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<div class="section" id="tripletmarginloss">
<h1>TripletMarginLoss<a class="headerlink" href="#tripletmarginloss" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="torch.nn.TripletMarginLoss">
<em class="property">class </em><code class="sig-prename descclassname">torch.nn.</code><code class="sig-name descname">TripletMarginLoss</code><span class="sig-paren">(</span><em class="sig-param">margin: float = 1.0</em>, <em class="sig-param">p: float = 2.0</em>, <em class="sig-param">eps: float = 1e-06</em>, <em class="sig-param">swap: bool = False</em>, <em class="sig-param">size_average=None</em>, <em class="sig-param">reduce=None</em>, <em class="sig-param">reduction: str = 'mean'</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/torch/nn/modules/loss.html#TripletMarginLoss"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.nn.TripletMarginLoss" title="Permalink to this definition">¶</a></dt>
<dd><p>Creates a criterion that measures the triplet loss given an input
tensors <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mn>1</mn></mrow><annotation encoding="application/x-tex">x1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord mathnormal">x</span><span class="mord">1</span></span></span></span>
</span>, <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mn>2</mn></mrow><annotation encoding="application/x-tex">x2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord mathnormal">x</span><span class="mord">2</span></span></span></span>
</span>, <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mn>3</mn></mrow><annotation encoding="application/x-tex">x3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord mathnormal">x</span><span class="mord">3</span></span></span></span>
</span> and a margin with a value greater than <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span></span></span></span>
</span>.
This is used for measuring a relative similarity between samples. A triplet
is composed by <cite>a</cite>, <cite>p</cite> and <cite>n</cite> (i.e., <cite>anchor</cite>, <cite>positive examples</cite> and <cite>negative
examples</cite> respectively). The shapes of all input tensors should be
<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>D</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(N, D)</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:0.02778em;">D</span><span class="mclose">)</span></span></span></span>
</span>.</p>
<p>The distance swap is described in detail in the paper <a class="reference external" href="http://www.bmva.org/bmvc/2016/papers/paper119/index.html">Learning shallow
convolutional feature descriptors with triplet losses</a> by
V. Balntas, E. Riba et al.</p>
<p>The loss function for each sample in the mini-batch is:</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 stretchy="false">(</mo><mi>a</mi><mo separator="true">,</mo><mi>p</mi><mo separator="true">,</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>max</mi><mo></mo><mo stretchy="false">{</mo><mi>d</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mi>i</mi></msub><mo separator="true">,</mo><msub><mi>p</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>−</mo><mi>d</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mi>i</mi></msub><mo separator="true">,</mo><msub><mi>n</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>+</mo><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow><mo separator="true">,</mo><mn>0</mn><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">L(a, p, n) = \max \{d(a_i, p_i) - d(a_i, n_i) + {\rm margin}, 0\}
</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="mord mathnormal">L</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">p</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">n</span><span class="mclose">)</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="mop">max</span><span class="mopen">{</span><span class="mord mathnormal">d</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><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">i</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="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><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">i</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="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:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">d</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><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">i</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="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><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">i</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="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:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord mathrm">m</span><span class="mord mathrm">a</span><span class="mord mathrm">r</span><span class="mord mathrm" style="margin-right:0.01389em;">g</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">0</span><span class="mclose">}</span></span></span></span></span>
</div><p>where</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>d</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo separator="true">,</mo><msub><mi>y</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mo fence="true">∥</mo><msub><mi mathvariant="bold">x</mi><mi>i</mi></msub><mo>−</mo><msub><mi mathvariant="bold">y</mi><mi>i</mi></msub><mo fence="true">∥</mo></mrow><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">d(x_i, y_i) = \left\lVert {\bf x}_i - {\bf y}_i \right\rVert_p
</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="mord mathnormal">d</span><span class="mopen">(</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:0.31166399999999994em;"><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">i</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="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</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="mclose">)</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:1.185808em;vertical-align:-0.435808em;"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em;">∥</span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">x</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><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 mathnormal mtight">i</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:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf" style="margin-right:0.01597em;">y</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><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 mathnormal mtight">i</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="mclose delimcenter" style="top:0em;">∥</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.0016920000000000268em;"><span style="top:-2.4003000000000005em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.435808em;"><span></span></span></span></span></span></span></span></span></span></span>
