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把重复卷积移到共享的整图特征","sha256":"cf3db484eb0f2dbf0275200bb253e1ae671909abea5d6caafe893594f649ea0f","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"region-computation-reuse","title":"多个区域怎样复用同一份视觉计算？"},"page":{"id":"region-shared-feature-computation","title":"把重复卷积移到共享的整图特征","number":1},"sectionTitle":"把重复卷积移到共享的整图特征","currentQuestion":"从逐区域编码到共享整图特征，哪些计算被保留，哪些接口必须重建？","sourceSlides":["l3-r2-p29"],"knowledgeBlock":null,"formulas":[],"previousBlock":null,"nextBlock":"b-e64688162cad19358a58a275","prerequisites":[{"id":"b-716e51bd6d64a37bee39a0ed","url":"#b-716e51bd6d64a37bee39a0ed","role":"problem-context"}],"relatedBlocks":[{"id":"b-3601d7688d8a4fbfc6a4067d","url":"#b-3601d7688d8a4fbfc6a4067d","relation":"figure-and-explanation"}]},{"id":"b-e64688162cad19358a58a275","type":"h2","scope":"explanation","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p29.html#b-e64688162cad19358a58a275","content":"## 解释、算例与证据","sha256":"d71cf15e707c8a3674b4c90a599efee783cb84da5b8c8236a1d01c3add7b4958","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"region-computation-reuse","title":"多个区域怎样复用同一份视觉计算？"},"page":{"id":"region-shared-feature-computation","title":"把重复卷积移到共享的整图特征","number":1},"sectionTitle":"把重复卷积移到共享的整图特征","currentQuestion":"从逐区域编码到共享整图特征，哪些计算被保留，哪些接口必须重建？","sourceSlides":["l3-r2-p29"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-f5f38adccad0df94f1f13d3d","nextBlock":"b-7b40a17c0ae02ccb3bd7d453","prerequisites":[{"id":"b-f5f38adccad0df94f1f13d3d","url":"#b-f5f38adccad0df94f1f13d3d","role":"section-title"},{"id":"b-716e51bd6d64a37bee39a0ed","url":"#b-716e51bd6d64a37bee39a0ed","role":"problem-context"}],"relatedBlocks":[{"id":"b-3601d7688d8a4fbfc6a4067d","url":"#b-3601d7688d8a4fbfc6a4067d","relation":"figure-and-explanation"}]},{"id":"b-7b40a17c0ae02ccb3bd7d453","type":"h1","scope":"document","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p29.html#b-7b40a17c0ae02ccb3bd7d453","content":"# P29 · 许多重叠区域，为什么要重复卷积？","sha256":"3465f343287ff67f5e3cd497a1c211aa141d35c17f39c259438de43579b5380a","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"region-computation-reuse","title":"多个区域怎样复用同一份视觉计算？"},"page":{"id":"region-shared-feature-computation","title":"把重复卷积移到共享的整图特征","number":1},"sectionTitle":"把重复卷积移到共享的整图特征","currentQuestion":"从逐区域编码到共享整图特征，哪些计算被保留，哪些接口必须重建？","sourceSlides":["l3-r2-p29"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-e64688162cad19358a58a275","nextBlock":"b-716e51bd6d64a37bee39a0ed","prerequisites":[{"id":"b-e64688162cad19358a58a275","url":"#b-e64688162cad19358a58a275","role":"section-title"},{"id":"b-716e51bd6d64a37bee39a0ed","url":"#b-716e51bd6d64a37bee39a0ed","role":"problem-context"}],"relatedBlocks":[{"id":"b-3601d7688d8a4fbfc6a4067d","url":"#b-3601d7688d8a4fbfc6a4067d","relation":"figure-and-explanation"}]},{"id":"b-716e51bd6d64a37bee39a0ed","type":"p","scope":"document","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p29.html#b-716e51bd6d64a37bee39a0ed","content":"同一个 CNN 权重处理多个裁剪，仍可能重复计算共同像素。