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XOR：信息保留与线性读出","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-26829b2ad8f30a9edea06a11","nextBlock":"b-e73664c719d92d0edd3da456","prerequisites":[{"id":"b-67d0ed5d646ec4ddd99a53e5","url":"#b-67d0ed5d646ec4ddd99a53e5","role":"section-title"},{"id":"b-b37b6692848d09a394099145","url":"#b-b37b6692848d09a394099145","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-e73664c719d92d0edd3da456","type":"p","scope":"block-c98ad8d2a25f41578ac66b80719df8db","url":"https://codingai-lec03.pages.dev/course/notebooks/33066318f5884adc8417068df0f40431.html#b-e73664c719d92d0edd3da456","content":"**学习路径：** [表示怎样迁移到新任务](/course/study/readout-transfer.html)","sha256":"efc07be0d238c97b2a0f2a3e1e141f27691e7d1aadb5b0bc2662d7d40218327f","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-use-and-evaluate","title":"怎样判断表示支持了哪种使用方式？"},"page":{"id":"reading-opening","title":"LAB 18 · XOR：信息保留与线性读出","number":1},"sectionTitle":"LAB 18 · XOR：信息保留与线性读出","currentQuestion":"LAB 18 · XOR：信息保留与线性读出","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-b42ce1e2673aa51839a067fb","nextBlock":"b-ef9b8e4dc3fc28c3a1e76ae8","prerequisites":[{"id":"b-67d0ed5d646ec4ddd99a53e5","url":"#b-67d0ed5d646ec4ddd99a53e5","role":"section-title"},{"id":"b-b37b6692848d09a394099145","url":"#b-b37b6692848d09a394099145","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-ef9b8e4dc3fc28c3a1e76ae8","type":"p","scope":"block-c98ad8d2a25f41578ac66b80719df8db","url":"https://codingai-lec03.pages.dev/course/notebooks/33066318f5884adc8417068df0f40431.html#b-ef9b8e4dc3fc28c3a1e76ae8","content":"这是[CLS 06](https://deepnote.com/project/38755e4e-23f6-4f5f-8c68-8a2e4114b1c1/notebook/c0645a4db6e04188ab5b119e87c53bed)的一项短检查：**信息还在，为什么一条直线仍读不出？**","sha256":"2ac5be1cf4f3a1fc463ede358690285856bbac56babfdac8b42a7bb6994a0b28","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-use-and-evaluate","title":"怎样判断表示支持了哪种使用方式？"},"page":{"id":"reading-opening","title":"LAB 18 · XOR：信息保留与线性读出","number":1},"sectionTitle":"LAB 18 · XOR：信息保留与线性读出","currentQuestion":"LAB 18 · XOR：信息保留与线性读出","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-e73664c719d92d0edd3da456","nextBlock":"b-a291d14b6a42782eba6a4b1c","prerequisites":[{"id":"b-67d0ed5d646ec4ddd99a53e5","url":"#b-67d0ed5d646ec4ddd99a53e5","role":"section-title"},{"id":"b-b37b6692848d09a394099145","url":"#b-b37b6692848d09a394099145","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-a291d14b6a42782eba6a4b1c","type":"p","scope":"block-c98ad8d2a25f41578ac66b80719df8db","url":"https://codingai-lec03.pages.dev/course/notebooks/33066318f5884adc8417068df0f40431.html#b-a291d14b6a42782eba6a4b1c","content":"先看[XOR四点与乘积特征图](/course/blocks/information-and-readable-form.html)，判断原四点是否碰撞，再比较h和z的线性读出。代码精确计算离散互信息：z保留XOR标签，却丢掉四个角点的完整身份。","sha256":"78ec3e8f54d9dfe0da9b56edfd73e372c02e1886a253bca6de514670c6da9f6e","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-use-and-evaluate","title":"怎样判断表示支持了哪种使用方式？"