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软目标与坍塌：三个数值检查"},"unit":{"id":"lab17-教师软目标与表示坍塌","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"page":{"id":"reading-opening","title":"LAB 17 · 软目标与坍塌：三个数值检查","number":1},"sectionTitle":"LAB 17 · 软目标与坍塌：三个数值检查","currentQuestion":"LAB 17 · 软目标与坍塌：三个数值检查","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-856342266f32ac90a8981f1a","nextBlock":"b-320c1f9cd6f88707d0bf9c7d","prerequisites":[{"id":"b-2f046326a5354873bd1a244a","url":"#b-2f046326a5354873bd1a244a","role":"section-title"},{"id":"b-c9c9981c9600a73aec31133d","url":"#b-c9c9981c9600a73aec31133d","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-320c1f9cd6f88707d0bf9c7d","type":"p","scope":"block-39d5a7ff74ae40e2a86056d0d8322096","url":"https://codingai-lec03.pages.dev/course/lab17-教师软目标与表示坍塌.html#b-320c1f9cd6f88707d0bf9c7d","content":"写下三个对象：谁提供目标，谁接收梯度，EMA平均什么。输入是解析二维数据，教师是手工线性函数；EMA没有参与前面的蒸馏优化。[教师来源与坍塌说明](/course/blocks/teacher-target-source-and-collapse.html)保留更完整的解释。若要观察EMA接入真实图像训练，再选[LAB 07](https://deepnote.com/project/38755e4e-23f6-4f5f-8c68-8a2e4114b1c1/notebook/0d1b8f6fbf6a476c93ffcc169f2ec1f4)。","sha256":"4147796ae4ead92b43e08522b105209b4a1034658b258e4d047f2bbbe1a55c8a","chapter":{"id":"course","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"unit":{"id":"lab17-教师软目标与表示坍塌","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"page":{"id":"reading-opening","title":"LAB 17 · 软目标与坍塌：三个数值检查","number":1},"sectionTitle":"LAB 17 · 软目标与坍塌：三个数值检查","currentQuestion":"LAB 17 · 软目标与坍塌：三个数值检查","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-a976f4e8a389cc8cecc551a4","nextBlock":"b-3c93c76ca83b94991ca7222c","prerequisites":[{"id":"b-2f046326a5354873bd1a244a","url":"#b-2f046326a5354873bd1a244a","role":"section-title"},{"id":"b-c9c9981c9600a73aec31133d","url":"#b-c9c9981c9600a73aec31133d","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-3c93c76ca83b94991ca7222c","type":"pre","scope":"block-89b4ff8dd23d4c6d89882682635269a5","url":"https://codingai-lec03.pages.dev/course/lab17-教师软目标与表示坍塌.html#b-3c93c76ca83b94991ca7222c","content":"```\n# Writable ephemeral workspace for detached readonly cloud runs.\nimport os, tempfile\nos.chdir(tempfile.mkdtemp(prefix='lec03_lab17_'))\n\nimport numpy as np\nrng=np.random.default_rng(17)\nX=rng.normal(size=(384,2)); X=np.c_[X,np.ones(len(X))]\nteacher=np.array([[2,-2,0],[0,1,-1],[.2,-.1,0.]])\ndef softmax(z):\n    e=np.exp(z-z.max(1,keepdims=True)); return e/e.sum(1,keepdims=True)\nT=2.; target=softmax(X@teacher/T); W=np.zeros((3,3))\ndef kl(q,p): return float((q*np.log((q+1e-12)/(p+1e-12))).sum(1).mean())\nbefore=kl(target[256:],softmax(X[256:]@W/T))\nfor step in range(600):\n    pred=softmax(X[:256]@W/T)\n    W-=.3*X[:256].T@(pred-target[:256])/256/T\nafter=kl(target[256:],softmax(X[256:]@W/T))\nconstant=np.ones((8,4)); diverse=rng.normal(size=(8,4))\nprint('heldout teacher/student KL',round(before,5),'->',round(after,5))\nprint('collapsed consistency loss',float(((constant-constant[::-1])**2).mean()),'variance',constant.var(0).tolist())\nprint('noncollapsed variance',diverse.var(0).round(3).tolist())\nema=np.zeros_like(W)\nfor t in range(3): ema=.9*ema+.1*W\nassert np.allclose(ema,(1-.9**3)*W)\nprint('3 EMA updates preserve factor',round(1-.9**3,3),'of fixed student parameters')\nprint('temperature teacher probabilities',softmax(np.array([[3.,1.,0.]])