整图共享改变的是一次推理的计算组织，与预训练参数迁移分开。共享之后每个区域仍需要自己的坐标和读出；计算重排并不保证与原来的裁剪路线数学等价。","sha256":"e000fe6edc6fe136c1722ebb0e45cf3feddac5bd500016f5f219b575e35fee52","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"region-computation-reuse","title":"多个区域怎样复用同一份视觉计算？"},"page":{"id":"region-shared-feature-computation","title":"把重复卷积移到共享的整图特征","number":1},"sectionTitle":"把重复卷积移到共享的整图特征","currentQuestion":"从逐区域编码到共享整图特征，哪些计算被保留，哪些接口必须重建？","sourceSlides":["l3-r2-p29"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-7b40a17c0ae02ccb3bd7d453","nextBlock":"b-3601d7688d8a4fbfc6a4067d","prerequisites":[{"id":"b-7b40a17c0ae02ccb3bd7d453","url":"#b-7b40a17c0ae02ccb3bd7d453","role":"section-title"}],"relatedBlocks":[{"id":"b-3601d7688d8a4fbfc6a4067d","url":"#b-3601d7688d8a4fbfc6a4067d","relation":"figure-and-explanation"}]},{"id":"b-3601d7688d8a4fbfc6a4067d","type":"figure","scope":"document","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p29.html#b-3601d7688d8a4fbfc6a4067d","content":"图内标签与数值：Lecture 03 课堂图解 P29；先裁区域：重叠内容反复编码；CNN；CNN；先算全图：再按区域读取；预训练复用的是过去学到的参数；这里复用的是当前图片已经算出的特征。\n\n左侧两个重叠红杯候选分别经过 CNN；右侧同一全图一次编码后读取两份区域特征。\n\n- 先裁区域：重叠内容反复编码\n- CNN\n- CNN\n- 先算全图：再按区域读取\n- 预训练复用的是过去学到的参数；这里复用的是当前图片已经算出的特征。左侧两个重叠红杯候选分别经过 CNN；右侧同一全图一次编码后读取两份区域特征。 [查看对应图解状态](/#/l3-r2-p29/1)[查看完整图解](/course/figures/l3-r2-p29-1.html)","sha256":"8e1ef4d09c4540c4e0a463b9ce55d3f6a7a09c745c1d7d10d73160594100bb7b","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"region-computation-reuse","title":"多个区域怎样复用同一份视觉计算？"},"page":{"id":"region-shared-feature-computation","title":"把重复卷积移到共享的整图特征","number":1},"sectionTitle":"把重复卷积移到共享的整图特征","currentQuestion":"从逐区域编码到共享整图特征，哪些计算被保留，哪些接口必须重建？","sourceSlides":["l3-r2-p29"],"knowledgeBlock":null,"formulas":[],"figure":{"caption":"左侧两个重叠红杯候选分别经过 CNN；右侧同一全图一次编码后读取两份区域特征。 查看对应图解状态","labels":["先裁区域：重叠内容反复编码","CNN","CNN","先算全图：再按区域读取","预训练复用的是过去学到的参数；这里复用的是当前图片已经算出的特征。"],"description":"左侧两个重叠红杯候选分别经过 CNN；右侧同一全图一次编码后读取两份区域特征。先裁区域：重叠内容反复编码CNNCNN先算全图：再按区域读取预训练复用的是过去学到的参数；这里复用的是当前图片已经算出的特征。","evidenceIdentity":"左侧两个重叠红杯候选分别经过 CNN；右侧同一全图一次编码后读取两份区域特征。 查看对应图解状态","images":[{"src":"/assets/display/8ced939a1fd55047fbf73ea5.webp","alt":""},{"src":"/assets/display/8ced939a1fd55047fbf73ea5.webp","alt":""},{"src":"/assets/display/8ced939a1fd55047fbf73ea5.webp","alt":""}]},"previousBlock":"b-716e51bd6d64a37bee39a0ed","nextBlock":"b-c8dc253c6a1434e2e306babc","prerequisites":[{"id":"b-7b40a17c0ae02ccb3bd7d453","url":"#b-7b40a17c0ae02ccb3bd7d453","role":"section-title"},{"id":"b-716e51bd6d64a37bee39a0ed","url":"#b-716e51bd6d64a37bee39a0ed","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-c8dc253c6a1434e2e306babc","type":"h2","scope":"narrative","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p29.html#b-c8dc253c6a1434e2e306babc","content":"## 课堂讲述","sha256":"786ce10a6b32a492259a3dccd0a54e61cd41d28a34382fb7b5386c5f03b7ad69","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"region-computation-reuse","title":"多个区域怎样复用同一份视觉计算？"