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0.09567","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":null,"nextBlock":"b-ac27c072595da802712dc263","prerequisites":[{"id":"b-ac27c072595da802712dc263","url":"#b-ac27c072595da802712dc263","role":"problem-context"}],"relatedBlocks":[{"id":"b-6e7237ff1d521f111f7a3f1d","url":"#b-6e7237ff1d521f111f7a3f1d","relation":"figure-and-explanation"}]},{"id":"b-ac27c072595da802712dc263","type":"p","scope":"clip-matrix-worked","url":"https://codingai-lec03.pages.dev/course/blocks/clip-matrix-worked.html#b-ac27c072595da802712dc263","content":"这页的数字能从单位向量完全复算：矩阵不是模型实测成绩。先看一行的三个竞争候选，再看一列，最后对两种方向取平均。温度改变 logits 和概率，不改变原始余弦本身。真实 CLIP 的结果需读取相应模型输出，不能沿用这里的教学数值。","sha256":"17775dd8144b9a7fd31777d1611efe47ffd56052acc4f240b8216acdaa2988d5","chapter":{"id":"III","title":"视觉与语言"},"unit":{"id":"clip-pairing-to-candidates","title":"已知图文配对怎样变成可用的文字候选接口？"},"page":{"id":"reading-opening","title":"三对图文的双向损失：从单位向量到 0.09567","number":1},"sectionTitle":"三对图文的双向损失：从单位向量到 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$.64+.09+.27=1$，所以点积确实是余弦。","sha256":"6c3a21981a8ce3f76bbf1f59e8561a530b19e1f6013e4938562d95ff978d4d51","chapter":{"id":"III","title":"视觉与语言"},"unit":{"id":"clip-pairing-to-candidates","title":"已知图文配对怎样变成可用的文字候选接口？"},"page":{"id":"reading-opening","title":"三对图文的双向损失：从单位向量到 0.09567","number":1},"sectionTitle":"三对图文的双向损失：从单位向量到 0.09567","currentQuestion":"三对图文的双向损失：从单位向量到 0.09567","sourceSlides":[],"knowledgeBlock":null,"formulas":[{"latex":"e_1,e_2,e_3","definitionContext":"三对图文的双向损失：从单位向量到 0.09567"},{"latex":"(.8,0,.3,\\sqrt{.27})","definitionContext":"三对图文的双向损失：从单位向量到 0.09567"},{"latex":"(.3,.8,0,\\sqrt{.27})","definitionContext":"三对图文的双向损失：从单位向量到 0.09567"},{"latex":"(0,.3,.8,\\sqrt{.27})","definitionContext":"三对图文的双向损失：从单位向量到 0.09567"},{"latex":".64+.09+.27=1","definitionContext":"三对图文的双向损失：从单位向量到 0.09567"}],"previousBlock":"b-ac27c072595da802712dc263","nextBlock":"b-5a42be83072cfae143153e38","prerequisites":[{"id":"b-9359367f9d1579ff873f5c6c","url":"#b-9359367f9d1579ff873f5c6c","role":"section-title"},{"id":"b-ac27c072595da802712dc263","url":"#b-ac27c072595da802712dc263","role":"problem-context"}],"relatedBlocks":[{"id":"b-6e7237ff1d521f111f7a3f1d","url":"#b-6e7237ff1d521f111f7a3f1d","relation":"figure-and-explanation"}]},{"id":"b-5a42be83072cfae143153e38","type":"p","scope":"clip-matrix-worked","url":"https://codingai-lec03.pages.dev/course/blocks/clip-matrix-worked.html#b-5a42be83072cfae143153e38","content":"$S=\\begin{bmatrix}.8&.3&0\\\\0&.8&.3\\\\.3&0&.8\\end{bmatrix}.$","sha256":"87efe740a2b21be719887a28b5b3cfd8c6d8e212a6b15ab44c84bdd96d693ac2","chapter":{"id":"III","title":"视觉与语言"},"unit":{"id":"clip-pairing-to-candidates","title":"已知图文配对怎样变成可用的文字候选接口？"