/T).round(4).tolist())\n```","sha256":"10d7d3d69237459a4954d8c8e7c4a25fe2adc35f5d4d9126659b142926fa445b","chapter":{"id":"course","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"unit":{"id":"lab17-教师软目标与表示坍塌","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"page":{"id":"reading-opening","title":"LAB 17 · 软目标与坍塌：三个数值检查","number":1},"sectionTitle":"LAB 17 · 软目标与坍塌：三个数值检查","currentQuestion":"LAB 17 · 软目标与坍塌：三个数值检查","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-320c1f9cd6f88707d0bf9c7d","nextBlock":null,"prerequisites":[{"id":"b-2f046326a5354873bd1a244a","url":"#b-2f046326a5354873bd1a244a","role":"section-title"},{"id":"b-c9c9981c9600a73aec31133d","url":"#b-c9c9981c9600a73aec31133d","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-dbbf4344a9e658eaa2fb6c12","type":"h2","scope":"block-7044913259924763a3b29542e91fbca8","url":"https://codingai-lec03.pages.dev/course/lab17-教师软目标与表示坍塌.html#b-dbbf4344a9e658eaa2fb6c12","content":"## 已完成的基准运行","sha256":"70efe3096d536ddf0d6f0f7335815da85d73017a47a0e52cac5d2621805a3c53","chapter":{"id":"course","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"unit":{"id":"lab17-教师软目标与表示坍塌","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"page":{"id":"reading-block-7044913259924763a3b29542e91fbca8","title":"已完成的基准运行","number":2},"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-8b63ea24bd80060e9ee1fad1","prerequisites":[{"id":"b-8b63ea24bd80060e9ee1fad1","url":"#b-8b63ea24bd80060e9ee1fad1","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-8b63ea24bd80060e9ee1fad1","type":"p","scope":"block-7044913259924763a3b29542e91fbca8","url":"https://codingai-lec03.pages.dev/course/lab17-教师软目标与表示坍塌.html#b-8b63ea24bd80060e9ee1fad1","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 17 · 软目标与坍塌：三个数值检查"},"unit":{"id":"lab17-教师软目标与表示坍塌","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"page":{"id":"reading-block-7044913259924763a3b29542e91fbca8","title":"已完成的基准运行","number":2},"sectionTitle":"已完成的基准运行","currentQuestion":"已完成的基准运行","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-dbbf4344a9e658eaa2fb6c12","nextBlock":"b-39e717f8748f09600e71873c","prerequisites":[{"id":"b-dbbf4344a9e658eaa2fb6c12","url":"#b-dbbf4344a9e658eaa2fb6c12","role":"section-title"}],"relatedBlocks":[]},{"id":"b-39e717f8748f09600e71873c","type":"pre","scope":"block-7044913259924763a3b29542e91fbca8","url":"https://codingai-lec03.pages.dev/course/lab17-教师软目标与表示坍塌.html#b-39e717f8748f09600e71873c","content":"```\nheldout teacher/student KL 0.24742 -> 1e-05\ncollapsed consistency loss 0.0 variance [0.0, 0.0, 0.0, 0.0]\nnoncollapsed variance [1.239, 0.712, 1.084, 1.199]\n3 EMA updates preserve factor 0.271 of fixed student parameters\ntemperature teacher probabilities [[0.6285, 0.2312, 