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<div class="section" id="unfold">
<h1>Unfold<a class="headerlink" href="#unfold" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="torch.nn.Unfold">
<em class="property">class </em><code class="sig-prename descclassname">torch.nn.</code><code class="sig-name descname">Unfold</code><span class="sig-paren">(</span><em class="sig-param">kernel_size: Union[T, Tuple[T, ...]], dilation: Union[T, Tuple[T, ...]] = 1, padding: Union[T, Tuple[T, ...]] = 0, stride: Union[T, Tuple[T, ...]] = 1</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/torch/nn/modules/fold.html#Unfold"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.nn.Unfold" title="Permalink to this definition">¶</a></dt>
<dd><p>Extracts sliding local blocks from a batched input tensor.</p>
<p>Consider a batched <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code> tensor of shape <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>N</mi><mo separator="true">,</mo><mi>C</mi><mo separator="true">,</mo><mo>∗</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(N, C, *)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">∗</span><span class="mclose">)</span></span></span></span>
</span>,
where <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>N</mi></mrow><annotation encoding="application/x-tex">N</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span></span></span></span>
</span> is the batch dimension, <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span></span></span></span>
</span> is the channel dimension,
and <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∗</mo></mrow><annotation encoding="application/x-tex">*</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.46528em;vertical-align:0em;"></span><span class="mord">∗</span></span></span></span>
</span> represent arbitrary spatial dimensions. This operation flattens
each sliding <code class="xref py py-attr docutils literal notranslate"><span class="pre">kernel_size</span></code>-sized block within the spatial dimensions
of <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code> into a column (i.e., last dimension) of a 3-D <code class="xref py py-attr docutils literal notranslate"><span class="pre">output</span></code>
tensor of shape <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>N</mi><mo separator="true">,</mo><mi>C</mi><mo>×</mo><mo>∏</mo><mo stretchy="false">(</mo><mtext>kernel_size</mtext><mo stretchy="false">)</mo><mo separator="true">,</mo><mi>L</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(N, C \times \prod(\text{kernel\_size}), L)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.06em;vertical-align:-0.31em;"></span><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∏</span><span class="mopen">(</span><span class="mord text"><span class="mord">kernel_size</span></span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">L</span><span class="mclose">)</span></span></span></span>
</span>, where
<span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mo>×</mo><mo>∏</mo><mo stretchy="false">(</mo><mtext>kernel_size</mtext><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">C \times \prod(\text{kernel\_size})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.06em;vertical-align:-0.31em;"></span><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∏</span><span class="mopen">(</span><span class="mord text"><span class="mord">kernel_size</span></span><span class="mclose">)</span></span></span></span>
</span> is the total number of values
within each block (a block has <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∏</mo><mo stretchy="false">(</mo><mtext>kernel_size</mtext><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\prod(\text{kernel\_size})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.06em;vertical-align:-0.31em;"></span><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∏</span><span class="mopen">(</span><span class="mord text"><span class="mord">kernel_size</span></span><span class="mclose">)</span></span></span></span>
</span> spatial
locations each containing a <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span></span></span></span>
</span>-channeled vector), and <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi></mrow><annotation encoding="application/x-tex">L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">L</span></span></span></span>
</span> is
the total number of such blocks:</p>
<div class="math">
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>L</mi><mo>=</mo><munder><mo>∏</mo><mi>d</mi></munder><mrow><mo fence="true">⌊</mo><mfrac><mrow><mtext>spatial_size</mtext><mo stretchy="false">[</mo><mi>d</mi><mo stretchy="false">]</mo><mo>+</mo><mn>2</mn><mo>×</mo><mtext>padding</mtext><mo stretchy="false">[</mo><mi>d</mi><mo stretchy="false">]</mo><mo>−</mo><mtext>dilation</mtext><mo stretchy="false">[</mo><mi>d</mi><mo stretchy="false">]</mo><mo>×</mo><mo stretchy="false">(</mo><mtext>kernel_size</mtext><mo stretchy="false">[</mo><mi>d</mi><mo stretchy="false">]</mo><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo>−</mo><mn>1</mn></mrow><mrow><mtext>stride</mtext><mo stretchy="false">[</mo><mi>d</mi><mo stretchy="false">]</mo></mrow></mfrac><mo>+</mo><mn>1</mn><mo fence="true">⌋</mo></mrow><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">L = \prod_d \left\lfloor\frac{\text{spatial\_size}[d] + 2 \times \text{padding}[d] %
- \text{dilation}[d] \times (\text{kernel\_size}[d] - 1) - 1}{\text{stride}[d]} + 1\right\rfloor,