},"page":{"id":"reading-opening","title":"三对图文的双向损失：从单位向量到 0.09567","number":1},"sectionTitle":"三对图文的双向损失：从单位向量到 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$(4,1.5,0)$，正确配对概率为","sha256":"5f5d03b18f32fe9ef45e0e47dc9459338e7af869590cf2a4f35f7c07b37ee552","chapter":{"id":"III","title":"视觉与语言"},"unit":{"id":"clip-pairing-to-candidates","title":"已知图文配对怎样变成可用的文字候选接口？"},"page":{"id":"reading-opening","title":"三对图文的双向损失：从单位向量到 0.09567","number":1},"sectionTitle":"三对图文的双向损失：从单位向量到 0.09567","currentQuestion":"三对图文的双向损失：从单位向量到 0.09567","sourceSlides":[],"knowledgeBlock":null,"formulas":[{"latex":"\\tau=.2","definitionContext":"三对图文的双向损失：从单位向量到 0.09567"},{"latex":"(4,1.5,0)","definitionContext":"三对图文的双向损失：从单位向量到 0.09567"}],"previousBlock":"b-5a42be83072cfae143153e38","nextBlock":"b-0ce69b470f37c9f54f797689","prerequisites":[{"id":"b-9359367f9d1579ff873f5c6c","url":"#b-9359367f9d1579ff873f5c6c","role":"section-title"},{"id":"b-ac27c072595da802712dc263","url":"#b-ac27c072595da802712dc263","role":"problem-context"}],"relatedBlocks":[{"id":"b-6e7237ff1d521f111f7a3f1d","url":"#b-6e7237ff1d521f111f7a3f1d","relation":"figure-and-explanation"}]},{"id":"b-0ce69b470f37c9f54f797689","type":"p","scope":"clip-matrix-worked","url":"https://codingai-lec03.pages.dev/course/blocks/clip-matrix-worked.html#b-0ce69b470f37c9f54f797689","content":"$p_{11}=\\frac{e^4}{e^4+e^{1.5}+1}=0.9087599243,\\qquad -\\log p_{11}=0.0956743294.$","sha256":"7cb63b04e1a0edf44bbd40f7be4f6471f882de0e7485d96ca394a8b321aeb6cb","chapter":{"id":"III","title":"视觉与语言"},"unit":{"id":"clip-pairing-to-candidates","title":"已知图文配对怎样变成可用的文字候选接口？"},"page":{"id":"reading-opening","title":"三对图文的双向损失：从单位向量到 0.09567","number":1},"sectionTitle":"三对图文的双向损失：从单位向量到 0.09567","currentQuestion":"三对图文的双向损失：从单位向量到 0.09567","sourceSlides":[],"knowledgeBlock":null,"formulas":[{"latex":"p_{11}=\\frac{e^4}{e^4+e^{1.5}+1}=0.9087599243,\\qquad -\\log p_{11}=0.0956743294.","definitionContext":"三对图文的双向损失：从单位向量到 0.09567"}],"previousBlock":"b-ad52db69c6e3408ab2f3e18a","nextBlock":"b-1f8b4643b6482dbdb426cf64","prerequisites":[{"id":"b-9359367f9d1579ff873f5c6c","url":"#b-9359367f9d1579ff873f5c6c","role":"section-title"},{"id":"b-ac27c072595da802712dc263","url":"#b-ac27c072595da802712dc263","role":"problem-context"}],"relatedBlocks":[{"id":"b-6e7237ff1d521f111f7a3f1d","url":"#b-6e7237ff1d521f111f7a3f1d","relation":"figure-and-explanation"}]},{"id":"b-1f8b4643b6482dbdb426cf64","type":"p","scope":"clip-matrix-worked","url":"https://codingai-lec03.pages.dev/course/blocks/clip-matrix-worked.html#b-1f8b4643b6482dbdb426cf64","content":"第一列只是将两个负项换序，概率不变；其他行列同理。双向平均损失为 $L=(L_{I\\to T}+L_{T\\to I})/2=0.0956743294$。一般情况下每行每列并不同分，必须分别计算，不能从一个最好看的单元格推总损失。","sha256":"997240b500a1857825d9d5e874382060b832ca04e5892cf1a198efaf8a4247a5","chapter":{"id":"III","title":"视觉与语言"},"unit":{"id":"clip-pairing-to-candidates","title":"已知图文配对怎样变成可用的文字候选接口？"