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inset: 0px; display: block; float: none; margin: 0px; height: 52px;"></div></div></div><article class="Post-Main Post-NormalMain" tabindex="-1"><header class="Post-Header"><h1 class="Post-Title">Fréchet Inception Distance (FID)</h1><div class="Post-Author"><div class="AuthorInfo" itemprop="author" itemscope="" itemtype="http://schema.org/Person"><meta itemprop="name" content="杨指北"><meta itemprop="image" content="https://pic4.zhimg.com/bf28449bb_l.jpg"><meta itemprop="url" content="https://www.zhihu.com/people/yin-xiang-nan"><meta itemprop="zhihu:followerCount"><span class="UserLink AuthorInfo-avatarWrapper"><div class="Popover"><div id="Popover9-toggle" aria-haspopup="true" aria-expanded="false" aria-owns="Popover9-content"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/yin-xiang-nan"><img class="Avatar Avatar--round AuthorInfo-avatar" src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/bf28449bb_xs.jpg" srcset="https://pic4.zhimg.com/bf28449bb_l.jpg 2x" alt="杨指北" width="38" height="38"></a></div></div></span><div class="AuthorInfo-content"><div class="AuthorInfo-head"><span class="UserLink AuthorInfo-name"><div class="Popover"><div id="Popover10-toggle" aria-haspopup="true" aria-expanded="false" aria-owns="Popover10-content"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/yin-xiang-nan">杨指北</a></div></div></span></div><div class="AuthorInfo-detail"><div class="AuthorInfo-badge"><div class="ztext AuthorInfo-badgeText">无业游民</div></div></div></div></div></div><div class="LabelContainer-wrapper"></div><div><span class="Voters"><span><span class="UserLink"><div class="Popover"><div id="Popover14-toggle" aria-haspopup="true" aria-expanded="false" aria-owns="Popover14-content"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/xiao-huang-ren-nao-can-fen">兔子老大</a></div></div></span></span><span>、<span class="UserLink"><div class="Popover"><div id="Popover15-toggle" aria-haspopup="true" aria-expanded="false" aria-owns="Popover15-content"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/zhang-shi-chang-10">我zsc</a></div></div></span></span> 等 <button type="button" class="Button Button--plain">113 人赞同了该文章</button></span></div></header><div class="Post-RichTextContainer"><div class="RichText ztext Post-RichText"><p>之前写了一篇文章介绍 Inception Score 的原理和局限性</p><a target="_blank" href="https://zhuanlan.zhihu.com/p/54146307" data-draft-node="block" data-draft-type="link-card" data-image="https://pic3.zhimg.com/equation_ipico.jpg" data-image-width="0" data-image-height="0" class="LinkCard LinkCard--hasImage" data-za-detail-view-id="172"><span class="LinkCard-backdrop" style="background-image:url(https://pic3.zhimg.com/equation_ipico.jpg)"></span><span class="LinkCard-content"><span class="LinkCard-text"><span class="LinkCard-title" data-text="true">尹相楠：Inception Score 的原理和局限性</span><span class="LinkCard-meta"><span style="display:inline-flex;align-items:center"><svg class="Zi Zi--InsertLink" fill="currentColor" viewBox="0 0 24 24" width="17" height="17"><path d="M13.414 4.222a4.5 4.5 0 1 1 6.364 6.364l-3.005 3.005a.5.5 0 0 1-.707 0l-.707-.707a.5.5 0 0 1 0-.707l3.005-3.005a2.5 2.5 0 1 0-3.536-3.536l-3.005 3.005a.5.5 0 0 1-.707 0l-.707-.707a.5.5 0 0 1 0-.707l3.005-3.005zm-6.187 6.187a.5.5 0 0 1 .638-.058l.07.058.706.707a.5.5 0 0 1 .058.638l-.058.07-3.005 3.004a2.5 2.5 0 0 0 3.405 3.658l.13-.122 3.006-3.005a.5.5 0 0 1 .638-.058l.069.058.707.707a.5.5 0 0 1 .058.638l-.058.069-3.005 3.005a4.5 4.5 0 0 1-6.524-6.196l.16-.168 3.005-3.005zm8.132-3.182a.25.25 0 0 1 .353 0l1.061 1.06a.25.25 0 0 1 0 .354l-8.132 8.132a.25.25 0 0 1-.353 0l-1.061-1.06a.25.25 0 0 1 0-.354l8.132-8.132z"></path></svg></span>zhuanlan.zhihu.com</span></span><span class="LinkCard-imageCell"><img class="LinkCard-image LinkCard-image--square" alt="图标" src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/equation_ipico.jpg"></span></span></a><h2><b>Inception Score 的问题</b></h2><p>首先回顾一下 Inception Score 的两个假设：</p><ol><li>越真实的图片，输入预训练的 Inception V3 ，分类的结果越明确。即在1000维的输出向量中，某一维很大，其余维很小。也就是说，输出的概率分布函数图越尖锐。</li><li>生成的图片多样性越强，那么类别的边缘分布就越平均，边缘分布的概率函数图像就越平整。</li></ol><p>Inception Score 通过计算 1 和 2 中两个概率分布的散度，来衡量生成模型的表现。</p><p>我们乍一看这两条假设，不难发现最明显的两个问题：</p><ol><li>针对第一个假设，是否越真实的图片，分类网络输出的概率分布函数越尖锐？显然是不见得的，如果某一个物体所属的类别在分类网络中并不存在，那么它的分布函数依然尖锐吗？</li><li>针
对第二个假设，是否输出图片均匀地覆盖每个类别，就意味着生成模型不存在 mode collapse？Inception net 输出 1000
类，假设生成模型在每类上都生成了 50 个图片，那么生成的图片的类别边缘分布是严格均匀分布的，按照 Inception Score
的假设，这种模型不存在 mode collapse，但是，如果各类中的50个图片，都是一模一样的，仍然是 mode
collapse。Inception Score 无法检测这种情况。</li></ol><p>除了上面最直观的两个硬伤，本文开头提到的文章中对
Inception Score 缺点做了详细分析。其中涉及到：使用 IS
时，分类模型应该和生成模型在同一个训练集上训练，否则分类模型计算的边缘分布将不准确，而分类模型对单个图片的预测，也将不能真实反映图片的清晰程度。</p><p>出现这一问题的本质原因是：<b>计
算 IS 时只考虑了生成样本，没有考虑真实数据，即 IS 无法反映真实数据和样本之间的距离，IS 判断数据真实性的依据，源于 Inception
V3 的训练集： ImageNet，在 Inception V3 的“世界观”下，凡是不像 ImageNet