},"page":{"id":"region-shared-feature-computation","title":"把重复卷积移到共享的整图特征","number":1},"sectionTitle":"把重复卷积移到共享的整图特征","currentQuestion":"从逐区域编码到共享整图特征，哪些计算被保留，哪些接口必须重建？","sourceSlides":["l3-r2-p29"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-3601d7688d8a4fbfc6a4067d","nextBlock":"b-02b347aa707989cf72d8d46c","prerequisites":[{"id":"b-7b40a17c0ae02ccb3bd7d453","url":"#b-7b40a17c0ae02ccb3bd7d453","role":"section-title"},{"id":"b-716e51bd6d64a37bee39a0ed","url":"#b-716e51bd6d64a37bee39a0ed","role":"problem-context"}],"relatedBlocks":[{"id":"b-3601d7688d8a4fbfc6a4067d","url":"#b-3601d7688d8a4fbfc6a4067d","relation":"figure-and-explanation"}]},{"id":"b-02b347aa707989cf72d8d46c","type":"p","scope":"narrative","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p29.html#b-02b347aa707989cf72d8d46c","content":"看两个相邻候选，它们覆盖的大部分像素相同。如果每个区域分别跑一次卷积，很多共同内容就被反复计算。\n于是可以调换组织顺序：先对整张图计算特征，再按区域从特征图中提取表示。这样我们复用的不仅是训练得到的参数，也复用了同一张图的计算结果。\n这两种复用不要混在一起。预训练回答“过去学到的知识能否帮助新任务”；共享特征回答“这一张图中哪些计算不必重复”。两个问题合在一起，才能把检测做成可用系统。换顺序后又有新要求：大小不同的区域，怎样得到后续预测器可以处理的表示？","sha256":"5c36666c4beba59f444b09e92f3e287e86f50afeed629303564a6dc6073da185","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"region-computation-reuse","title":"多个区域怎样复用同一份视觉计算？"},"page":{"id":"region-shared-feature-computation","title":"把重复卷积移到共享的整图特征","number":1},"sectionTitle":"把重复卷积移到共享的整图特征","currentQuestion":"从逐区域编码到共享整图特征，哪些计算被保留，哪些接口必须重建？","sourceSlides":["l3-r2-p29"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-c8dc253c6a1434e2e306babc","nextBlock":"b-426f81833557d8e0e85471ab","prerequisites":[{"id":"b-c8dc253c6a1434e2e306babc","url":"#b-c8dc253c6a1434e2e306babc","role":"section-title"},{"id":"b-716e51bd6d64a37bee39a0ed","url":"#b-716e51bd6d64a37bee39a0ed","role":"problem-context"}],"relatedBlocks":[{"id":"b-3601d7688d8a4fbfc6a4067d","url":"#b-3601d7688d8a4fbfc6a4067d","relation":"figure-and-explanation"}]},{"id":"b-426f81833557d8e0e85471ab","type":"h3","scope":"shared-convolution-reuse","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p29.html#b-426f81833557d8e0e85471ab","content":"### 参数复用与一次前向结果的复用","sha256":"ce28d0892ce009960af7e3027b0021575941fb10bf923db47eb3f27a7f0ed930","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"region-computation-reuse","title":"多个区域怎样复用同一份视觉计算？"