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<div class="section" id="instancenorm2d">
<h1>InstanceNorm2d<a class="headerlink" href="#instancenorm2d" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="torch.nn.InstanceNorm2d">
<em class="property">class </em><code class="sig-prename descclassname">torch.nn.</code><code class="sig-name descname">InstanceNorm2d</code><span class="sig-paren">(</span><em class="sig-param">num_features: int</em>, <em class="sig-param">eps: float = 1e-05</em>, <em class="sig-param">momentum: float = 0.1</em>, <em class="sig-param">affine: bool = False</em>, <em class="sig-param">track_running_stats: bool = False</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/torch/nn/modules/instancenorm.html#InstanceNorm2d"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.nn.InstanceNorm2d" title="Permalink to this definition">¶</a></dt>
<dd><p>Applies Instance Normalization over a 4D input (a mini-batch of 2D inputs
with additional channel dimension) as described in the paper
<a class="reference external" href="https://arxiv.org/abs/1607.08022">Instance Normalization: The Missing Ingredient for Fast Stylization</a>.</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>y</mi><mo>=</mo><mfrac><mrow><mi>x</mi><mo>−</mo><mi mathvariant="normal">E</mi><mo stretchy="false">[</mo><mi>x</mi><mo stretchy="false">]</mo></mrow><msqrt><mrow><mrow><mi mathvariant="normal">V</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi></mrow><mo stretchy="false">[</mo><mi>x</mi><mo stretchy="false">]</mo><mo>+</mo><mi>ϵ</mi></mrow></msqrt></mfrac><mo>∗</mo><mi>γ</mi><mo>+</mo><mi>β</mi></mrow><annotation encoding="application/x-tex">y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</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:2.557em;vertical-align:-1.13em;"></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:1.427em;"><span style="top:-2.175em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.935em;"><span class="svg-align" style="top:-3.2em;"><span class="pstrut" style="height:3.2em;"></span><span class="mord" style="padding-left:1em;"><span class="mord"><span class="mord mathrm" style="margin-right:0.01389em;">V</span><span class="mord mathrm">a</span><span class="mord mathrm">r</span></span><span class="mopen">[</span><span class="mord mathnormal">x</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 mathnormal">ϵ</span></span></span><span style="top:-2.8950000000000005em;"><span class="pstrut" style="height:3.2em;"></span><span class="hide-tail" style="min-width:1.02em;height:1.28em;"><svg width='400em' height='1.28em' viewBox='0 0 400000 1296' preserveAspectRatio='xMinYMin slice'><path d='M263,681c0.7,0,18,39.7,52,119
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M1001 80h400000v40h-400000z'/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.30499999999999994em;"><span></span></span></span></span></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:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">x</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"><span class="mord mathrm">E</span></span><span class="mopen">[</span><span class="mord mathnormal">x</span><span class="mclose">]</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.13em;"><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><span class="base"><span class="strut" style="height:0.7777700000000001em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.05556em;">γ</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:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.05278em;">β</span></span></span></span></span>
</div><p>The mean and standard-deviation are calculated per-dimension separately
for each object in a mini-batch. <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>γ</mi></mrow><annotation encoding="application/x-tex">\gamma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.05556em;">γ</span></span></span></span>
</span> and <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>β</mi></mrow><annotation encoding="application/x-tex">\beta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.05278em;">β</span></span></span></span>
</span> are learnable parameter vectors
of size <cite>C</cite> (where <cite>C</cite> is the input size) if <code class="xref py py-attr docutils literal notranslate"><span class="pre">affine</span></code> is <code class="docutils literal notranslate"><span class="pre">True</span></code>.