的数据，都是不真实的，都不能保证输出一个 sharp 的 predition distribution。</b></p><h2><b>Fréchet Inception Distance</b></h2><p>而 Fréchet Inception Distance (FID) 则是计算了真实图片和假图片在 feature 层面的距离，因此显得更有道理一点。FID 的公式如下：</p><p><img src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/equation_003.svg" alt="[公式]" eeimg="1" data-formula="\mathrm{FID} = ||\mu_r-\mu_g||^2+Tr\big(\Sigma_r+\Sigma_g-2(\Sigma_r\Sigma_g)^{1/2}\big)\tag{1}"> </p><p>众所周知，预训练好的神经网络顶层可以提取图片的高级信息，一定程度能反映图片的本质。因此，FID 的提出者通过预训练的 Inception V3 来提取全连接层之前的 2048 维向量，作为图片的特征。公式 (1) 中：</p><p><img src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/equation_004.svg" alt="[公式]" eeimg="1" data-formula="\mu_r"> ：真实图片的特征的均值</p><p><img src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/equation.svg" alt="[公式]" eeimg="1" data-formula="\mu_g"> ：生成的图片的特征的均值</p><p><img src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/equation_002.svg" alt="[公式]" eeimg="1" data-formula="\Sigma_r"> : 真实图片的特征的协方差矩阵</p><p><img src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/equation_005.svg" alt="[公式]" eeimg="1" data-formula="\Sigma_g"> : 生成图片的特征的协方差矩阵</p><p>FID 用以衡量两个多元正态分布的距离，具体的来源见论文：</p><a target="_blank" href="https://link.zhihu.com/?target=https%3A//www.sciencedirect.com/science/article/pii/0047259X8290077X" data-draft-node="block" data-draft-type="link-card" data-image="https://pic4.zhimg.com/v2-ddcd0b2442ccbb84dd6c697d3df43a9f_120x160.jpg" data-image-width="110" data-image-height="150" class="LinkCard LinkCard--hasImage" data-za-detail-view-id="172"><span class="LinkCard-backdrop" style="background-image:url(https://pic4.zhimg.com/v2-ddcd0b2442ccbb84dd6c697d3df43a9f_120x160.jpg)"></span><span class="LinkCard-content"><span class="LinkCard-text"><span class="LinkCard-title" data-text="true">The Fréchet distance between multivariate normal distributions</span><span class="LinkCard-meta"><span style="display:inline-flex;align-items:center"><svg class="Zi Zi--InsertLink" fill="currentColor" viewBox="0 0 24 24" width="17" height="17"><path d="M13.414 4.222a4.5 4.5 0 1 1 6.364 6.364l-3.005 3.005a.5.5 0 0 1-.707 0l-.707-.707a.5.5 0 0 1 0-.707l3.005-3.005a2.5 2.5 0 1 0-3.536-3.536l-3.005 3.005a.5.5 0 0 1-.707 0l-.707-.707a.5.5 0 0 1 0-.707l3.005-3.005zm-6.187 6.187a.5.5 0 0 1 .638-.058l.07.058.706.707a.5.5 0 0 1 .058.638l-.058.07-3.005 3.004a2.5 2.5 0 0 0 3.405 3.658l.13-.122 3.006-3.005a.5.5 0 0 1 .638-.058l.069.058.707.707a.5.5 0 0 1 .058.638l-.058.069-3.005 3.005a4.5 4.5 0 0 1-6.524-6.196l.16-.168 3.005-3.005zm8.132-3.182a.25.25 0 0 1 .353 0l1.061 1.06a.25.25 0 0 1 0 .354l-8.132 8.132a.25.25 0 0 1-.353 0l-1.061-1.06a.25.25 0 0 1 0-.354l8.132-8.132z"></path></svg></span>www.sciencedirect.com</span></span><span class="LinkCard-imageCell"><img class="LinkCard-image LinkCard-image--vertical" alt="图标" src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/v2-ddcd0b2442ccbb84dd6c697d3df43a9f_120x160.jpg"></span></span></a><p>我数学能力有限，实在读不懂，好在最后的距离公式还是比较简单的，直接套进去就能用了。</p><p>FID
只把 Inception V3 作为特征提取器，并不依赖它判断图片的具体类别，hang因此不必担心 Inception V3
的训练数据和生成模型的训练数据不同。同时，由于直接衡量生成数据和真实数据的分布之间的距离，也不必担心每个类别内部只产生一模一样的图片这种形式的
mode collapse。完美避开了很多 Inception Score 的缺陷。</p><h2><b>总结</b></h2><p>综上所述，对比 IS，FID 有如下优点：</p><ol><li>生成模型的训练集和 Inception V3 的训练集可以不同。</li><li>计算 FID 时同时用到了生成的数据和真实数据，比起 IS 来更灵活。可以理解成，IS 判断真实性与否，是把生成数据和 ImageNet 数据做比较，而 FID 是把生成数据和训练数据做比较，因此更 reasonable。</li><li>以优化 FID 为目标，不会产生对抗样本。因为优化的是 lantent space feature，不是最终的输出图片，不会导致最终的生成图片失真。</li></ol><p>但是基于我的上篇文章 <a href="https://zhuanlan.zhihu.com/p/54146307" class="internal" data-za-detail-view-id="1043">尹相楠：Inception Score 的原理和局限性</a>，FID 仍然存在一些和 IS 同样的问题：</p><ol><li>FID 只是某一层的特征的分布，是否足以衡量真实数据分布与生成数据分布的距离？同时，提出 FID 公式计算的是多元正态分布的距离，显然神经网络提取的特征并不是多元正态分布。</li><li>针对同一个生成模型，不同框架下预训练的 Inception V3 算出的 FID 差别是否可以忽略？</li><li>FID 无法反映生成模型过拟合的情况，如果某个生成模型只是简单拷贝训练数据，FID 会非常小，认为这是一个完美的生成模型，因此，使用 FID 时同时也要通过别的手段证明生成模型没有过拟合。</li></ol><h2><b>代码实现</b></h2><p>下面的链接是基于 pytorch 的计算 FID 的代码。</p><a target="_blank" href="https://link.zhihu.com/?target=https%3A//github.com/mseitzer/pytorch-fid" data-draft-node="block" data-draft-type="link-card" data-image="https://pic4.zhimg.com/v2-3829d5a1202fe70b5e50fbd4116fc867_ipico.jpg" data-image-width="400" data-image-height="400" class="LinkCard LinkCard--hasImage" data-za-detail-view-id="172"><span class="LinkCard-backdrop" style="background-image:url(https://pic4.zhimg.com/v2-3829d5a1202fe70b5e50fbd4116fc867_ipico.jpg)"></span><span class="LinkCard-content"><span class="LinkCard-text"><span class="LinkCard-title" data-text="true">mseitzer/pytorch-fid</span><span class="LinkCard-meta"><span style="display:inline-flex;align-items:center"><svg class="Zi Zi--InsertLink" fill="currentColor" viewBox="0 0 24 24" width="17" height="17"><path d="M13.414 4.222a4.5 4.5 0 1 1 6.364 6.364l-3.005 3.005a.5.5 0 0 1-.707 0l-.707-.707a.5.5 0 0 1 0-.707l3.005-3.005a2.5 2.5 0 1 0-3.536-3.536l-3.005 3.005a.5.5 0 0 1-.707 0l-.707-.707a.5.5 0 0 1 0-.707l3.005-3.005zm-6.187 6.187a.5.5 0 0 1 .638-.058l.07.058.706.707a.5.5 0 0 1 .058.638l-.058.07-3.005 3.004a2.5 2.5 0 0 0 3.405 3.658l.13-.122 3.006-3.005a.5.5 0 0 1 .638-.058l.069.058.707.707a.5.5 0 0 1 .058.638l-.058.069-3.005 3.005a4.5 4.5 0 0 1-6.524-6.196l.16-.168 3.005-3.005zm8.132-3.182a.25.25 0 0 1 .353 0l1.061 1.06a.25.25 0 0 1 0 .354l-8.132 8.132a.25.25 0 0 1-.353 0l-1.061-1.06a.25.25 0 0 1 0-.354l8.132-8.132z"></path></svg></span>github.com</span></span><span class="LinkCard-imageCell"><img class="LinkCard-image LinkCard-image--square" alt="图标" src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/v2-3829d5a1202fe70b5e50fbd4116fc867_ipico.jpg"></span></span></a><p class="ztext-empty-paragraph"><br></p><p><i>~~