},"page":{"id":"reading-opening","title":"LAB 18 · XOR：信息保留与线性读出","number":1},"sectionTitle":"LAB 18 · XOR：信息保留与线性读出","currentQuestion":"LAB 18 · XOR：信息保留与线性读出","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-ef9b8e4dc3fc28c3a1e76ae8","nextBlock":"b-cf93f29ccb77c88d6496ef61","prerequisites":[{"id":"b-67d0ed5d646ec4ddd99a53e5","url":"#b-67d0ed5d646ec4ddd99a53e5","role":"section-title"},{"id":"b-b37b6692848d09a394099145","url":"#b-b37b6692848d09a394099145","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-cf93f29ccb77c88d6496ef61","type":"p","scope":"block-c98ad8d2a25f41578ac66b80719df8db","url":"https://codingai-lec03.pages.dev/course/notebooks/33066318f5884adc8417068df0f40431.html#b-cf93f29ccb77c88d6496ef61","content":"产出一组对照：把任务从XOR改成“第一坐标是否为正”，说明同一个z为什么不再足够。bit数只适用于本构造，不能直接变成连续图像表示的通用评分。[P23](/course/pages/l3-r2-p23.html)连接评价协议；想在图像上看读出差异，再用[LAB 01](https://deepnote.com/project/38755e4e-23f6-4f5f-8c68-8a2e4114b1c1/notebook/4dd8605ed9904820919ea9e13d9e7d7c)。","sha256":"a4fbc37d3f3bcbb4bfdeb69f7344581f9b5a6f3532934575a69633754ed8ebe5","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-use-and-evaluate","title":"怎样判断表示支持了哪种使用方式？"},"page":{"id":"reading-opening","title":"LAB 18 · XOR：信息保留与线性读出","number":1},"sectionTitle":"LAB 18 · XOR：信息保留与线性读出","currentQuestion":"LAB 18 · XOR：信息保留与线性读出","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-a291d14b6a42782eba6a4b1c","nextBlock":"b-23594656647f06a8295caa35","prerequisites":[{"id":"b-67d0ed5d646ec4ddd99a53e5","url":"#b-67d0ed5d646ec4ddd99a53e5","role":"section-title"},{"id":"b-b37b6692848d09a394099145","url":"#b-b37b6692848d09a394099145","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-23594656647f06a8295caa35","type":"pre","scope":"block-c5113894a7934003bb3fd12a1d78f39c","url":"https://codingai-lec03.pages.dev/course/notebooks/33066318f5884adc8417068df0f40431.html#b-23594656647f06a8295caa35","content":"```\n# Writable ephemeral workspace for detached readonly cloud runs.\nimport os, tempfile\nos.chdir(tempfile.mkdtemp(prefix='lec03_lab21_'))\n\nimport numpy as np\nfrom collections import Counter\nh=[(-1,-1),(-1,1),(1,-1),(1,1)]; y=[0,1,1,0]; z=[a*b for a,b in h]; c=[0]*4\ndef mutual(a,b):\n    n=len(a); joint=Counter(zip(a,b)); ca=Counter(a); cb=Counter(b)\n    return sum(v/n*np.log2(v*n/(ca[x]*cb[t])) for (x,t),v in joint.items())\ndef fit(X,y):\n    X=np.c_[X,np.ones(len(y))]; w=np.zeros(X.shape[1]); y=np.array(y)\n    for _ in range(500):\n        p=1/(1+np.exp(-X@w)); w-=.2*X.T@(p-y)/len(y)\n    return (1/(1+np.exp(-X@w))).round(4)\nprint('I(h;y), I(z;y), I(constant;y) bits',mutual(h,y),mutual(z,y),mutual(c,y))\nprint('I(h;h), I(h;z) bits',mutual(h,h),mutual(h,z))\nprint('linear probabilities on h',fit(np.array(h),y).tolist(),'on z',fit(np.array(z)[:,None],y).tolist())\nassert mutual(h,y)==mutual(z,y)==1 and mutual(h,h)==2 and mutual(h,z)==1\nprint('z keeps XOR label, loses which corner: label sufficiency is task dependent')\n```","sha256":"d9aee452ec06f68596a2209ada94de8574256f0031c7a90eb656ce270306d533","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-use-and-evaluate","title":"怎样判断表示支持了哪种使用方式？"},"page":{"id":"reading-opening","title":"LAB 18 · XOR：信息保留与线性读出","number":1},"sectionTitle":"LAB 18 · XOR：信息保留与线性读出","currentQuestion":"LAB 18 · XOR：信息保留与线性读出","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-cf93f29ccb77c88d6496ef61","nextBlock":null,"prerequisites":[{"id":"b-67d0ed5d646ec4ddd99a53e5","url":"#b-67d0ed5d646ec4ddd99a53e5","role":"section-title"},{"id":"b-b37b6692848d09a394099145","url":"#b-b37b6692848d09a394099145","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-d069454077551cf736ddcfba","type":"h2","scope":"block-202bf43aba9a4bc88dd38e6ce6b76405","url":"https://codingai-lec03.pages.dev/course/notebooks/33066318f5884adc8417068df0f40431.html#b-d069454077551cf736ddcfba","content":"## 已完成的基准运行","sha256":"70efe3096d536ddf0d6f0f7335815da85d73017a47a0e52cac5d2621805a3c53","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-use-and-evaluate","title":"怎样判断表示支持了哪种使用方式？"