">d</span>
<span class="go">ScalarTensor(N=5, value=2)</span>
<span class="gp">>>> </span><span class="n">d</span><span class="o">.</span><span class="n">tensor</span><span class="p">()</span>
<span class="go">tensor([[2., 0., 0., 0., 0.],</span>
<span class="go"> [0., 2., 0., 0., 0.],</span>
<span class="go"> [0., 0., 2., 0., 0.],</span>
<span class="go"> [0., 0., 0., 2., 0.],</span>
<span class="go"> [0., 0., 0., 0., 2.]])</span>
</pre></div>
</div>
<p>If we try to use this object with the <a class="reference internal" href="../torch.html#module-torch" title="torch"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch</span></code></a> API, we will run
into issues:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">torch</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">d</span><span class="p">)</span>
<span class="go">TypeError: mean(): argument 'input' (position 1) must be Tensor, not ScalarTensor</span>
</pre></div>
</div>
<p>Adding a <code class="docutils literal notranslate"><span class="pre">__torch_function__</span></code> implementation to <code class="docutils literal notranslate"><span class="pre">ScalarTensor</span></code> makes it
possible for the above operation to succeed. Let’s re-do our implementation,
this time adding a <code class="docutils literal notranslate"><span class="pre">__torch_function__</span></code> implementation:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">HANDLED_FUNCTIONS</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">class</span> <span class="nc">ScalarTensor</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">N</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_N</span> <span class="o">=</span> <span class="n">N</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_value</span> <span class="o">=</span> <span class="n">value</span>
<span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="s2">"ScalarTensor(N=</span><span class="si">{}</span><span class="s2">, value=</span><span class="si">{}</span><span class="s2">)"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_N</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_value</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">tensor</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_value</span> <span class="o">*</span> <span class="n">torch</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_N</span><span class="p">)</span>
<span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">__torch_function__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">types</span><span class="p">,</span> <span class="n">args</span><span class="o">=</span><span class="p">(),</span> <span class="n">kwargs</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="k">if</span> <span class="n">kwargs</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">kwargs</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">if</span> <span class="n">func</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">HANDLED_FUNCTIONS</span> <span class="ow">or</span> <span class="ow">not</span> <span class="nb">all</span><span class="p">(</span>
<span class="nb">issubclass</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span> <span class="n">ScalarTensor</span><span class="p">))</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">types</span>
<span class="p">):</span>
<span class="k">return</span> <span class="bp">NotImplemented</span>
<span class="k">return</span> <span class="n">HANDLED_FUNCTIONS</span><span class="p">[</span><span class="n">func</span><span class="p">](</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
</pre></div>
</div>
<p>The <code class="docutils literal notranslate"><span class="pre">__torch_function__</span></code> method takes four arguments: <code class="docutils literal notranslate"><span class="pre">func</span></code>, a reference
to the torch API function that is being overridden, <code class="docutils literal notranslate"><span class="pre">types</span></code>, the list of
types of Tensor-likes that implement <code class="docutils literal notranslate"><span class="pre">__torch_function__</span></code>, <code class="docutils literal notranslate"><span class="pre">args</span></code>, the
tuple of arguments passed to the function, and <code class="docutils literal notranslate"><span class="pre">kwargs</span></code>, the dict of keyword
arguments passed to the function. It uses a global dispatch table named
<code class="docutils literal notranslate"><span class="pre">HANDLED_FUNCTIONS</span></code> to store custom implementations. The keys of this
dictionary are functions in the <code class="docutils literal notranslate"><span class="pre">torch</span></code> namespace and the values are
implementations for <code class="docutils literal notranslate"><span class="pre">ScalarTensor</span></code>.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Using a global dispatch table is not a mandated part of the
<code class="docutils literal notranslate"><span class="pre">__torch_function__</span></code> API, it is just a useful design pattern for
structuring your override implementations.</p>
</div>
<p>This class definition isn’t quite enough to make <code class="docutils literal notranslate"><span class="pre">torch.mean</span></code> do the right
thing when we pass it a <code class="docutils literal notranslate"><span class="pre">ScalarTensor</span></code> – we also need to define an
implementation for <code class="docutils literal notranslate"><span class="pre">torch.mean</span></code> for <code class="docutils literal notranslate"><span class="pre">ScalarTensor</span></code> operands and add the
implementation to the <code class="docutils literal notranslate"><span class="pre">HANDLED_FUNCTIONS</span></code> dispatch table dictionary. One way
of doing this is to define a decorator:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">functools</span>
<span class="k">def</span> <span class="nf">implements</span><span class="p">(</span><span class="n">torch_function</span><span class="p">):</span>
<span class="sd">"""Register a torch function override for ScalarTensor"""</span>
<span class="k">def</span> <span class="nf">decorator</span><span class="p">(</span><span class="n">func</span><span class="p">):</span>
<span class="n">functools</span><span class="o">.</span><span class="n">update_wrapper</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">torch_function</span><span class="p">)</span>
<span class="n">HANDLED_FUNCTIONS</span><span class="p">[</span><span class="n">torch_function</span><span class="p">]</span> <span class="o">=</span> <span class="n">func</span>
<span class="k">return</span> <span class="n">func</span>
<span class="k">return</span> <span class="n">decorator</span>
</pre></div>
</div>
<p>which can be applied to the implementation of our override:</p>