注意作者在源码中并没有加载 Inception V3 的权重，因此千万不要直接套用。建议读者自己继承一下 pytorch Inception
V3 的类，修改 forward 函数，让它返回全连接层前面的 2048 维向量，这样就可以直接加载 pytorch 官方的Inception
V3 的权重了。~~ </i></p><p>之前没有仔细看代码贸然提了个 issue，发现作者其实加载了 Inception V3 的权重，在inception.py文件的第 60 行。</p><p></p><p></p></div></div><div class="ContentItem-time">编辑于 2019-01-07</div><div><div class="Reward"><button class="Reward-activateBtn">开启赞赏</button><div class="Reward-activateHint">赞赏开启后，读者将可以付费支持你的创作。</div></div></div><div class="Post-topicsAndReviewer"><div class="TopicList Post-Topics"><div class="Tag Topic" data-za-detail-view-path-module="TopicItem" data-za-extra-module="{"card":{"content":{"type":"Topic","token":"20070859"}}}"><span class="Tag-content"><a class="TopicLink" href="https://www.zhihu.com/topic/20070859" target="_blank"><div class="Popover"><div id="Popover2-toggle" aria-haspopup="true" aria-expanded="false" aria-owns="Popover2-content">生成对抗网络（GAN）</div></div></a></span></div><div class="Tag Topic" data-za-detail-view-path-module="TopicItem" data-za-extra-module="{"card":{"content":{"type":"Topic","token":"19590195"}}}"><span class="Tag-content"><a class="TopicLink" 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Button--primary Button--blue">发布</button></div></div><div><div class="CommentListV2"><ul class="NestComment"><li class="NestComment--rootComment"><div class="CommentItemV2"><div><div class="CommentItemV2-meta"><span class="UserLink CommentItemV2-avatar"><div class="Popover"><div id="Popover18-toggle" aria-haspopup="true" aria-expanded="false" aria-owns="Popover18-content"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/fuckSBzhihu"><img class="Avatar UserLink-avatar" src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/da8e974dc_s.jpg" srcset="https://pic2.zhimg.com/da8e974dc_xs.jpg?source=06d4cd63 2x" alt="「已注销」" width="24" height="24"></a></div></div></span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/fuckSBzhihu">「已注销」</a></span><span class="CommentItemV2-time">2019-01-26</span></div><div class="CommentItemV2-metaSibling"><div class="CommentRichText CommentItemV2-content CommentItemV2-shield"><div class="RichText ztext">该评论已删除</div></div></div></div></div></li><li class="NestComment--child"><div class="CommentItemV2"><div><div class="CommentItemV2-meta"><span class="UserLink CommentItemV2-avatar"><div class="Popover"><div id="Popover19-toggle" aria-haspopup="true" aria-expanded="false" aria-owns="Popover19-content"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/yin-xiang-nan"><img class="Avatar UserLink-avatar" src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/bf28449bb_s_003.jpg" srcset="https://pic2.zhimg.com/bf28449bb_xs.jpg?source=06d4cd63 2x" alt="杨指北" width="24" height="24"></a></div></div></span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/yin-xiang-nan">杨指北</a></span><span class="CommentItemV2-roleInfo"> (作者) </span><span class="CommentItemV2-reply">回复</span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/fuckSBzhihu">「已注销」</a></span><span class="CommentItemV2-time">2019-01-26</span></div><div class="CommentItemV2-metaSibling"><div class="CommentRichText CommentItemV2-content"><div class="RichText ztext">都反映不了吧，fid只是计算生成分布和真实分布的距离，如果直接从真实分布往外拷贝，最后距离不就是0了嘛</div></div><div class="CommentItemV2-footer"><button type="button" disabled="disabled" class="Button CommentItemV2-likeBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Like" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M14.445 9h5.387s2.997.154 1.95 3.669c-.168.51-2.346 6.911-2.346 6.911s-.763 1.416-2.86 1.416H8.989c-1.498 0-2.005-.896-1.989-2v-7.998c0-.987.336-2.032 1.114-2.639 4.45-3.773 3.436-4.597 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src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/v2-2516c194153e9a39dcf40b68dbdb1df5_s.jpg" srcset="https://pic4.zhimg.com/v2-2516c194153e9a39dcf40b68dbdb1df5_xs.jpg?source=06d4cd63 2x" alt="zhaoshir" width="24" height="24"></a></div></div></span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/pan-zhi-qi">zhaoshir</a></span><span class="CommentItemV2-reply">回复</span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/yin-xiang-nan">杨指北</a></span><span class="CommentItemV2-roleInfo"> (作者) </span><span class="CommentItemV2-time">2019-07-28</span></div><div class="CommentItemV2-metaSibling"><div class="CommentRichText CommentItemV2-content"><div class="RichText ztext"><p>对