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">L</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.7521129999999996em;vertical-align:-1.3021129999999999em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0500050000000005em;"><span style="top:-1.847887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∏</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.3021129999999999em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">⌊</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">stride</span></span><span class="mopen">[</span><span class="mord mathnormal">d</span><span class="mclose">]</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.6999999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">spatial_size</span></span><span class="mopen">[</span><span class="mord mathnormal">d</span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord text"><span class="mord">padding</span></span><span class="mopen">[</span><span class="mord mathnormal">d</span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord text"><span class="mord">dilation</span></span><span class="mopen">[</span><span class="mord mathnormal">d</span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord text"><span class="mord">kernel_size</span></span><span class="mopen">[</span><span class="mord mathnormal">d</span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">1</span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">⌋</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mpunct">,</span></span></span></span></span>
</div><p>where <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>spatial_size</mtext></mrow><annotation encoding="application/x-tex">\text{spatial\_size}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.00444em;vertical-align:-0.31em;"></span><span class="mord text"><span class="mord">spatial_size</span></span></span></span></span>
</span> is formed by the spatial dimensions
of <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code> (<span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∗</mo></mrow><annotation encoding="application/x-tex">*</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.46528em;vertical-align:0em;"></span><span class="mord">∗</span></span></span></span>
</span> above), and <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi></mrow><annotation encoding="application/x-tex">d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal">d</span></span></span></span>
</span> is over all spatial
dimensions.</p>
<p>Therefore, indexing <code class="xref py py-attr docutils literal notranslate"><span class="pre">output</span></code> at the last dimension (column dimension)
gives all values within a certain block.</p>
<p>The <code class="xref py py-attr docutils literal notranslate"><span class="pre">padding</span></code>, <code class="xref py py-attr docutils literal notranslate"><span class="pre">stride</span></code> and <code class="xref py py-attr docutils literal notranslate"><span class="pre">dilation</span></code> arguments specify
how the sliding blocks are retrieved.</p>
<ul class="simple">
<li><p><code class="xref py py-attr docutils literal notranslate"><span class="pre">stride</span></code> controls the stride for the sliding blocks.</p></li>
<li><p><code class="xref py py-attr docutils literal notranslate"><span class="pre">padding</span></code> controls the amount of implicit zero-paddings on both
sides for <code class="xref py py-attr docutils literal notranslate"><span class="pre">padding</span></code> number of points for each dimension before
reshaping.</p></li>
<li><p><code class="xref py py-attr docutils literal notranslate"><span class="pre">dilation</span></code> controls the spacing between the kernel points; also known as the à trous algorithm.
It is harder to describe, but this <a class="reference external" href="https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md">link</a> has a nice visualization of what <code class="xref py py-attr docutils literal notranslate"><span class="pre">dilation</span></code> does.</p></li>
</ul>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>kernel_size</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em> or </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.9)"><em>tuple</em></a>) – the size of the sliding blocks</p></li>
<li><p><strong>stride</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em> or </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.9)"><em>tuple</em></a><em>, </em><em>optional</em>) – the stride of the sliding blocks in the input
spatial dimensions. Default: 1</p></li>
<li><p><strong>padding</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em> or </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.9)"><em>tuple</em></a><em>, </em><em>optional</em>) – implicit zero padding to be added on
both sides of input. Default: 0</p></li>
<li><p><strong>dilation</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em> or </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.9)"><em>tuple</em></a><em>, </em><em>optional</em>) – a parameter that controls the
stride of elements within the
neighborhood. Default: 1</p></li>
</ul>
</dd>
</dl>
<ul class="simple">
<li><p>If <code class="xref py py-attr docutils literal notranslate"><span class="pre">kernel_size</span></code>, <code class="xref py py-attr docutils literal notranslate"><span class="pre">dilation</span></code>, <code class="xref py py-attr docutils literal notranslate"><span class="pre">padding</span></code> or
<code class="xref py py-attr docutils literal notranslate"><span class="pre">stride</span></code> is an int or a tuple of length 1, their values will be
replicated across all spatial dimensions.</p></li>
<li><p>For the case of two input spatial dimensions this operation is sometimes
called <code class="docutils literal notranslate"><span class="pre">im2col</span></code>.</p></li>
</ul>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p><a class="reference internal" href="torch.nn.Fold.html#torch.nn.Fold" title="torch.nn.Fold"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fold</span></code></a> calculates each combined value in the resulting
large tensor by summing all values from all containing blocks.