},"page":{"id":"reading-block-202bf43aba9a4bc88dd38e6ce6b76405","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-d34270d67b034533957207e5","prerequisites":[{"id":"b-d34270d67b034533957207e5","url":"#b-d34270d67b034533957207e5","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-d34270d67b034533957207e5","type":"p","scope":"block-202bf43aba9a4bc88dd38e6ce6b76405","url":"https://codingai-lec03.pages.dev/course/notebooks/33066318f5884adc8417068df0f40431.html#b-d34270d67b034533957207e5","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":"I","title":"学习信号与表示"},"unit":{"id":"i-use-and-evaluate","title":"怎样判断表示支持了哪种使用方式？"},"page":{"id":"reading-block-202bf43aba9a4bc88dd38e6ce6b76405","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-d069454077551cf736ddcfba","nextBlock":"b-650e631008bbc0b9c2fe1997","prerequisites":[{"id":"b-d069454077551cf736ddcfba","url":"#b-d069454077551cf736ddcfba","role":"section-title"}],"relatedBlocks":[]},{"id":"b-650e631008bbc0b9c2fe1997","type":"pre","scope":"block-202bf43aba9a4bc88dd38e6ce6b76405","url":"https://codingai-lec03.pages.dev/course/notebooks/33066318f5884adc8417068df0f40431.html#b-650e631008bbc0b9c2fe1997","content":"```\nI(h;y), I(z;y), I(constant;y) bits 1.0 1.0 0.0\nI(h;h), I(h;z) bits 2.0 1.0\nlinear probabilities on h [0.5, 0.5, 0.5, 0.5] on z [0.0102, 0.9898, 0.9898, 0.0102]\nz keeps XOR label, loses which corner: label sufficiency is task dependent\n\n```","sha256":"28a56258967a76ffb626729cc878f288e95f4dac25e56b04964c0de1025e383e","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-use-and-evaluate","title":"怎样判断表示支持了哪种使用方式？"},"page":{"id":"reading-block-202bf43aba9a4bc88dd38e6ce6b76405","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-d34270d67b034533957207e5","nextBlock":"b-5ab65aee7797ddd62fbb594b","prerequisites":[{"id":"b-d069454077551cf736ddcfba","url":"#b-d069454077551cf736ddcfba","role":"section-title"},{"id":"b-d34270d67b034533957207e5","url":"#b-d34270d67b034533957207e5","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-5ab65aee7797ddd62fbb594b","type":"p","scope":"block-202bf43aba9a4bc88dd38e6ce6b76405","url":"https://codingai-lec03.pages.dev/course/notebooks/33066318f5884adc8417068df0f40431.html#b-5ab65aee7797ddd62fbb594b","content":"h→z是确定映射，数据处理不能创造关于y的新信息；这里I(h;y)=I(z;y)=1bit，但z降低了读出难度。若下游任务换成“x₁是否为正”，z将无法区分两种答案。这给颜色增强提供了精确类比：某个目标需要忽略颜色，不代表其他目标也不需要。逻辑回归h的对称初始化停在0.5符合凸损失对称最优，不能把二分类threshold的偶然准确率称为XOR已学会。连接LAB06的h/z实训练，再检查有限样本与函数类的限制。","sha256":"c932a40493a7bfe15ab86eaa55efd1a0ccd9796d87cfccb7f7a30de81f06475d","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-use-and-evaluate","title":"怎样判断表示支持了哪种使用方式？"},"page":{"id":"reading-block-202bf43aba9a4bc88dd38e6ce6b76405","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-650e631008bbc0b9c2fe1997","nextBlock":null,"prerequisites":[{"id":"b-d069454077551cf736ddcfba","url":"#b-d069454077551cf736ddcfba","role":"section-title"},{"id":"b-d34270d67b034533957207e5","url":"#b-d34270d67b034533957207e5","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-f007678556ba06516c9faf14","type":"h2","scope":"block-eec26396f50540529159208805f0276f","url":"https://codingai-lec03.pages.dev/course/notebooks/33066318f5884adc8417068df0f40431.html#b-f007678556ba06516c9faf14","content":"## 旧版热身（历史参考）","sha256":"22776016622c2addaf705c770c88971c82973c938ae33e183a9feb3b49e49de1","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-use-and-evaluate","title":"怎样判断表示支持了哪种使用方式？"