了，关于过拟合这个情况，我记得Goodfellow在NIPS2016里提到过，他的观点是，生成器其实不太可能简单地拷贝训练数据，因为生成器从始自
终都没有「直接地」见过这些原始的训练数据，而是「间接地」从backprop返回的gradient里见到过这些数据（从判别器backprop回生成
器的gradient里）。也就是说，生成器没办法直接拷贝训练数据，它根本不知道训练数据本来长啥样。</p></div></div><div class="CommentItemV2-footer"><button type="button" class="Button CommentItemV2-likeBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Like" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M14.445 9h5.387s2.997.154 1.95 3.669c-.168.51-2.346 6.911-2.346 6.911s-.763 1.416-2.86 1.416H8.989c-1.498 0-2.005-.896-1.989-2v-7.998c0-.987.336-2.032 1.114-2.639 4.45-3.773 3.436-4.597 4.45-5.83.985-1.13 3.2-.5 3.037 2.362C15.201 7.397 14.445 9 14.445 9zM3 9h2a1 1 0 0 1 1 1v10a1 1 0 0 1-1 1H3a1 1 0 0 1-1-1V10a1 1 0 0 1 1-1z" fill-rule="evenodd"></path></svg></span>13</button><button type="button" class="Button CommentItemV2-hoverBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Reply" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M22.959 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data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/gu-shu-yang">古纾旸</a></span><span class="CommentItemV2-time">2019-02-27</span></div><div class="CommentItemV2-metaSibling"><div class="CommentRichText CommentItemV2-content"><div class="RichText ztext"><p>优化FID也会产生对抗样本吧</p></div></div><div class="CommentItemV2-footer"><button type="button" class="Button CommentItemV2-likeBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Like" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M14.445 9h5.387s2.997.154 1.95 3.669c-.168.51-2.346 6.911-2.346 6.911s-.763 1.416-2.86 1.416H8.989c-1.498 0-2.005-.896-1.989-2v-7.998c0-.987.336-2.032 1.114-2.639 4.45-3.773 3.436-4.597 4.45-5.83.985-1.13 3.2-.5 3.037 2.362C15.201 7.397 14.445 9 14.445 9zM3 9h2a1 1 0 0 1 1 1v10a1 1 0 0 1-1 1H3a1 1 0 0 1-1-1V10a1 1 0 0 1 1-1z" fill-rule="evenodd"></path></svg></span>赞</button><button 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alt="zhaoshir" width="24" height="24"></a></div></div></span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/pan-zhi-qi">zhaoshir</a></span><span class="CommentItemV2-time">2019-07-28</span></div><div class="CommentItemV2-metaSibling"><div class="CommentRichText CommentItemV2-content"><div class="RichText ztext"><p>写得很清楚很容易懂，十分感谢你！</p></div></div><div class="CommentItemV2-footer"><button type="button" class="Button CommentItemV2-likeBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Like" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M14.445 9h5.387s2.997.154 1.95 3.669c-.168.51-2.346 6.911-2.346 6.911s-.763 1.416-2.86 1.416H8.989c-1.498 0-2.005-.896-1.989-2v-7.998c0-.987.336-2.032 1.114-2.639 4.45-3.773 3.436-4.597 4.45-5.83.985-1.13 3.2-.5 3.037 2.362C15.201 7.397 14.445 9 14.445 9zM3 9h2a1 1 0 0 1 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srcset="https://pic4.zhimg.com/79af5f4cf3198e2118cbe60b06a5242c_xs.jpg?source=06d4cd63 2x" alt="Fantasy" width="24" height="24"></a></div></div></span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/fantasyjxf">Fantasy</a></span><span class="CommentItemV2-time">2019-09-04</span></div><div class="CommentItemV2-metaSibling"><div class="CommentRichText CommentItemV2-content"><div class="RichText ztext"><p>关于IS, FID, KID看上去都是在一定规模的数据集上计算统计意义上的参数，是否有方法能对单个样本的表现进行评估呢</p></div></div><div class="CommentItemV2-footer"><button type="button" class="Button CommentItemV2-likeBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Like" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M14.445 9h5.387s2.997.154 1.95 3.669c-.168.51-2.346 6.911-2.346 6.911s-.763 1.416-2.86 1.416H8.989c-1.498 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src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/bf28449bb_s_002.jpg" srcset="https://pic4.zhimg.com/bf28449bb_xs.jpg?source=06d4cd63 2x" alt="杨指北" width="24" height="24"></a></div></div></span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/yin-xiang-nan">杨指北</a></span><span class="CommentItemV2-roleInfo"> (作者) </span><span class="CommentItemV2-reply">回复</span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/fantasyjxf">Fantasy</a></span><span class="CommentItemV2-time">2019-09-04</span></div><div class="CommentItemV2-metaSibling"><div class="CommentRichText CommentItemV2-content"><div class="RichText ztext"><p>没办法吧，单个样本如何评价它的质量好坏呢？除非有个ground truth。。