0.1402]]\n\n```","sha256":"13e29b78b8d0a1f4f050e2921be6922b57a1ce33eb2476ef38cb073de50ae730","chapter":{"id":"course","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"unit":{"id":"lab17-教师软目标与表示坍塌","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"page":{"id":"reading-block-7044913259924763a3b29542e91fbca8","title":"已完成的基准运行","number":2},"sectionTitle":"已完成的基准运行","currentQuestion":"已完成的基准运行","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-8b63ea24bd80060e9ee1fad1","nextBlock":"b-bb24e58b99dd846a4ce58499","prerequisites":[{"id":"b-dbbf4344a9e658eaa2fb6c12","url":"#b-dbbf4344a9e658eaa2fb6c12","role":"section-title"},{"id":"b-8b63ea24bd80060e9ee1fad1","url":"#b-8b63ea24bd80060e9ee1fad1","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-bb24e58b99dd846a4ce58499","type":"p","scope":"block-7044913259924763a3b29542e91fbca8","url":"https://codingai-lec03.pages.dev/course/lab17-教师软目标与表示坍塌.html#b-bb24e58b99dd846a4ce58499","content":"保留集 KL 降低表示学生更接近这个教师的概率分布；不能据此宣称视觉迁移更好。增大温度让非最大类别得到更多质量，也会改变梯度尺度；正式蒸馏常乘 T² 补偿，本代码明确不乘，比较学习率时要一起考虑。","sha256":"14189f16ad31f6c007e850d7f40b9ec49763f1b096690f95039e3e8cb55b7c2c","chapter":{"id":"course","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"unit":{"id":"lab17-教师软目标与表示坍塌","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"page":{"id":"reading-block-7044913259924763a3b29542e91fbca8","title":"已完成的基准运行","number":2},"sectionTitle":"已完成的基准运行","currentQuestion":"已完成的基准运行","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-39e717f8748f09600e71873c","nextBlock":"b-6b86f784acee4f70db11f780","prerequisites":[{"id":"b-dbbf4344a9e658eaa2fb6c12","url":"#b-dbbf4344a9e658eaa2fb6c12","role":"section-title"},{"id":"b-8b63ea24bd80060e9ee1fad1","url":"#b-8b63ea24bd80060e9ee1fad1","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-6b86f784acee4f70db11f780","type":"p","scope":"block-7044913259924763a3b29542e91fbca8","url":"https://codingai-lec03.pages.dev/course/lab17-教师软目标与表示坍塌.html#b-6b86f784acee4f70db11f780","content":"EMA 平滑参数变化，stop-gradient 限制梯度路径，但“常量也能获得零一致性损失”的反例并未因此从数学上消失。MoCo 还用负例；BYOL/DINO 的训练设计和经验条件应分别解释。先到 [CLS 05](https://deepnote.com/project/38755e4e-23f6-4f5f-8c68-8a2e4114b1c1/notebook/b8320404134f4a2e858ccfe7d50a71d3) 区分训练目标与 probe，再只改变 T=1/4 比较分布与KL曲线。来源：[知识蒸馏论文](https://arxiv.org/abs/1503.02531)、[BYOL](https://arxiv.org/abs/2006.07733)。","sha256":"edc6493162bad77efc1c2b2dcb5b0d275aefb6a0fd1ed97313d5e1201d128242","chapter":{"id":"course","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"unit":{"id":"lab17-教师软目标与表示坍塌","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"page":{"id":"reading-block-7044913259924763a3b29542e91fbca8","title":"已完成的基准运行","number":2},"sectionTitle":"已完成的基准运行","currentQuestion":"已完成的基准运行","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-bb24e58b99dd846a4ce58499","nextBlock":null,"prerequisites":[{"id":"b-dbbf4344a9e658eaa2fb6c12","url":"#b-dbbf4344a9e658eaa2fb6c12","role":"section-title"},{"id":"b-8b63ea24bd80060e9ee1fad1","url":"#b-8b63ea24bd80060e9ee1fad1","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-05c7e40e62cf0af310b4519a","type":"h2","scope":"block-1658d972c93e45b4a3bb0d957f2e33d2","url":"https://codingai-lec03.pages.dev/course/lab17-教师软目标与表示坍塌.html#b-05c7e40e62cf0af310b4519a","content":"## 