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10](https://deepnote.com/project/38755e4e-23f6-4f5f-8c68-8a2e4114b1c1/notebook/a14237bfa9dd413d959ab4e458e11f42)。","sha256":"933fb07ec46fa465c33aff50bfb9969547b90d30ed8775d71768acd5290079dc","chapter":{"id":"course","title":"LAB 20 · 尺度跨度与两对象匹配"},"unit":{"id":"lab23-尺度与集合输出","title":"LAB 20 · 尺度跨度与两对象匹配"},"page":{"id":"reading-block-6ab1753a596940e5aceba3b7dd7537c5","title":"同一组对象换了排列，损失不该凭空变大","number":2},"sectionTitle":"同一组对象换了排列，损失不该凭空变大","currentQuestion":"同一组对象换了排列，损失不该凭空变大","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-8f6ffc543ab2341b55270bc8","nextBlock":"b-9ff9e9055f2ed20ad252911c","prerequisites":[{"id":"b-712c1ccd2fb57ebf309cbcb9","url":"#b-712c1ccd2fb57ebf309cbcb9","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-9ff9e9055f2ed20ad252911c","type":"h2","scope":"block-6ab1753a596940e5aceba3b7dd7537c5","url":"https://codingai-lec03.pages.dev/course/lab23-尺度与集合输出.html#b-9ff9e9055f2ed20ad252911c","content":"## 同一组对象换了排列，损失不该凭空变大","sha256":"89ab347c49c038f4fc87d04e6c621a44d1d385ecb10882358138acdc8c892309","chapter":{"id":"course","title":"LAB 20 · 尺度跨度与两对象匹配"},"unit":{"id":"lab23-尺度与集合输出","title":"LAB 20 · 尺度跨度与两对象匹配"},"page":{"id":"reading-block-6ab1753a596940e5aceba3b7dd7537c5","title":"同一组对象换了排列，损失不该凭空变大","number":2},"sectionTitle":"同一组对象换了排列，损失不该凭空变大","currentQuestion":"同一组对象换了排列，损失不该凭空变大","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-06c438907888afd5514a1813","nextBlock":"b-2c683d934ab4da88d101e059","prerequisites":[{"id":"b-712c1ccd2fb57ebf309cbcb9","url":"#b-712c1ccd2fb57ebf309cbcb9","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-2c683d934ab4da88d101e059","type":"p","scope":"block-6ab1753a596940e5aceba3b7dd7537c5","url":"https://codingai-lec03.pages.dev/course/lab23-尺度与集合输出.html#b-2c683d934ab4da88d101e059","content":"检测输出是对象集合。两个预测slot与两个真值框没有天然同序关系。本例从类别概率、归一化框L1距离与IoU构造成本 Cᵢⱼ=−log pᵢ(cⱼ)+2||bᵢ−gⱼ||₁+(1−IoU)，穷举2!种排列得到最小匹配。系数是教学设定；DETR常用的分类/L1/GIoU组合须按实际实现区分。","sha256":"f7ba3349d6be423fd7ddd5c14a7622396e705783715f61b4536d5c42f254403e","chapter":{"id":"course","title":"LAB 20 · 尺度跨度与两对象匹配"},"unit":{"id":"lab23-尺度与集合输出","title":"LAB 20 · 尺度跨度与两对象匹配"},"page":{"id":"reading-block-6ab1753a596940e5aceba3b7dd7537c5","title":"同一组对象换了排列，损失不该凭空变大","number":2},"sectionTitle":"同一组对象换了排列，损失不该凭空变大","currentQuestion":"同一组对象换了排列，损失不该凭空变大","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-9ff9e9055f2ed20ad252911c","nextBlock":"b-a02e83017ee64d50d5be3f1f","prerequisites":[{"id":"b-9ff9e9055f2ed20ad252911c","url":"#b-9ff9e9055f2ed20ad252911c","role":"section-title"},{"id":"b-712c1ccd2fb57ebf309cbcb9","url":"#b-712c1ccd2fb57ebf309cbcb9","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-a02e83017ee64d50d5be3f1f","type":"p","scope":"block-6ab1753a596940e5aceba3b7dd7537c5","url":"https://codingai-lec03.pages.dev/course/lab23-尺度与集合输出.html#b-a02e83017ee64d50d5be3f1f","content":"前置尺度算例记录16px目标在stride4/8/16/32上对应的连续跨度4/2/1/0.5格，不把0.5格误说为必定完全消失。