</p></div></div><div class="CommentItemV2-footer"><button type="button" disabled="disabled" class="Button CommentItemV2-likeBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Like" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M14.445 9h5.387s2.997.154 1.95 3.669c-.168.51-2.346 6.911-2.346 6.911s-.763 1.416-2.86 1.416H8.989c-1.498 0-2.005-.896-1.989-2v-7.998c0-.987.336-2.032 1.114-2.639 4.45-3.773 3.436-4.597 4.45-5.83.985-1.13 3.2-.5 3.037 2.362C15.201 7.397 14.445 9 14.445 9zM3 9h2a1 1 0 0 1 1 1v10a1 1 0 0 1-1 1H3a1 1 0 0 1-1-1V10a1 1 0 0 1 1-1z" fill-rule="evenodd"></path></svg></span>4</button><button type="button" class="Button Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Recommend" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M6.433 14.285l-.918 5.355c-.219 1.274.532 1.82 1.676 1.218l4.81-2.528 4.807 2.528c1.145.601 1.896.056 1.677-1.218l-.918-5.355 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class="CommentItemV2-meta"><span class="UserLink CommentItemV2-avatar"><div class="Popover"><div id="Popover25-toggle" aria-haspopup="true" aria-expanded="false" aria-owns="Popover25-content"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/fantasyjxf"><img class="Avatar UserLink-avatar" src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/79af5f4cf3198e2118cbe60b06a5242c_s_002.jpg" srcset="https://pic2.zhimg.com/79af5f4cf3198e2118cbe60b06a5242c_xs.jpg?source=06d4cd63 2x" alt="Fantasy" width="24" height="24"></a></div></div></span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/fantasyjxf">Fantasy</a></span><span class="CommentItemV2-reply">回复</span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/yin-xiang-nan">杨指北</a></span><span class="CommentItemV2-roleInfo"> (作者) </span><span class="CommentItemV2-time">2019-09-05</span></div><div class="CommentItemV2-metaSibling"><div class="CommentRichText CommentItemV2-content"><div class="RichText ztext">像检测、分割、识别任务感觉还能根据一些阈值设置对结果进行一下限制。<br>GAN这种怎么着都得生成一张图片，通过无参考图像评价方法理论上可能可以过滤掉一些引起生理不适的结果？<br><br>对于图像转换这样的任务，比如自拍转卡通头像，这样算是有ground truth吗？ 希望生成的图片长得像原图，又具有动漫风格，能否指点一下谢谢</div></div><div class="CommentItemV2-footer"><button type="button" class="Button CommentItemV2-likeBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Like" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M14.445 9h5.387s2.997.154 1.95 3.669c-.168.51-2.346 6.911-2.346 6.911s-.763 1.416-2.86 1.416H8.989c-1.498 0-2.005-.896-1.989-2v-7.998c0-.987.336-2.032 1.114-2.639 4.45-3.773 3.436-4.597 4.45-5.83.985-1.13 3.2-.5 3.037 2.362C15.201 7.397 14.445 9 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srcset="https://pic2.zhimg.com/da8e974dc_xs.jpg?source=06d4cd63 2x" alt="Crystal" width="24" height="24"></a></div></div></span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/crystal-99-68-70">Crystal</a></span><span class="CommentItemV2-time">2019-09-05</span></div><div class="CommentItemV2-metaSibling"><div class="CommentRichText CommentItemV2-content"><div class="RichText ztext"><p>论文不是很看得懂，在算FID的时候，是否需要真实的图片和测试的图片是同一张图（内容是一样的）算FID才有意义？</p></div></div><div class="CommentItemV2-footer"><button type="button" class="Button CommentItemV2-likeBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Like" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M14.445 9h5.387s2.997.154 1.95 3.669c-.168.51-2.346 6.911-2.346 6.911s-.763 1.416-2.86 1.416H8.989c-1.498 0-2.005-.896-1.989-2v-7.998c0-.987.336-2.032 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src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/bf28449bb_s.jpg" srcset="https://pic1.zhimg.com/bf28449bb_xs.jpg?source=06d4cd63 2x" alt="杨指北" width="24" height="24"></a></div></div></span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/yin-xiang-nan">杨指北</a></span><span class="CommentItemV2-roleInfo"> (作者) </span><span class="CommentItemV2-reply">回复</span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/crystal-99-68-70">Crystal</a></span><span class="CommentItemV2-time">2019-09-08</span></div><div class="CommentItemV2-metaSibling"><div class="CommentRichText CommentItemV2-content"><div class="RichText ztext"><p>不是，它算的是生成的多张图片在feature 空间上的概率分布和真实图片的差距</p></div></div><div class="CommentItemV2-footer"><button type="button" disabled="disabled" class="Button CommentItemV2-likeBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Like" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M14.445 9h5.387s2.997.154 1.95 3.669c-.168.51-2.346 6.911-2.346 6.911s-.763 1.416-2.86 1.416H8.989c-1.498 0-2.005-.896-1.989-2v-7.998c0-.987.336-2.032 1.114-2.639 4.45-3.773 3.436-4.597 4.45-5.83.985-1.13 3.2-.5 3.037 2.362C15.201 7.397 14.445 9 14.445 9zM3 9h2a1 1 0 0 1 1 1v10a1 1 0 0 1-1 1H3a1 1 0 0 1-1-1V10a1 1 0 0 1 1-1z" fill-rule="evenodd"></path></svg></span>赞</button><button type="button" class="Button Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Recommend" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M6.433 14.285l-.918 5.355c-.219 1.274.532 1.82 1.676 1.218l4.81-2.528 4.807 2.528c1.145.601 1.896.056 1.677-1.218l-.918-5.355 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class="CommentItemV2"><div><div class="CommentItemV2-meta"><span class="UserLink CommentItemV2-avatar"><div class="Popover"><div