},"page":{"id":"region-shared-feature-computation","title":"把重复卷积移到共享的整图特征","number":1},"sectionTitle":"参数复用与一次前向结果的复用","currentQuestion":"从逐区域编码到共享整图特征，哪些计算被保留，哪些接口必须重建？","sourceSlides":["l3-r2-p29"],"knowledgeBlock":"shared-convolution-reuse","formulas":[],"previousBlock":"b-02b347aa707989cf72d8d46c","nextBlock":"b-41cbe1ad474df1c2eb4a2ff8","prerequisites":[{"id":"b-c8dc253c6a1434e2e306babc","url":"#b-c8dc253c6a1434e2e306babc","role":"section-title"},{"id":"b-716e51bd6d64a37bee39a0ed","url":"#b-716e51bd6d64a37bee39a0ed","role":"problem-context"}],"relatedBlocks":[{"id":"b-3601d7688d8a4fbfc6a4067d","url":"#b-3601d7688d8a4fbfc6a4067d","relation":"figure-and-explanation"},{"id":"b-41cbe1ad474df1c2eb4a2ff8","url":"#b-41cbe1ad474df1c2eb4a2ff8","relation":"same-reasoning"},{"id":"b-7c23ea17d9c2b96551e66040","url":"#b-7c23ea17d9c2b96551e66040","relation":"same-reasoning"},{"id":"b-0d214d575811481844c1a307","url":"#b-0d214d575811481844c1a307","relation":"same-reasoning"},{"id":"b-c857d86889e503d0a4f7507c","url":"#b-c857d86889e503d0a4f7507c","relation":"same-reasoning"}]},{"id":"b-41cbe1ad474df1c2eb4a2ff8","type":"p","scope":"shared-convolution-reuse","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p29.html#b-41cbe1ad474df1c2eb4a2ff8","content":"两张重叠裁剪都使用同一个 CNN，已经共享了参数，但仍分别执行卷积。假如它们都包含杯沿和桌面，这些像素会参与两次运算。SPP-net 和 Fast R-CNN 的路线把较重的卷积移到整图：先计算 $F=f_\\theta(I)$，每个候选再用自己的框 $b_i$ 读取 $r_i=R(F,b_i)$。","sha256":"932bf95223423530aa77b5a75c4d8e358fb6dd24d080002540e34220fbb056c7","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"region-computation-reuse","title":"多个区域怎样复用同一份视觉计算？"},"page":{"id":"region-shared-feature-computation","title":"把重复卷积移到共享的整图特征","number":1},"sectionTitle":"参数复用与一次前向结果的复用","currentQuestion":"从逐区域编码到共享整图特征，哪些计算被保留，哪些接口必须重建？","sourceSlides":["l3-r2-p29"],"knowledgeBlock":"shared-convolution-reuse","formulas":[{"latex":"F=f_\\theta(I)","definitionContext":"两张重叠裁剪都使用同一个 CNN，已经共享了参数，但仍分别执行卷积。假如它们都包含杯沿和桌面，这些像素会参与两次运算。SPP-net 和 Fast R-CNN 的路线把较重的卷积移到整图：先计算 $F=f_\\theta(I)$，每个候选再用自己的框 $b_i$ 读取 $r_i=R(F,b_i)$。\n这里有两种复用。预训练让新的任务借用过去学到的参数；整图共享则让同一次推理中的多个区域借用已算出的中间结果。前者减少从头学习的需要，后者减少重复工作，不能用同一个“迁移”概念含糊带过。\n若有 N 个候选，逐区域成本近似为 N 次卷积加区域预测；共享方式近似为一次整图卷积加 N 次轻量读取与预测。这是计算组织的估算，不是实测加速倍数，因为整图与裁剪的分辨率不同，内存、候选产生和预测头也占时间。\n先裁再编码与先编码再读取不严格相等：前者改变对象尺度并裁去上下文；后者的感受野可能跨出 RoI。方法的贡献是在这样的取舍下找到能训练、有效率的共享接口。"},{"latex":"b_i","definitionContext":"两张重叠裁剪都使用同一个 CNN，已经共享了参数，但仍分别执行卷积。假如它们都包含杯沿和桌面，这些像素会参与两次运算。SPP-net 和 Fast R-CNN 的路线把较重的卷积移到整图：先计算 $F=f_\\theta(I)$，每个候选再用自己的框 $b_i$ 读取 $r_i=R(F,b_i)$。\n这里有两种复用。预训练让新的任务借用过去学到的参数；整图共享则让同一次推理中的多个区域借用已算出的中间结果。前者减少从头学习的需要，后者减少重复工作，不能用同一个“迁移”概念含糊带过。\n若有 N 个候选，逐区域成本近似为 N 次卷积加区域预测；共享方式近似为一次整图卷积加 N 次轻量读取与预测。这是计算组织的估算，不是实测加速倍数，因为整图与裁剪的分辨率不同，内存、候选产生和预测头也占时间。\n先裁再编码与先编码再读取不严格相等：前者改变对象尺度并裁去上下文；后者的感受野可能跨出 RoI。方法的贡献是在这样的取舍下找到能训练、有效率的共享接口。"},{"latex":"r_i=R(F,b_i)","definitionContext":"两张重叠裁剪都使用同一个 CNN，已经共享了参数，但仍分别执行卷积。假如它们都包含杯沿和桌面，这些像素会参与两次运算。SPP-net 和 Fast R-CNN 的路线把较重的卷积移到整图：先计算 $F=f_\\theta(I)$，每个候选再用自己的框 $b_i$ 读取 $r_i=R(F,b_i)$。\n这里有两种复用。预训练让新的任务借用过去学到的参数；整图共享则让同一次推理中的多个区域借用已算出的中间结果。前者减少从头学习的需要，后者减少重复工作，不能用同一个“迁移”概念含糊带过。\n若有 N 个候选，逐区域成本近似为 N 次卷积加区域预测；共享方式近似为一次整图卷积加 N 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