旧版热身（历史参考）","sha256":"22776016622c2addaf705c770c88971c82973c938ae33e183a9feb3b49e49de1","chapter":{"id":"course","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"unit":{"id":"lab17-教师软目标与表示坍塌","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"page":{"id":"reading-block-1658d972c93e45b4a3bb0d957f2e33d2","title":"旧版热身（历史参考）","number":3},"sectionTitle":"旧版热身（历史参考）","currentQuestion":"旧版热身（历史参考）","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":null,"nextBlock":"b-dfd190074bc5986bf1c1b61d","prerequisites":[{"id":"b-dfd190074bc5986bf1c1b61d","url":"#b-dfd190074bc5986bf1c1b61d","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-dfd190074bc5986bf1c1b61d","type":"p","scope":"block-1658d972c93e45b4a3bb0d957f2e33d2","url":"https://codingai-lec03.pages.dev/course/lab17-教师软目标与表示坍塌.html#b-dfd190074bc5986bf1c1b61d","content":"旧版热身仅保留为历史参考，不参与当前基准运行；当前解释与计算以上方完整实验为准。","sha256":"e5c542ac9eaa3e8830cbf8ff2616dedc089473c3d44be23349ecd3d049b6d0f9","chapter":{"id":"course","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"unit":{"id":"lab17-教师软目标与表示坍塌","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"page":{"id":"reading-block-1658d972c93e45b4a3bb0d957f2e33d2","title":"旧版热身（历史参考）","number":3},"sectionTitle":"旧版热身（历史参考）","currentQuestion":"旧版热身（历史参考）","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-05c7e40e62cf0af310b4519a","nextBlock":"b-cfca1dc6231d98d89888d21e","prerequisites":[{"id":"b-05c7e40e62cf0af310b4519a","url":"#b-05c7e40e62cf0af310b4519a","role":"section-title"}],"relatedBlocks":[]},{"id":"b-cfca1dc6231d98d89888d21e","type":"h4","scope":"block-1658d972c93e45b4a3bb0d957f2e33d2","url":"https://codingai-lec03.pages.dev/course/lab17-教师软目标与表示坍塌.html#b-cfca1dc6231d98d89888d21e","content":"#### 展开查看旧版代码（仅展示，不执行）","sha256":"b5f2d755e2ad018e90a28a20600c873333e0691cce1a7f018f374a7d482cbaf3","chapter":{"id":"course","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"unit":{"id":"lab17-教师软目标与表示坍塌","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"page":{"id":"reading-block-1658d972c93e45b4a3bb0d957f2e33d2","title":"旧版热身（历史参考）","number":3},"sectionTitle":"旧版热身（历史参考）","currentQuestion":"旧版热身（历史参考）","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-dfd190074bc5986bf1c1b61d","nextBlock":"b-fde5fbb9185821aa3e55b996","prerequisites":[{"id":"b-05c7e40e62cf0af310b4519a","url":"#b-05c7e40e62cf0af310b4519a","role":"section-title"},{"id":"b-dfd190074bc5986bf1c1b61d","url":"#b-dfd190074bc5986bf1c1b61d","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-fde5fbb9185821aa3e55b996","type":"pre","scope":"block-1658d972c93e45b4a3bb0d957f2e33d2","url":"https://codingai-lec03.pages.dev/course/lab17-教师软目标与表示坍塌.html#b-fde5fbb9185821aa3e55b996","content":"```\nimport numpy as np\nz=np.ones((8,4)); print('collapsed variance',z.var(0),'pair loss',((z-z[::-1])**2).mean())\nrng=np.random.default_rng(3); student=rng.normal(size=4); teacher=np.zeros(4)\nfor _ in range(3): teacher=.9*teacher+.1*student\nprint('EMA teacher',teacher.round(3),'stop-gradient is one component, not a proof')\n\n```","sha256":"7ec8bd14f07ee73afaacf592a08b2b09425037e648306447bf035cd5ee7ab9f7","chapter":{"id":"course","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"unit":{"id":"lab17-教师软目标与表示坍塌","title":"LAB 17 · 软目标与坍塌：三个数值检查"},"page":{"id":"reading-block-1658d972c93e45b4a3bb0d957f2e33d2","title":"旧版热身（历史参考）","number":3},"sectionTitle":"旧版热身（历史参考）","currentQuestion":"旧版热身（历史参考）","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-cfca1dc6231d98d89888d21e","nextBlock":null,"prerequisites":[{"id":"b-cfca1dc6231d98d89888d21e","url":"#b-cfca1dc6231d98d89888d21e","role":"section-title"},{"id":"b-dfd190074bc5986bf1c1b61d","url":"#b-dfd190074bc5986bf1c1b61d","role":"problem-context"}],"relatedBlocks":[]}]}