id="Popover28-toggle" aria-haspopup="true" aria-expanded="false" aria-owns="Popover28-content"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/six_god_happy"><img class="Avatar UserLink-avatar" src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/v2-b3972b0910fb289835fde7f924d0c327_s.jpg" srcset="https://pic1.zhimg.com/v2-b3972b0910fb289835fde7f924d0c327_xs.jpg?source=06d4cd63 2x" alt="SixGod" width="24" height="24"></a></div></div></span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/six_god_happy">SixGod</a></span><span class="CommentItemV2-time">2019-09-07</span></div><div class="CommentItemV2-metaSibling"><div class="CommentRichText CommentItemV2-content"><div class="RichText ztext"><p>在计算协方差那一半，会有可能存在负数开平方，这个怎么解决</p></div></div><div class="CommentItemV2-footer"><button type="button" class="Button CommentItemV2-likeBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Like" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M14.445 9h5.387s2.997.154 1.95 3.669c-.168.51-2.346 6.911-2.346 6.911s-.763 1.416-2.86 1.416H8.989c-1.498 0-2.005-.896-1.989-2v-7.998c0-.987.336-2.032 1.114-2.639 4.45-3.773 3.436-4.597 4.45-5.83.985-1.13 3.2-.5 3.037 2.362C15.201 7.397 14.445 9 14.445 9zM3 9h2a1 1 0 0 1 1 1v10a1 1 0 0 1-1 1H3a1 1 0 0 1-1-1V10a1 1 0 0 1 1-1z" fill-rule="evenodd"></path></svg></span>赞</button><button type="button" class="Button CommentItemV2-hoverBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Reply" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M22.959 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class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/six_god_happy">SixGod</a></span><span class="CommentItemV2-time">2019-09-08</span></div><div class="CommentItemV2-metaSibling"><div class="CommentRichText CommentItemV2-content"><div class="RichText ztext"><p>协方差矩阵的对角线上都是正数</p></div></div><div class="CommentItemV2-footer"><button type="button" disabled="disabled" class="Button CommentItemV2-likeBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Like" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M14.445 9h5.387s2.997.154 1.95 3.669c-.168.51-2.346 6.911-2.346 6.911s-.763 1.416-2.86 1.416H8.989c-1.498 0-2.005-.896-1.989-2v-7.998c0-.987.336-2.032 1.114-2.639 4.45-3.773 3.436-4.597 4.45-5.83.985-1.13 3.2-.5 3.037 2.362C15.201 7.397 14.445 9 14.445 9zM3 9h2a1 1 0 0 1 1 1v10a1 1 0 0 1-1 1H3a1 1 0 0 1-1-1V10a1 1 0 0 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CommentItemV2-avatar"><div class="Popover"><div id="Popover31-toggle" aria-haspopup="true" aria-expanded="false" aria-owns="Popover31-content"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/a-ke-ke-ke-55"><img class="Avatar UserLink-avatar" src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/v2-18bd3faf7a0557cfbaa6bee6532925ac_s.jpg" srcset="https://pic4.zhimg.com/v2-18bd3faf7a0557cfbaa6bee6532925ac_xs.jpg?source=06d4cd63 2x" alt="小扣子" width="24" height="24"></a></div></div></span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/a-ke-ke-ke-55">小扣子</a></span><span class="CommentItemV2-time">2019-10-29</span></div><div class="CommentItemV2-metaSibling"><div class="CommentRichText CommentItemV2-content"><div class="RichText ztext"><p>您好，打扰一下，想问一下‘分类模型和生成模型在不同的数据集上训练’，如果我的生成模型是关于人脸的，但是Inception V3是关于物体分类的，这也也可以用Inception Net来提取特征么？谢谢！</p></div></div><div class="CommentItemV2-footer"><button type="button" class="Button CommentItemV2-likeBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Like" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M14.445 9h5.387s2.997.154 1.95 3.669c-.168.51-2.346 6.911-2.346 6.911s-.763 1.416-2.86 1.416H8.989c-1.498 0-2.005-.896-1.989-2v-7.998c0-.987.336-2.032 1.114-2.639 4.45-3.773 3.436-4.597 4.45-5.83.985-1.13 3.2-.5 3.037 2.362C15.201 7.397 14.445 9 14.445 9zM3 9h2a1 1 0 0 1 1 1v10a1 1 0 0 1-1 1H3a1 1 0 0 1-1-1V10a1 1 0 0 1 1-1z" fill-rule="evenodd"></path></svg></span>赞</button><button type="button" class="Button CommentItemV2-hoverBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Reply" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M22.959 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class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/a-ke-ke-ke-55">小扣子</a></span><span class="CommentItemV2-time">2019-11-28</span></div><div class="CommentItemV2-metaSibling"><div class="CommentRichText CommentItemV2-content"><div class="RichText ztext"><p>嗨咯 你最后用什么来评价的啊 我生成的也是关于人脸的</p></div></div><div class="CommentItemV2-footer"><button type="button" class="Button CommentItemV2-likeBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Like" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M14.445 9h5.387s2.997.154 1.95 3.669c-.168.51-2.346 6.911-2.346 6.911s-.763 1.416-2.86 1.416H8.989c-1.498 0-2.005-.896-1.989-2v-7.998c0-.987.336-2.032 1.114-2.639 4.45-3.773 3.436-4.597 4.45-5.83.985-1.13 3.2-.5 3.037 2.362C15.201 7.397 14.445 