FPN负责多尺度表示；二分匹配负责输出对应，两者不能相互替代。","sha256":"ff0896feb96cdd255b1dfd2ba91d1734d56b3c3376ae877d50718e3060e83b61","chapter":{"id":"course","title":"LAB 20 · 尺度跨度与两对象匹配"},"unit":{"id":"lab23-尺度与集合输出","title":"LAB 20 · 尺度跨度与两对象匹配"},"page":{"id":"reading-block-6ab1753a596940e5aceba3b7dd7537c5","title":"同一组对象换了排列，损失不该凭空变大","number":2},"sectionTitle":"同一组对象换了排列，损失不该凭空变大","currentQuestion":"同一组对象换了排列，损失不该凭空变大","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-2c683d934ab4da88d101e059","nextBlock":"b-e4042dd86658c598324589c7","prerequisites":[{"id":"b-9ff9e9055f2ed20ad252911c","url":"#b-9ff9e9055f2ed20ad252911c","role":"section-title"},{"id":"b-712c1ccd2fb57ebf309cbcb9","url":"#b-712c1ccd2fb57ebf309cbcb9","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-e4042dd86658c598324589c7","type":"p","scope":"block-6ab1753a596940e5aceba3b7dd7537c5","url":"https://codingai-lec03.pages.dev/course/lab23-尺度与集合输出.html#b-e4042dd86658c598324589c7","content":"本册没有图像编码器或参数训练；真实图像到框的完整链在 [LAB 10](https://deepnote.com/workspace/ise3309jingao-5ba66b0a-4283-4f5a-ae06-3f68d3201e99/project/38755e4e-23f6-4f5f-8c68-8a2e4114b1c1/notebook/a14237bfa9dd413d959ab4e458e11f42?utm_source=openai&utm_medium=mcp&utm_campaign=openaimcp&utm_content=a14237bfa9dd413d959ab4e458e11f42&utm_term=get_notebook)。","sha256":"cb255c1d61af05f31fd9fddf08e3c4cf45908c203ad789411dbe34ebde2c8c42","chapter":{"id":"course","title":"LAB 20 · 尺度跨度与两对象匹配"},"unit":{"id":"lab23-尺度与集合输出","title":"LAB 20 · 尺度跨度与两对象匹配"},"page":{"id":"reading-block-6ab1753a596940e5aceba3b7dd7537c5","title":"同一组对象换了排列，损失不该凭空变大","number":2},"sectionTitle":"同一组对象换了排列，损失不该凭空变大","currentQuestion":"同一组对象换了排列，损失不该凭空变大","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-a02e83017ee64d50d5be3f1f","nextBlock":"b-27cf520ac489798198ef1b70","prerequisites":[{"id":"b-9ff9e9055f2ed20ad252911c","url":"#b-9ff9e9055f2ed20ad252911c","role":"section-title"},{"id":"b-712c1ccd2fb57ebf309cbcb9","url":"#b-712c1ccd2fb57ebf309cbcb9","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-27cf520ac489798198ef1b70","type":"pre","scope":"block-0f45eba379c5437685bb52cf7ae38a2d","url":"https://codingai-lec03.pages.dev/course/lab23-尺度与集合输出.html#b-27cf520ac489798198ef1b70","content":"```\n# Writable ephemeral workspace for detached readonly cloud runs.