官方文档

https://pytorch.org/docs/master/nn.functional.html#torch.nn.functional.cross_entropy

作用

ignore_index用于忽略ground-truth中某些不需要参与计算的类。假设有两类{0:背景，1：前景}，若想在计算交叉熵时忽略背景(0)类，则可令ignore_index=0（同理忽略前景计算可设ignore_index=1）。

代码示例

import torch
import torch.nn.functional as F
pred = torch.Tensor([[0.9, 0.1],[0.8, 0.2],[0.7, 0.3]]
)  # shape=(N,C)=(3,2)，N为样本数，C为类数
label = torch.LongTensor([1, 0, 1])  # shape=(N)=(3)，3个样本的label分别为1，0，1
out = F.cross_entropy(pred, label, ignore_index=0)  # 忽略0类
print(out)

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输出

tensor(1.0421)

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验证

pytorch的CrossEntropy使用公式：

计算：

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width: 0px; height: 4.005em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.005em;"></span></span><span style="position: absolute; width: 100%; clip: rect(3.195em, 1004em, 4.157em, -999.997em); top: -1.619em; left: 0em;"><span class="mtd" id="MathJax-Span-78"><span class="mrow" id="MathJax-Span-79"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.195em, 1004em, 4.157em, -999.997em); top: -4em; left: 50%; margin-left: -2.024em;"><span class="mi" id="MathJax-Span-80"></span><span class="mo" id="MathJax-Span-81" style="font-family: MathJax_Main; padding-left: 0.256em;">=</span><span class="mn" id="MathJax-Span-82" style="font-family: MathJax_Main; padding-left: 0.256em;">1.0421</span><span style="display: inline-block; width: 0px; height: 4.005em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.005em;"></span></span></span><span style="display: inline-block; width: 0px; height: 6.488em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 6.64em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 6.64em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -2.685em; border-left: 0px solid; width: 0px; height: 5.894em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd><mi>l</mi><mi>o</mi><mi>s</mi><mi>s</mi></mtd><mtd><mi></mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mo fence="false" stretchy="false">{</mo><mo stretchy="false">[</mo><mo>−</mo><mn>0.1</mn><mo>+</mo><mi>l</mi><mi>n</mi><mo stretchy="false">(</mo><msup><mi>e</mi><mrow class="MJX-TeXAtom-ORD"><mn>0.9</mn></mrow></msup><mo>+</mo><msup><mi>e</mi><mrow class="MJX-TeXAtom-ORD"><mn>0.1</mn></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>+</mo><mo stretchy="false">[</mo><mo>−</mo><mn>0.3</mn><mo>+</mo><mi>l</mi><mi>n</mi><mo stretchy="false">(</mo><msup><mi>e</mi><mrow class="MJX-TeXAtom-ORD"><mn>0.7</mn></mrow></msup><mo>+</mo><msup><mi>e</mi><mrow class="MJX-TeXAtom-ORD"><mn>0.3</mn></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mo stretchy="false">(</mo><mn>1.1711</mn><mo>+</mo><mn>0.9130</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mn>1.0421</mn></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-1">\begin{aligned} loss&=\frac{1}{2}\times\{[-0.1+ln(e^{0.9}+e^{0.1})]+[-0.3+ln(e^{0.7}+e^{0.3})]\}\\ &=\frac{1}{2}\times(1.1711+0.9130)\\ &=1.0421 \end{aligned}</script></span><span class="katex-html"><span class="base"><span class="strut" style="height: 6.11488em; vertical-align: -2.80744em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 3.30744em;"><span class="" style="top: -5.30744em;"><span class="pstrut" style="height: 3.32144em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right: 0.01968em;">l</span><span class="mord mathdefault">o</span><span class="mord mathdefault">s</span><span class="mord mathdefault">s</span></span></span><span class="" style="top: -3em;"><span class="pstrut" style="height: 3.32144em;"></span><span class="mord"></span></span><span class="" style="top: -1.174em;"><span class="pstrut" style="height: 3.32144em;"></span><span class="mord"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 2.80744em;"><span class=""></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 3.30744em;"><span class="" style="top: -5.30744em;"><span class="pstrut" style="height: 3.32144em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right: 0.277778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.277778em;"></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: 1.32144em;"><span class="" style="top: -2.314em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord">2</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line" style="border-bottom-width: 0.04em;"></span></span><span class="" style="top: -3.677em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.686em;"><span class=""></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mopen">{<!-- --></span><span class="mopen">[</span><span class="mord">−</span><span class="mord">0</span><span class="mord">.</span><span class="mord">1</span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mord mathdefault" style="margin-right: 0.01968em;">l</span><span class="mord mathdefault">n</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.864108em;"><span class="" style="top: -3.113em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span><span class="mord mtight">.</span><span class="mord mtight">9</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mord"><span class="mord mathdefault">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.864108em;"><span class="" style="top: -3.113em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span><span class="mord mtight">.</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mclose">]</span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mopen">[</span><span class="mord">−</span><span class="mord">0</span><span class="mord">.</span><span class="mord">3</span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mord mathdefault" style="margin-right: 0.01968em;">l</span><span class="mord mathdefault">n</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.864108em;"><span class="" style="top: -3.113em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span><span class="mord mtight">.</span><span class="mord mtight">7</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mord"><span class="mord mathdefault">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.864108em;"><span class="" style="top: -3.113em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span><span class="mord mtight">.</span><span class="mord mtight">3</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mclose">]</span><span class="mclose">}</span></span></span><span class="" style="top: -3em;"><span class="pstrut" style="height: 3.32144em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right: 0.277778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.277778em;"></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: 1.32144em;"><span class="" style="top: -2.314em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord">2</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line" style="border-bottom-width: 0.04em;"></span></span><span class="" style="top: -3.677em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.686em;"><span class=""></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mord">.</span><span class="mord">1</span><span class="mord">7</span><span class="mord">1</span><span class="mord">1</span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">9</span><span class="mord">1</span><span class="mord">3</span><span class="mord">0</span><span class="mclose">)</span></span></span><span class="" style="top: -1.174em;"><span class="pstrut" style="height: 3.32144em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right: 0.277778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.277778em;"></span><span class="mord">1</span><span class="mord">.</span><span class="mord">0</span><span class="mord">4</span><span class="mord">2</span><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 2.80744em;"><span class=""></span></span></span></span></span></span></span></span></span></span></span></p>