9 14.445 9zM3 9h2a1 1 0 0 1 1 1v10a1 1 0 0 1-1 1H3a1 1 0 0 1-1-1V10a1 1 0 0 1 1-1z" 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srcset="https://pic4.zhimg.com/v2-da5078b15e07690f887598287901b582_xs.jpg?source=06d4cd63 2x" alt="药师" width="24" height="24"></a></div></div></span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/ling-luan-85-32">药师</a></span><span class="CommentItemV2-time">2019-11-06</span></div><div class="CommentItemV2-metaSibling"><div class="CommentRichText CommentItemV2-content"><div class="RichText ztext">请问一下，计算CIFAR10的FID的时候，选取多少图片合适呢</div></div><div class="CommentItemV2-footer"><button type="button" class="Button CommentItemV2-likeBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Like" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M14.445 9h5.387s2.997.154 1.95 3.669c-.168.51-2.346 6.911-2.346 6.911s-.763 1.416-2.86 1.416H8.989c-1.498 0-2.005-.896-1.989-2v-7.998c0-.987.336-2.032 1.114-2.639 4.45-3.773 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UserLink-avatar" src="Fr%C3%A9chet%20Inception%20Distance%20(FID)%20-%20%E7%9F%A5%E4%B9%8E_files/v2-5162d6b5b662360500c4583bc06192be_s.jpg" srcset="https://pic2.zhimg.com/v2-5162d6b5b662360500c4583bc06192be_xs.jpg?source=06d4cd63 2x" alt="bugmaker" width="24" height="24"></a></div></div></span><span class="UserLink"><a class="UserLink-link" data-za-detail-view-element_name="User" target="_blank" href="https://www.zhihu.com/people/zhao-xing-bo-85">bugmaker</a></span><span class="CommentItemV2-time">2020-07-04</span></div><div class="CommentItemV2-metaSibling"><div class="CommentRichText CommentItemV2-content"><div class="RichText ztext"><p>请问除了IS与FID外，近两年是否还有类似的评价指标论文出现呢</p></div></div><div class="CommentItemV2-footer"><button type="button" class="Button CommentItemV2-likeBtn Button--plain"><span style="display: inline-flex; align-items: center;"><svg class="Zi Zi--Like" style="margin-right: 5px;" fill="currentColor" viewBox="0 0 24 24" width="16" height="16"><path d="M14.445 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data-image=\"https:\u002F\u002Fpic1.zhimg.com\u002Fequation_ipico.jpg\" data-image-width=\"0\" data-image-height=\"0\" class=\"internal\"\u003E尹相楠：Inception Score 的原理和局限性\u003C\u002Fa\u003E\u003Cb\u003EInception Score 的问题\u003C\u002Fb\u003E首先回顾一下 Inception Score 的两个假设： 越真实的图片，输入预训练的 Inception V3 ，分类的结果越明确。即在1000维的输出向量中，…","created":1546820525,"updated":1546854924,"author":{"isFollowed":false,"avatarUrlTemplate":"https:\u002F\u002Fpic1.zhimg.com\u002Fbf28449bb.jpg?source=172ae18b","uid":"28236180357120","userType":"people","isFollowing":false,"urlToken":"yin-xiang-nan","id":"2bcb30744c0f014ce6702f4d94922945","description":"","name":"杨指北","isAdvertiser":false,"headline":"无业游民","gender":1,"url":"\u002Fpeople\u002F2bcb30744c0f014ce6702f4d94922945","avatarUrl":"https:\u002F\u002Fpic1.zhimg.com\u002Fbf28449bb_l.jpg?source=172ae18b","isOrg":false,"type":"people","vipInfo":{"isVip":true,"vipIcon":{"url":"https:\u002F\u002Fpic4.zhimg.com\u002Fv2-4812630bc27d642f7cafcd6cdeca3d7a_r.png?source=172ae18b","nightModeUrl":"https:\u002F\u002Fpic1.zhimg.com\u002Fv2-c9686ff064ea3579730756ac6c289978_r.png?source=172ae18b"}},"levelInfo":{"exp":150802,"level":8,"nicknameColor":{"color":"","nightModeColor":""},"levelIcon":"https:\u002F\u002Fpic1.zhimg.com\u002Fv2-ce2d9b858d70d9e107f14c57a0ceb563_l.png","iconInfo":{"url":"https:\u002F\u002Fpic1.zhimg.com\u002Fv2-ce2d9b858d70d9e107f14c57a0ceb563_l.png","nightModeUrl":"https:\u002F\u002Fpic2.zhimg.com\u002Fv2-2c1a38e54e53ce62f8b7bc346a043c61_l.png","width":93,"height":51}},"badge":[],"badgeV2":{"title":"","mergedBadges":[],"detailBadges":[],"icon":"","nightIcon":""},"exposedMedal":{"medalId":"1124316222665379841","medalName":"我的知乎 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，分类的结果越明确。即在1000维的输出向量中，某一维很大，其余维很小。也就是说，输出的概率分布函数图越尖锐。\u003C\u002Fli\u003E\u003Cli\u003E生成的图片多样性越强，那么类别的边缘分布就越平均，边缘分布的概率函数图像就越平整。\u003C\u002Fli\u003E\u003C\u002Fol\u003E\u003Cp\u003EInception Score 通过计算 1 和 2 中两个概率分布的散度，来衡量生成模型的表现。\u003C\u002Fp\u003E\u003Cp\u003E我们乍一看这两条假设，不难发现最明显的两个问题：\u003C\u002Fp\u003E\u003Col\u003E\u003Cli\u003E针对第一个假设，是否越真实的图片，分类网络输出的概率分布函数越尖锐？显然是不见得的，如果某一个物体所属的类别在分类网络中并不存在，那么它的分布函数依然尖锐吗？\u003C\u002Fli\u003E\u003Cli\u003E针对第二个假设，是否输出图片均匀地覆盖每个类别，就意味着生成模型不存在 mode collapse？Inception net 输出 1000 类，假设生成模型在每类上都生成了 50 个图片，那么生成的图片的类别边缘分布是严格均匀分布的，按照 Inception Score 的假设，这种模型不存在 mode collapse，但是，如果各类中的50个图片，都是一模一样的，仍然是 mode collapse。Inception Score 无法检测这种情况。\u003C\u002Fli\u003E\u003C\u002Fol\u003E\u003Cp\u003E除了上面最直观的两个硬伤，本文开头提到的文章中对 Inception Score 缺点做了详细分析。其中涉及到：使用 IS 时，分类模型应该和生成模型在同一个训练集上训练，否则分类模型计算的边缘分布将不准确，而分类模型对单个图片的预测，也将不能真实反映图片的清晰程度。\u003C\u002Fp\u003E\u003Cp\u003E出现这一问题的本质原因是：\u003Cb\u003E计算 IS 时只考虑了生成样本，没有考虑真实数据，即 IS 无法反映真实数据和样本之间的距离，IS 判断数据真实性的依据，源于 Inception V3 的训练集： ImageNet，在 Inception V3 的“世界观”下，凡是不像 ImageNet 的数据，都是不真实的，都不能保证输出一个 sharp 的 predition distribution。