The standard-deviation is calculated via the biased estimator, equivalent to
<cite>torch.var(input, unbiased=False)</cite>.</p>
<p>By default, this layer uses instance statistics computed from input data in
both training and evaluation modes.</p>
<p>If <code class="xref py py-attr docutils literal notranslate"><span class="pre">track_running_stats</span></code> is set to <code class="docutils literal notranslate"><span class="pre">True</span></code>, during training this
layer keeps running estimates of its computed mean and variance, which are
then used for normalization during evaluation. The running estimates are
kept with a default <code class="xref py py-attr docutils literal notranslate"><span class="pre">momentum</span></code> of 0.1.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This <code class="xref py py-attr docutils literal notranslate"><span class="pre">momentum</span></code> argument is different from one used in optimizer
classes and the conventional notion of momentum. Mathematically, the
update rule for running statistics here is
<span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>x</mi><mo>^</mo></mover><mtext>new</mtext></msub><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mtext>momentum</mtext><mo stretchy="false">)</mo><mo>×</mo><mover accent="true"><mi>x</mi><mo>^</mo></mover><mo>+</mo><mtext>momentum</mtext><mo>×</mo><msub><mi>x</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momentum} \times x_t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">x</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord">^</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord text mtight"><span class="mord mtight">new</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></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:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</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:1em;vertical-align:-0.25em;"></span><span class="mord text"><span class="mord">momentum</span></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><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">x</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord">^</span></span></span></span></span></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><span class="base"><span class="strut" style="height:0.69841em;vertical-align:-0.08333em;"></span><span class="mord text"><span class="mord">momentum</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><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></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><mover accent="true"><mi>x</mi><mo>^</mo></mover></mrow><annotation encoding="application/x-tex">\hat{x}</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 accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">x</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord">^</span></span></span></span></span></span></span></span></span></span>
</span> is the estimated statistic and <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">x_t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>
</span> is the
new observed value.</p>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p><a class="reference internal" href="#torch.nn.InstanceNorm2d" title="torch.nn.InstanceNorm2d"><code class="xref py py-class docutils literal notranslate"><span class="pre">InstanceNorm2d</span></code></a> and <a class="reference internal" href="torch.nn.LayerNorm.html#torch.nn.LayerNorm" title="torch.nn.LayerNorm"><code class="xref py py-class docutils literal notranslate"><span class="pre">LayerNorm</span></code></a> are very similar, but
have some subtle differences. <a class="reference internal" href="#torch.nn.InstanceNorm2d" title="torch.nn.InstanceNorm2d"><code class="xref py py-class docutils literal notranslate"><span class="pre">InstanceNorm2d</span></code></a> is applied
on each channel of channeled data like RGB images, but
<a class="reference internal" href="torch.nn.LayerNorm.html#torch.nn.LayerNorm" title="torch.nn.LayerNorm"><code class="xref py py-class docutils literal notranslate"><span class="pre">LayerNorm</span></code></a> is usually applied on entire sample and often in NLP
tasks. Additionally, <a class="reference internal" href="torch.nn.LayerNorm.html#torch.nn.LayerNorm" title="torch.nn.LayerNorm"><code class="xref py py-class docutils literal notranslate"><span class="pre">LayerNorm</span></code></a> applies elementwise affine
transform, while <a class="reference internal" href="#torch.nn.InstanceNorm2d" title="torch.nn.InstanceNorm2d"><code class="xref py py-class docutils literal notranslate"><span class="pre">InstanceNorm2d</span></code></a> usually don’t apply affine
transform.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>num_features</strong> – <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> from an expected input of size
<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><mi>H</mi><mo separator="true">,</mo><mi>W</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(N, C, H, W)</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 mathnormal" style="margin-right:0.08125em;">H</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mclose">)</span></span></span></span>
</span></p></li>
<li><p><strong>eps</strong> – a value added to the denominator for numerical stability. Default: 1e-5</p></li>
<li><p><strong>momentum</strong> – the value used for the running_mean and running_var computation. Default: 0.1</p></li>
<li><p><strong>affine</strong> – a boolean value that when set to <code class="docutils literal notranslate"><span class="pre">True</span></code>, this module has
learnable affine parameters, initialized the same way as done for batch normalization.
Default: <code class="docutils literal notranslate"><span class="pre">False</span></code>.</p></li>
<li><p><strong>track_running_stats</strong> – a boolean value that when set to <code class="docutils literal notranslate"><span class="pre">True</span></code>, this
module tracks the running mean and variance, and when set to <code class="docutils literal notranslate"><span class="pre">False</span></code>,
this module does not track such statistics and always uses batch
statistics in both training and eval modes. Default: <code class="docutils literal notranslate"><span class="pre">False</span></code></p></li>
</ul>
</dd>
</dl>
<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><mi>H</mi><mo separator="true">,</mo><mi>W</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(N, C, H, W)</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 mathnormal" style="margin-right:0.08125em;">H</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">W</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 separator="true">,</mo><mi>H</mi><mo separator="true">,</mo><mi>W</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(N, C, H, W)</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 mathnormal" style="margin-right:0.08125em;">H</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mclose">)</span></span></span></span>
</span> (same shape as input)</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="c1"># Without Learnable Parameters</span>
<span class="gp">>>> </span><span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">InstanceNorm2d</span><span class="p">(</span><span class="mi">100</span><span class="p">)</span>
<span class="gp">>>> </span><span class="c1"># With Learnable Parameters</span>
<span class="gp">>>> </span><span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">InstanceNorm2d</span><span class="p">(</span><span class="mi">100</span><span class="p">,</span> <span class="n">affine</span><span class="o">=</span><span class="kc">True</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">20</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">35</span><span class="p">,</span> <span class="mi">45</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">output</span> <span class="o">=</span> <span class="n">m</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
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