\nimport os, tempfile\nos.chdir(tempfile.mkdtemp(prefix='lec03_lab23_'))\n\nimport numpy as np\nfrom itertools import permutations\nboxes=np.array([[.61,.12,.91,.43],[.08,.10,.32,.40]])\ntruth=np.array([[.10,.10,.35,.42],[.60,.10,.90,.45]])\nprob=np.array([[.15,.85],[.9,.1]]); labels=np.array([0,1])\ndef iou(a,b):\n    wh=np.maximum(0,np.minimum(a[2:],b[2:])-np.maximum(a[:2],b[:2])); inter=wh.prod()\n    return inter/(np.prod(a[2:]-a[:2])+np.prod(b[2:]-b[:2])-inter)\nC=np.array([[-np.log(prob[i,labels[j]])+2*abs(boxes[i]-truth[j]).sum()+1-iou(boxes[i],truth[j]) for j in range(2)] for i in range(2)])\ncosts={str(p):sum(C[i,j] for i,j in enumerate(p)) for p in permutations(range(2))}\nprint('cost matrix',C.round(4).tolist(),'assignment costs',costs,'selected',min(costs,key=costs.get))\nassert min(costs,key=costs.get)=='(1, 0)'\nfor stride in [4,8,16,32]: print('stride',stride,'target span',16/stride,'cells')\nprint('with 3 predictions/2 targets, unmatched slot needs no-object classification, not an invented third target')\n```","sha256":"5714c01e6f12168c1ae96d2c020af303805871c916cd8e924051dbea3aa808d3","chapter":{"id":"course","title":"LAB 20 · 尺度跨度与两对象匹配"},"unit":{"id":"lab23-尺度与集合输出","title":"LAB 20 · 尺度跨度与两对象匹配"},"page":{"id":"reading-block-6ab1753a596940e5aceba3b7dd7537c5","title":"同一组对象换了排列，损失不该凭空变大","number":2},"sectionTitle":"同一组对象换了排列，损失不该凭空变大","currentQuestion":"同一组对象换了排列，损失不该凭空变大","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-e4042dd86658c598324589c7","nextBlock":null,"prerequisites":[{"id":"b-9ff9e9055f2ed20ad252911c","url":"#b-9ff9e9055f2ed20ad252911c","role":"section-title"},{"id":"b-712c1ccd2fb57ebf309cbcb9","url":"#b-712c1ccd2fb57ebf309cbcb9","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-c59f3115bc6a6d34d0a575bb","type":"h2","scope":"block-3cdc52c2a4254fcebc30f166d5043b8f","url":"https://codingai-lec03.pages.dev/course/lab23-尺度与集合输出.html#b-c59f3115bc6a6d34d0a575bb","content":"## 已完成的基准运行","sha256":"70efe3096d536ddf0d6f0f7335815da85d73017a47a0e52cac5d2621805a3c53","chapter":{"id":"course","title":"LAB 20 · 尺度跨度与两对象匹配"},"unit":{"id":"lab23-尺度与集合输出","title":"LAB 20 · 尺度跨度与两对象匹配"},"page":{"id":"reading-block-3cdc52c2a4254fcebc30f166d5043b8f","title":"已完成的基准运行","number":3},"sectionTitle":"已完成的基准运行","currentQuestion":"已完成的基准运行","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":null,"nextBlock":"b-26dcb4fa251ffdcada4ceee5","prerequisites":[{"id":"b-26dcb4fa251ffdcada4ceee5","url":"#b-26dcb4fa251ffdcada4ceee5","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-26dcb4fa251ffdcada4ceee5","type":"p","scope":"block-3cdc52c2a4254fcebc30f166d5043b8f","url":"https://codingai-lec03.pages.dev/course/lab23-尺度与集合输出.html#b-26dcb4fa251ffdcada4ceee5","content":"以下是本轮本地独立 Python 进程的实际标准输出，云端执行另行记录。","sha256":"ff4e2caa2efcd2a7e24e155ecad4f46e58bf2f1bb641ebcf47707b657cc53d56","chapter":{"id":"course","title":"LAB 20 · 尺度跨度与两对象匹配"},"unit":{"id":"lab23-尺度与集合输出","title":"LAB 20 · 