\u003C\u002Fb\u003E\u003C\u002Fp\u003E\u003Ch2\u003E\u003Cb\u003EFréchet Inception Distance\u003C\u002Fb\u003E\u003C\u002Fh2\u003E\u003Cp\u003E而 Fréchet Inception Distance (FID) 则是计算了真实图片和假图片在 feature 层面的距离，因此显得更有道理一点。FID 的公式如下：\u003C\u002Fp\u003E\u003Cp\u003E\u003Cimg src=\"https:\u002F\u002Fwww.zhihu.com\u002Fequation?tex=%5Cmathrm%7BFID%7D+%3D+%7C%7C%5Cmu_r-%5Cmu_g%7C%7C%5E2%2BTr%5Cbig%28%5CSigma_r%2B%5CSigma_g-2%28%5CSigma_r%5CSigma_g%29%5E%7B1%2F2%7D%5Cbig%29%5Ctag%7B1%7D\" alt=\"\\mathrm{FID} = ||\\mu_r-\\mu_g||^2+Tr\\big(\\Sigma_r+\\Sigma_g-2(\\Sigma_r\\Sigma_g)^{1\u002F2}\\big)\\tag{1}\" eeimg=\"1\"\u002F\u003E \u003C\u002Fp\u003E\u003Cp\u003E众所周知，预训练好的神经网络顶层可以提取图片的高级信息，一定程度能反映图片的本质。因此，FID 的提出者通过预训练的 Inception V3 来提取全连接层之前的 2048 维向量，作为图片的特征。公式 (1) 中：\u003C\u002Fp\u003E\u003Cp\u003E\u003Cimg src=\"https:\u002F\u002Fwww.zhihu.com\u002Fequation?tex=%5Cmu_r\" alt=\"\\mu_r\" eeimg=\"1\"\u002F\u003E ：真实图片的特征的均值\u003C\u002Fp\u003E\u003Cp\u003E\u003Cimg src=\"https:\u002F\u002Fwww.zhihu.com\u002Fequation?tex=%5Cmu_g\" alt=\"\\mu_g\" eeimg=\"1\"\u002F\u003E ：生成的图片的特征的均值\u003C\u002Fp\u003E\u003Cp\u003E\u003Cimg src=\"https:\u002F\u002Fwww.zhihu.com\u002Fequation?tex=%5CSigma_r\" alt=\"\\Sigma_r\" eeimg=\"1\"\u002F\u003E : 真实图片的特征的协方差矩阵\u003C\u002Fp\u003E\u003Cp\u003E\u003Cimg src=\"https:\u002F\u002Fwww.zhihu.com\u002Fequation?tex=%5CSigma_g\" alt=\"\\Sigma_g\" eeimg=\"1\"\u002F\u003E : 生成图片的特征的协方差矩阵\u003C\u002Fp\u003E\u003Cp\u003EFID 用以衡量两个多元正态分布的距离，具体的来源见论文：\u003C\u002Fp\u003E\u003Ca href=\"https:\u002F\u002Flink.zhihu.com\u002F?target=https%3A\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002F0047259X8290077X\" data-draft-node=\"block\" data-draft-type=\"link-card\" data-image=\"https:\u002F\u002Fpic4.zhimg.com\u002Fv2-ddcd0b2442ccbb84dd6c697d3df43a9f_120x160.jpg\" data-image-width=\"110\" data-image-height=\"150\" class=\" wrap external\" target=\"_blank\" rel=\"nofollow noreferrer\"\u003EThe Fréchet distance between multivariate normal distributions\u003C\u002Fa\u003E\u003Cp\u003E我数学能力有限，实在读不懂，好在最后的距离公式还是比较简单的，直接套进去就能用了。\u003C\u002Fp\u003E\u003Cp\u003EFID 只把 Inception V3 作为特征提取器，并不依赖它判断图片的具体类别，hang因此不必担心 Inception V3 的训练数据和生成模型的训练数据不同。同时，由于直接衡量生成数据和真实数据的分布之间的距离，也不必担心每个类别内部只产生一模一样的图片这种形式的 mode collapse。完美避开了很多 Inception Score 的缺陷。\u003C\u002Fp\u003E\u003Ch2\u003E\u003Cb\u003E总结\u003C\u002Fb\u003E\u003C\u002Fh2\u003E\u003Cp\u003E综上所述，对比 IS，FID 有如下优点：\u003C\u002Fp\u003E\u003Col\u003E\u003Cli\u003E生成模型的训练集和 Inception V3 的训练集可以不同。\u003C\u002Fli\u003E\u003Cli\u003E计算 FID 时同时用到了生成的数据和真实数据，比起 IS 来更灵活。可以理解成，IS 判断真实性与否，是把生成数据和 ImageNet 数据做比较，而 FID 是把生成数据和训练数据做比较，因此更 reasonable。\u003C\u002Fli\u003E\u003Cli\u003E以优化 FID 为目标，不会产生对抗样本。因为优化的是 lantent space feature，不是最终的输出图片，不会导致最终的生成图片失真。\u003C\u002Fli\u003E\u003C\u002Fol\u003E\u003Cp\u003E但是基于我的上篇文章 \u003Ca href=\"https:\u002F\u002Fzhuanlan.zhihu.com\u002Fp\u002F54146307\" class=\"internal\"\u003E尹相楠：Inception Score 的原理和局限性\u003C\u002Fa\u003E，FID 仍然存在一些和 IS 同样的问题：\u003C\u002Fp\u003E\u003Col\u003E\u003Cli\u003EFID 只是某一层的特征的分布，是否足以衡量真实数据分布与生成数据分布的距离？同时，提出 FID 公式计算的是多元正态分布的距离，显然神经网络提取的特征并不是多元正态分布。\u003C\u002Fli\u003E\u003Cli\u003E针对同一个生成模型，不同框架下预训练的 Inception V3 算出的 FID 差别是否可以忽略？\u003C\u002Fli\u003E\u003Cli\u003EFID 无法反映生成模型过拟合的情况，如果某个生成模型只是简单拷贝训练数据，FID 会非常小，认为这是一个完美的生成模型，因此，使用 FID 时同时也要通过别的手段证明生成模型没有过拟合。\u003C\u002Fli\u003E\u003C\u002Fol\u003E\u003Ch2\u003E\u003Cb\u003E代码实现\u003C\u002Fb\u003E\u003C\u002Fh2\u003E\u003Cp\u003E下面的链接是基于 pytorch 的计算 FID 的代码。\u003C\u002Fp\u003E\u003Ca href=\"https:\u002F\u002Flink.zhihu.com\u002F?target=https%3A\u002F\u002Fgithub.com\u002Fmseitzer\u002Fpytorch-fid\" data-draft-node=\"block\" data-draft-type=\"link-card\" data-image=\"https:\u002F\u002Fpic4.zhimg.com\u002Fv2-3829d5a1202fe70b5e50fbd4116fc867_ipico.jpg\" data-image-width=\"400\" data-image-height=\"400\" class=\" wrap external\" target=\"_blank\" rel=\"nofollow noreferrer\"\u003Emseitzer\u002Fpytorch-fid\u003C\u002Fa\u003E\u003Cp class=\"ztext-empty-paragraph\"\u003E\u003Cbr\u002F\u003E\u003C\u002Fp\u003E\u003Cp\u003E\u003Ci\u003E~~注意作者在源码中并没有加载 Inception V3 的权重，因此千万不要直接套用。建议读者自己继承一下 pytorch Inception V3 的类，修改 forward 函数，让它返回全连接层前面的 2048 维向量，这样就可以直接加载 pytorch 官方的Inception V3 的权重了。~~ \u003C\u002Fi\u003E\u003C\u002Fp\u003E\u003Cp\u003E之前没有仔细看代码贸然提了个 issue，发现作者其实加载了 Inception V3 的权重，在inception.py文件的第 60 行。\u003C\u002Fp\u003E\u003Cp\u003E\u003C\u002Fp\u003E\u003Cp\u003E\u003C\u002Fp\u003E","adminClosedComment":false,"topics":[{"url":"https:\u002F\u002Fwww.zhihu.com\u002Fapi\u002Fv4\u002Ftopics\u002F20070859","type":"topic","id":"20070859","name":"生成对抗网络（GAN）"},{"url":"https:\u002F\u002Fwww.zhihu.com\u002Fapi\u002Fv4\u002Ftopics\u002F19590195","type":"topic","id":"19590195","name":"计算机视觉"},{"url":"https:\u002F\u002Fwww.zhihu.com\u002Fapi\u002Fv4\u002Ftopics\u002F19813032","type":"topic","id":"19813032","name":"深度学习（Deep 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