},"page":{"id":"reading-opening","title":"三对图文的双向损失：从单位向量到 0.09567","number":1},"sectionTitle":"三对图文的双向损失：从单位向量到 0.09567","currentQuestion":"三对图文的双向损失：从单位向量到 0.09567","sourceSlides":[],"knowledgeBlock":null,"formulas":[{"latex":"L=(L_{I\\to T}+L_{T\\to I})/2=0.0956743294","definitionContext":"三对图文的双向损失：从单位向量到 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的区分程度。更换批次会更换竞争候选；两段都适合狗图的文字也可能在配对表里互为负项，因此学习目标与语义真值并不完全重合。","sha256":"003f4000ef5478872af45c630b0aee2f6ce26c9522cbfa443a8343611fd3f829","chapter":{"id":"III","title":"视觉与语言"},"unit":{"id":"clip-pairing-to-candidates","title":"已知图文配对怎样变成可用的文字候选接口？"},"page":{"id":"reading-opening","title":"三对图文的双向损失：从单位向量到 0.09567","number":1},"sectionTitle":"三对图文的双向损失：从单位向量到 0.09567","currentQuestion":"三对图文的双向损失：从单位向量到 0.09567","sourceSlides":[],"knowledgeBlock":null,"formulas":[{"latex":"[-1,1]","definitionContext":"三对图文的双向损失：从单位向量到 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0.8\n- 0.3\n- 0.3\n- 0.0\n- 0.8\n- 文字找图像 ↓\n- τ = 0.2\n- 第一列 logits：4, 0, 1.5\n- p(正确配对) ≈ 0.909\n- −log p ≈ 0.0957\n- 行目标 + 列目标\n- 在批次中辨认配对\n- 对角线来自配对顺序；数值是由明确单位向量构造的教学矩阵，不是 CLIP 实测分数。矩阵、温度、行列概率使用同一组数值；每个对角概率约为 0.909。 [查看对应图解状态](/#/l3-r2-p57/1)[查看完整图解](/#/l3-r2-p57/1)","sha256":"2c230910c3be0a987a3af170b2b8a0da8e1a6bdca4189f84265fa8087070d7c5","chapter":{"id":"III","title":"视觉与语言"},"unit":{"id":"clip-pairing-to-candidates","title":"已知图文配对怎样变成可用的文字候选接口？"},"page":{"id":"reading-opening","title":"三对图文的双向损失：从单位向量到 0.09567","number":1},"sectionTitle":"三对图文的双向损失：从单位向量到 0.09567","currentQuestion":"三对图文的双向损失：从单位向量到 0.09567","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"figure":{"caption":"矩阵、温度、行列概率使用同一组数值；每个对角概率约为 0.909。 查看对应图解状态","labels":["单位向量点积 Sᵢⱼ；教学构造","I1","T1","红杯","I2","T2","蓝杯","I3","T3","人物","0.8","0.3","0.0","0.0","0.8","0.3","0.3","0.0","0.8","文字找图像 ↓","τ = 0.2","第一列 logits：4, 0, 1.5","p(正确配对) ≈ 0.909","−log p ≈ 0.0957","行目标 + 列目标","在批次中辨认配对","对角线来自配对顺序；数值是由明确单位向量构造的教学矩阵，不是 CLIP 实测分数。"],"description":"矩阵、温度、行列概率使用同一组数值；每个对角概率约为 0.909。 查看对应图解状态单位向量点积 Sᵢⱼ；教学构造I1T1红杯I2T2蓝杯I3T3人物0.80.30.00.00.80.30.30.00.8文字找图像 ↓τ = 0.2第一列 logits：4, 0, 1.5p(正确配对) ≈ 0.909−log p ≈ 0.0957行目标 + 列目标在批次中辨认配对对角线来自配对顺序；数值是由明确单位向量构造的教学矩阵，不是 CLIP 实测分数。","evidenceIdentity":"矩阵、温度、行列概率使用同一组数值；每个对角概率约为 0.909。 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0.09567","number":1},"sectionTitle":"三对图文的双向损失：从单位向量到 0.09567","currentQuestion":"三对图文的双向损失：从单位向量到 0.09567","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-6e7237ff1d521f111f7a3f1d","nextBlock":null,"prerequisites":[{"id":"b-9359367f9d1579ff873f5c6c","url":"#b-9359367f9d1579ff873f5c6c","role":"section-title"},{"id":"b-ac27c072595da802712dc263","url":"#b-ac27c072595da802712dc263","role":"problem-context"}],"relatedBlocks":[{"id":"b-6e7237ff1d521f111f7a3f1d","url":"#b-6e7237ff1d521f111f7a3f1d","relation":"figure-and-explanation"}]}]}