尺度跨度与两对象匹配"},"page":{"id":"reading-block-3cdc52c2a4254fcebc30f166d5043b8f","title":"已完成的基准运行","number":3},"sectionTitle":"已完成的基准运行","currentQuestion":"已完成的基准运行","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-c59f3115bc6a6d34d0a575bb","nextBlock":"b-bdcbc4eeb8d88e4feceefdfa","prerequisites":[{"id":"b-c59f3115bc6a6d34d0a575bb","url":"#b-c59f3115bc6a6d34d0a575bb","role":"section-title"}],"relatedBlocks":[]},{"id":"b-bdcbc4eeb8d88e4feceefdfa","type":"pre","scope":"block-3cdc52c2a4254fcebc30f166d5043b8f","url":"https://codingai-lec03.pages.dev/course/lab23-尺度与集合输出.html#b-bdcbc4eeb8d88e4feceefdfa","content":"```\ncost matrix [[5.0971, 0.4509], [0.4779, 5.6026]] assignment costs {'(0, 1)': np.float64(10.699705077879926), '(1, 0)': np.float64(0.9288002118875242)} selected (1, 0)\nstride 4 target span 4.0 cells\nstride 8 target span 2.0 cells\nstride 16 target span 1.0 cells\nstride 32 target span 0.5 cells\nwith 3 predictions/2 targets, unmatched slot needs no-object classification, not an invented third target\n\n```","sha256":"4a2587c0973bf49253d61d71eec489a36a70abfc8ffbffd2a57326b581057eec","chapter":{"id":"course","title":"LAB 20 · 尺度跨度与两对象匹配"},"unit":{"id":"lab23-尺度与集合输出","title":"LAB 20 · 尺度跨度与两对象匹配"},"page":{"id":"reading-block-3cdc52c2a4254fcebc30f166d5043b8f","title":"已完成的基准运行","number":3},"sectionTitle":"已完成的基准运行","currentQuestion":"已完成的基准运行","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-26dcb4fa251ffdcada4ceee5","nextBlock":"b-bee50b3d4594d9132b71c39d","prerequisites":[{"id":"b-c59f3115bc6a6d34d0a575bb","url":"#b-c59f3115bc6a6d34d0a575bb","role":"section-title"},{"id":"b-26dcb4fa251ffdcada4ceee5","url":"#b-26dcb4fa251ffdcada4ceee5","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-bee50b3d4594d9132b71c39d","type":"p","scope":"block-3cdc52c2a4254fcebc30f166d5043b8f","url":"https://codingai-lec03.pages.dev/course/lab23-尺度与集合输出.html#b-bee50b3d4594d9132b71c39d","content":"本例左侧预测实际上来自slot1，因此交叉匹配便宜。只交换预测slot顺序，最小总成本应保持；固定按索引配对则会改变损失。若只有一个预测正确，匹配仍会选最低成本，但这并不意味着两物体均被成功检测。框损失、分类损失与评价是不同对象。[DETR官方matcher](https://github.com/facebookresearch/detr/blob/main/models/matcher.py)可对照这里的教学成本；LAB10展示从真实图像得到候选的前半条链。","sha256":"3345c147cd1b8dab6fc43a257359dc025f3ed9429ffcebb6023d87182e31c3b9","chapter":{"id":"course","title":"LAB 20 · 尺度跨度与两对象匹配"},"unit":{"id":"lab23-尺度与集合输出","title":"LAB 20 · 尺度跨度与两对象匹配"},"page":{"id":"reading-block-3cdc52c2a4254fcebc30f166d5043b8f","title":"已完成的基准运行","number":3},"sectionTitle":"已完成的基准运行","currentQuestion":"已完成的基准运行","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-bdcbc4eeb8d88e4feceefdfa","nextBlock":null,"prerequisites":[{"id":"b-c59f3115bc6a6d34d0a575bb","url":"#b-c59f3115bc6a6d34d0a575bb","role":"section-title"},{"id":"b-26dcb4fa251ffdcada4ceee5","url":"#b-26dcb4fa251ffdcada4ceee5","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-4491cfb17ee7a528752df3a2","type":"h4","scope":"block-043de8a70dd54f4c88bdb062e0590d04","url":"https://codingai-lec03.pages.dev/course/lab23-尺度与集合输出.html#b-4491cfb17ee7a528752df3a2","content":"#### 