</div><p>See also <a class="reference internal" href="torch.nn.TripletMarginWithDistanceLoss.html#torch.nn.TripletMarginWithDistanceLoss" title="torch.nn.TripletMarginWithDistanceLoss"><code class="xref py py-class docutils literal notranslate"><span class="pre">TripletMarginWithDistanceLoss</span></code></a>, which computes the
triplet margin loss for input tensors using a custom distance function.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>margin</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – Default: <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span>
</span>.</p></li>
<li><p><strong>p</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>, </em><em>optional</em>) – The norm degree for pairwise distance. Default: <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn></mrow><annotation encoding="application/x-tex">2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span></span></span></span>
</span>.</p></li>
<li><p><strong>swap</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.9)"><em>bool</em></a><em>, </em><em>optional</em>) – The distance swap is described in detail in the paper
<cite>Learning shallow convolutional feature descriptors with triplet losses</cite> by
V. Balntas, E. Riba et al. Default: <code class="docutils literal notranslate"><span class="pre">False</span></code>.</p></li>
<li><p><strong>size_average</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.9)"><em>bool</em></a><em>, </em><em>optional</em>) – Deprecated (see <code class="xref py py-attr docutils literal notranslate"><span class="pre">reduction</span></code>). By default,
the losses are averaged over each loss element in the batch. Note that for
some losses, there are multiple elements per sample. If the field <code class="xref py py-attr docutils literal notranslate"><span class="pre">size_average</span></code>
is set to <code class="docutils literal notranslate"><span class="pre">False</span></code>, the losses are instead summed for each minibatch. Ignored
when reduce is <code class="docutils literal notranslate"><span class="pre">False</span></code>. Default: <code class="docutils literal notranslate"><span class="pre">True</span></code></p></li>
<li><p><strong>reduce</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.9)"><em>bool</em></a><em>, </em><em>optional</em>) – Deprecated (see <code class="xref py py-attr docutils literal notranslate"><span class="pre">reduction</span></code>). By default, the
losses are averaged or summed over observations for each minibatch depending
on <code class="xref py py-attr docutils literal notranslate"><span class="pre">size_average</span></code>. When <code class="xref py py-attr docutils literal notranslate"><span class="pre">reduce</span></code> is <code class="docutils literal notranslate"><span class="pre">False</span></code>, returns a loss per
batch element instead and ignores <code class="xref py py-attr docutils literal notranslate"><span class="pre">size_average</span></code>. Default: <code class="docutils literal notranslate"><span class="pre">True</span></code></p></li>
<li><p><strong>reduction</strong> (<em>string</em><em>, </em><em>optional</em>) – Specifies the reduction to apply to the output:
<code class="docutils literal notranslate"><span class="pre">'none'</span></code> | <code class="docutils literal notranslate"><span class="pre">'mean'</span></code> | <code class="docutils literal notranslate"><span class="pre">'sum'</span></code>. <code class="docutils literal notranslate"><span class="pre">'none'</span></code>: no reduction will be applied,
<code class="docutils literal notranslate"><span class="pre">'mean'</span></code>: the sum of the output will be divided by the number of
elements in the output, <code class="docutils literal notranslate"><span class="pre">'sum'</span></code>: the output will be summed. Note: <code class="xref py py-attr docutils literal notranslate"><span class="pre">size_average</span></code>
and <code class="xref py py-attr docutils literal notranslate"><span class="pre">reduce</span></code> are in the process of being deprecated, and in the meantime,
specifying either of those two args will override <code class="xref py py-attr docutils literal notranslate"><span class="pre">reduction</span></code>. Default: <code class="docutils literal notranslate"><span class="pre">'mean'</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>D</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(N, D)</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:0.02778em;">D</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>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:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span></span></span></span>
</span> is the vector dimension.</p></li>
<li><dl class="simple">
<dt>Output: A 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 stretchy="false">)</mo></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:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mclose">)</span></span></span></span>
</span> if <code class="xref py py-attr docutils literal notranslate"><span class="pre">reduction</span></code> is <code class="docutils literal notranslate"><span class="pre">'none'</span></code>, or a scalar</dt><dd><p>otherwise.</p>
</dd>
</dl>
</li>
</ul>
</dd>
</dl>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">triplet_loss</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">TripletMarginLoss</span><span class="p">(</span><span class="n">margin</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">p</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">anchor</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">100</span><span class="p">,</span> <span class="mi">128</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="gp">>>> </span><span class="n">positive</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">100</span><span class="p">,</span> <span class="mi">128</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="gp">>>> </span><span class="n">negative</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">100</span><span class="p">,</span> <span class="mi">128</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="gp">>>> </span><span class="n">output</span> <span class="o">=</span> <span class="n">triplet_loss</span><span class="p">(</span><span class="n">anchor</span><span class="p">,</span> <span class="n">positive</span><span class="p">,</span> <span class="n">negative</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">output</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
</pre></div>
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