},"page":{"id":"reading-block-eec26396f50540529159208805f0276f","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-6751a8e6147903ad0915eaa8","prerequisites":[{"id":"b-6751a8e6147903ad0915eaa8","url":"#b-6751a8e6147903ad0915eaa8","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-6751a8e6147903ad0915eaa8","type":"p","scope":"block-eec26396f50540529159208805f0276f","url":"https://codingai-lec03.pages.dev/course/notebooks/33066318f5884adc8417068df0f40431.html#b-6751a8e6147903ad0915eaa8","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。旧版的 identity is preserved 表述已纠正：z 保留 XOR 标签信息，但没有保留四个角点的完整身份。","sha256":"bc090315a57a3fe90a4b713fa79244ee0f6fa80712bcf0ffd9e0037d0e061eef","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-use-and-evaluate","title":"怎样判断表示支持了哪种使用方式？"},"page":{"id":"reading-block-eec26396f50540529159208805f0276f","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-f007678556ba06516c9faf14","nextBlock":"b-3e4080fcec48205ece7754c4","prerequisites":[{"id":"b-f007678556ba06516c9faf14","url":"#b-f007678556ba06516c9faf14","role":"section-title"}],"relatedBlocks":[]},{"id":"b-3e4080fcec48205ece7754c4","type":"h4","scope":"block-eec26396f50540529159208805f0276f","url":"https://codingai-lec03.pages.dev/course/notebooks/33066318f5884adc8417068df0f40431.html#b-3e4080fcec48205ece7754c4","content":"#### 展开查看旧版代码（仅展示，不执行）","sha256":"b5f2d755e2ad018e90a28a20600c873333e0691cce1a7f018f374a7d482cbaf3","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-use-and-evaluate","title":"怎样判断表示支持了哪种使用方式？"},"page":{"id":"reading-block-eec26396f50540529159208805f0276f","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-6751a8e6147903ad0915eaa8","nextBlock":"b-af0a2e48f6fd7b6a580fc544","prerequisites":[{"id":"b-f007678556ba06516c9faf14","url":"#b-f007678556ba06516c9faf14","role":"section-title"},{"id":"b-6751a8e6147903ad0915eaa8","url":"#b-6751a8e6147903ad0915eaa8","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-af0a2e48f6fd7b6a580fc544","type":"pre","scope":"block-eec26396f50540529159208805f0276f","url":"https://codingai-lec03.pages.dev/course/notebooks/33066318f5884adc8417068df0f40431.html#b-af0a2e48f6fd7b6a580fc544","content":"```\nh=[(-1,-1),(-1,1),(1,-1),(1,1)]; y=[0,1,1,0]; z=[a*b for a,b in h]; pred=[int(v<0) for v in z]\nprint('h unique',len(set(h)),'nonlinear feature',z,'readout',pred); assert pred==y\nprint('identity is preserved; linear separability is a different question')\n\n```","sha256":"c035f8bf568a86c650d884058bf3e1b3afce819c27a30ec54c696bf09d9c320c","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-use-and-evaluate","title":"怎样判断表示支持了哪种使用方式？"},"page":{"id":"reading-block-eec26396f50540529159208805f0276f","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-3e4080fcec48205ece7754c4","nextBlock":null,"prerequisites":[{"id":"b-3e4080fcec48205ece7754c4","url":"#b-3e4080fcec48205ece7754c4","role":"section-title"},{"id":"b-6751a8e6147903ad0915eaa8","url":"#b-6751a8e6147903ad0915eaa8","role":"problem-context"}],"relatedBlocks":[]}]}