先心算一个更小的匹配例","sha256":"8c9fea44e455c761cdd0ac37acf39c07bf0d125445ce3eabd871fcbbda2a49b2","chapter":{"id":"course","title":"LAB 20 · 尺度跨度与两对象匹配"},"unit":{"id":"lab23-尺度与集合输出","title":"LAB 20 · 尺度跨度与两对象匹配"},"page":{"id":"reading-block-043de8a70dd54f4c88bdb062e0590d04","title":"先心算一个更小的匹配例","number":4},"sectionTitle":"先心算一个更小的匹配例","currentQuestion":"先心算一个更小的匹配例","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":null,"nextBlock":"b-93579220af0ff9d843b74995","prerequisites":[{"id":"b-93579220af0ff9d843b74995","url":"#b-93579220af0ff9d843b74995","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-93579220af0ff9d843b74995","type":"p","scope":"block-043de8a70dd54f4c88bdb062e0590d04","url":"https://codingai-lec03.pages.dev/course/lab23-尺度与集合输出.html#b-93579220af0ff9d843b74995","content":"成本矩阵为 `[[1.2,.3],[.2,1.0]]`。按相同索引对应，总代价 2.2；交换对应，总代价 .5，因此选交叉。上方当前代码进一步从类别概率、真实坐标和 IoU 得到成本，说明这些数并非只能手填。","sha256":"4d6802ddf08a4df32d9fbf0dac61145b5fdd301efbc6f85b7fa8a14dd11546cf","chapter":{"id":"course","title":"LAB 20 · 尺度跨度与两对象匹配"},"unit":{"id":"lab23-尺度与集合输出","title":"LAB 20 · 尺度跨度与两对象匹配"},"page":{"id":"reading-block-043de8a70dd54f4c88bdb062e0590d04","title":"先心算一个更小的匹配例","number":4},"sectionTitle":"先心算一个更小的匹配例","currentQuestion":"先心算一个更小的匹配例","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-4491cfb17ee7a528752df3a2","nextBlock":"b-46c99cb478d9d9ed24f857b6","prerequisites":[{"id":"b-4491cfb17ee7a528752df3a2","url":"#b-4491cfb17ee7a528752df3a2","role":"section-title"}],"relatedBlocks":[]},{"id":"b-46c99cb478d9d9ed24f857b6","type":"p","scope":"block-043de8a70dd54f4c88bdb062e0590d04","url":"https://codingai-lec03.pages.dev/course/lab23-尺度与集合输出.html#b-46c99cb478d9d9ed24f857b6","content":"想比较匹配与难例加权，读 [选读：难例权重和对象匹配不是一件事](/course/blocks/focal-versus-assignment.html)；两者解决不同问题。","sha256":"1c81be1097bb47b6650329d503f951f0b2d053186a97e6dc796a85af82073191","chapter":{"id":"course","title":"LAB 20 · 尺度跨度与两对象匹配"},"unit":{"id":"lab23-尺度与集合输出","title":"LAB 20 · 尺度跨度与两对象匹配"},"page":{"id":"reading-block-043de8a70dd54f4c88bdb062e0590d04","title":"先心算一个更小的匹配例","number":4},"sectionTitle":"先心算一个更小的匹配例","currentQuestion":"先心算一个更小的匹配例","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-93579220af0ff9d843b74995","nextBlock":null,"prerequisites":[{"id":"b-4491cfb17ee7a528752df3a2","url":"#b-4491cfb17ee7a528752df3a2","role":"section-title"},{"id":"b-93579220af0ff9d843b74995","url":"#b-93579220af0ff9d843b74995","role":"problem-context"}],"relatedBlocks":[]}]}