<a class="reference internal" href="#torch.nn.Unfold" title="torch.nn.Unfold"><code class="xref py py-class docutils literal notranslate"><span class="pre">Unfold</span></code></a> extracts the values in the local blocks by
copying from the large tensor. So, if the blocks overlap, they are not
inverses of each other.</p>
<p>In general, folding and unfolding operations are related as
follows. Consider <a class="reference internal" href="torch.nn.Fold.html#torch.nn.Fold" title="torch.nn.Fold"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fold</span></code></a> and
<a class="reference internal" href="#torch.nn.Unfold" title="torch.nn.Unfold"><code class="xref py py-class docutils literal notranslate"><span class="pre">Unfold</span></code></a> instances created with the same
parameters:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">fold_params</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="n">kernel_size</span><span class="o">=...</span><span class="p">,</span> <span class="n">dilation</span><span class="o">=...</span><span class="p">,</span> <span class="n">padding</span><span class="o">=...</span><span class="p">,</span> <span class="n">stride</span><span class="o">=...</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">fold</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Fold</span><span class="p">(</span><span class="n">output_size</span><span class="o">=...</span><span class="p">,</span> <span class="o">**</span><span class="n">fold_params</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">unfold</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Unfold</span><span class="p">(</span><span class="o">**</span><span class="n">fold_params</span><span class="p">)</span>
</pre></div>
</div>
<p>Then for any (supported) <code class="docutils literal notranslate"><span class="pre">input</span></code> tensor the following
equality holds:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">fold</span><span class="p">(</span><span class="n">unfold</span><span class="p">(</span><span class="nb">input</span><span class="p">))</span> <span class="o">==</span> <span class="n">divisor</span> <span class="o">*</span> <span class="nb">input</span>
</pre></div>
</div>
<p>where <code class="docutils literal notranslate"><span class="pre">divisor</span></code> is a tensor that depends only on the shape
and dtype of the <code class="docutils literal notranslate"><span class="pre">input</span></code>:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">input_ones</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="nb">input</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">input</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">divisor</span> <span class="o">=</span> <span class="n">fold</span><span class="p">(</span><span class="n">unfold</span><span class="p">(</span><span class="n">input_ones</span><span class="p">))</span>
</pre></div>
</div>
<p>When the <code class="docutils literal notranslate"><span class="pre">divisor</span></code> tensor contains no zero elements, then
<code class="docutils literal notranslate"><span class="pre">fold</span></code> and <code class="docutils literal notranslate"><span class="pre">unfold</span></code> operations are inverses of each
other (up to constant divisor).</p>
</div>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>Currently, only 4-D input tensors (batched image-like tensors) are
supported.</p>
</div>
<dl class="simple">
<dt>Shape:</dt><dd><ul class="simple">
<li><p>Input: <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>N</mi><mo separator="true">,</mo><mi>C</mi><mo separator="true">,</mo><mo>∗</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(N, C, *)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">∗</span><span class="mclose">)</span></span></span></span>
</span></p></li>
<li><p>Output: <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>N</mi><mo separator="true">,</mo><mi>C</mi><mo>×</mo><mo>∏</mo><mo stretchy="false">(</mo><mtext>kernel_size</mtext><mo stretchy="false">)</mo><mo separator="true">,</mo><mi>L</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(N, C \times \prod(\text{kernel\_size}), L)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.06em;vertical-align:-0.31em;"></span><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∏</span><span class="mopen">(</span><span class="mord text"><span class="mord">kernel_size</span></span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">L</span><span class="mclose">)</span></span></span></span>
</span> as described above</p></li>
</ul>
</dd>
</dl>
<p>Examples:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">unfold</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Unfold</span><span class="p">(</span><span class="n">kernel_size</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
<span class="gp">>>> </span><span class="nb">input</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">output</span> <span class="o">=</span> <span class="n">unfold</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
<span class="gp">>>> </span><span class="c1"># each patch contains 30 values (2x3=6 vectors, each of 5 channels)</span>
<span class="gp">>>> </span><span class="c1"># 4 blocks (2x3 kernels) in total in the 3x4 input</span>
<span class="gp">>>> </span><span class="n">output</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
<span class="go">torch.Size([2, 30, 4])</span>
<span class="gp">>>> </span><span class="c1"># Convolution is equivalent with Unfold + Matrix Multiplication + Fold (or view to output shape)</span>
<span class="gp">>>> </span><span class="n">inp</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">12</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">w</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">inp_unf</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">functional</span><span class="o">.</span><span class="n">unfold</span><span class="p">(</span><span class="n">inp</span><span class="p">,</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">out_unf</span> <span class="o">=</span> <span class="n">inp_unf</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">w</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">w</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">t</span><span class="p">())</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">out</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">functional</span><span class="o">.</span><span class="n">fold</span><span class="p">(</span><span class="n">out_unf</span><span class="p">,</span> <span class="p">(</span><span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
<span class="gp">>>> </span><span class="c1"># or equivalently (and avoiding a copy),</span>
<span class="gp">>>> </span><span class="c1"># out = out_unf.view(1, 2, 7, 8)</span>
<span class="gp">>>> </span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">functional</span><span class="o">.</span><span class="n">conv2d</span><span class="p">(</span><span class="n">inp</span><span class="p">,</span> <span class="n">w</span><span class="p">)</span> <span class="o">-</span> <span class="n">out</span><span class="p">)</span><span class="o">.</span><span class="n">abs</span><span class="p">()</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
<span class="go">tensor(1.9073e-06)</span>
</pre></div>
</div>
</dd></dl>
</div>
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