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解释、算例与证据","sha256":"d71cf15e707c8a3674b4c90a599efee783cb84da5b8c8236a1d01c3add7b4958","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-view-objective","title":"视图关系怎样成为学习目标，又会牺牲什么？"},"page":{"id":"h-i-contrastive-choice","title":"从三个候选算出一次选择损失","number":1},"sectionTitle":"从三个候选算出一次选择损失","currentQuestion":"视图关系怎样成为学习目标，又会牺牲什么？","sourceSlides":["l3-r2-p10"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-a609340de9f4c98c639b5a19","nextBlock":"b-901ef17381bd7e373e02cf5c","prerequisites":[{"id":"b-a609340de9f4c98c639b5a19","url":"#b-a609340de9f4c98c639b5a19","role":"section-title"},{"id":"b-dbf9f62230b4bdff27af2c34","url":"#b-dbf9f62230b4bdff27af2c34","role":"problem-context"}],"relatedBlocks":[{"id":"b-c3db11a480c42febc9a33fe3","url":"#b-c3db11a480c42febc9a33fe3","relation":"figure-and-explanation"}]},{"id":"b-901ef17381bd7e373e02cf5c","type":"h1","scope":"document","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p10.html#b-901ef17381bd7e373e02cf5c","content":"# P10 · 一次对比，就是一次有答案的选择","sha256":"816b88c5ec645a7b3c65198c0878e5cfafcf53fc0dbb4e57668de2c4950697d1","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-view-objective","title":"视图关系怎样成为学习目标，又会牺牲什么？"},"page":{"id":"h-i-contrastive-choice","title":"从三个候选算出一次选择损失","number":1},"sectionTitle":"从三个候选算出一次选择损失","currentQuestion":"视图关系怎样成为学习目标，又会牺牲什么？","sourceSlides":["l3-r2-p10"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-0062a66b159b8321641a31bc","nextBlock":"b-dbf9f62230b4bdff27af2c34","prerequisites":[{"id":"b-0062a66b159b8321641a31bc","url":"#b-0062a66b159b8321641a31bc","role":"section-title"},{"id":"b-dbf9f62230b4bdff27af2c34","url":"#b-dbf9f62230b4bdff27af2c34","role":"problem-context"}],"relatedBlocks":[{"id":"b-c3db11a480c42febc9a33fe3","url":"#b-c3db11a480c42febc9a33fe3","relation":"figure-and-explanation"}]},{"id":"b-dbf9f62230b4bdff27af2c34","type":"p","scope":"document","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p10.html#b-dbf9f62230b4bdff27af2c34","content":"这一页把相似关系变成可优化的概率与损失。分数、温度、softmax和负对数必须能对上同一组数。","sha256":"617994cb9e9eba93f0bf3265ec9ed81f11bc03c1613f1ad98c4222386b3673c8","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-view-objective","title":"视图关系怎样成为学习目标，又会牺牲什么？"},"page":{"id":"h-i-contrastive-choice","title":"从三个候选算出一次选择损失","number":1},"sectionTitle":"从三个候选算出一次选择损失","currentQuestion":"视图关系怎样成为学习目标，又会牺牲什么？","sourceSlides":["l3-r2-p10"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-901ef17381bd7e373e02cf5c","nextBlock":"b-c3db11a480c42febc9a33fe3","prerequisites":[{"id":"b-901ef17381bd7e373e02cf5c","url":"#b-901ef17381bd7e373e02cf5c","role":"section-title"}],"relatedBlocks":[{"id":"b-c3db11a480c42febc9a33fe3","url":"#b-c3db11a480c42febc9a33fe3","relation":"figure-and-explanation"}]},{"id":"b-c3db11a480c42febc9a33fe3","type":"figure","scope":"document","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p10.html#b-c3db11a480c42febc9a33fe3","content":"图内标签与数值：P10 学习表示机制图，状态 2；三候选教学算例 · 指定第 1 项为正例；相似度 s；除以温度 τ = 0.5；归一化概率 p；k⁺；1；2；0.665；k₁；0.5；1；0.245；k₂；0；0；0.090；pⱼ = exp(sⱼ / τ) / Σₗ exp(sₗ / τ)；L = −ln p⁺ = 0.408\n\n三候选相似度1、0.5、0经过温度0.5缩放成2、1、0，概率0.665、0.245、0.090，指定正项损失0.408。\n\n- 三候选教学算例 · 指定第 1 项为正例\n- 相似度 s\n- 除以温度 τ = 0.5\n- 归一化概率 p\n- k⁺\n- 1\n- 2\n- 0.665\n- k₁\n- 0.5\n- 1\n- 0.245\n- k₂\n- 0\n- 0\n- 0.090\n- pⱼ = exp(sⱼ / τ) / Σₗ exp(sₗ / τ)\n- L = −ln p⁺ = 0.408三候选相似度1、0.5、0经过温度0.5缩放成2、1、0，概率0.665、0.245、0.090，指定正项损失0.408。 [查看对应图解状态](/#/l3-r2-p10/1)[查看完整图解](/course/figures/l3-r2-p10-1.html)","sha256":"4d4fd3fda021683648885f34532489ec341f3515a65d48be5b2584589c4fc7c1","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-view-objective","title":"视图关系怎样成为学习目标，又会牺牲什么？"},"page":{"id":"h-i-contrastive-choice","title":"从三个候选算出一次选择损失","number":1},"sectionTitle":"从三个候选算出一次选择损失","currentQuestion":"视图关系怎样成为学习目标，又会牺牲什么？","sourceSlides":["l3-r2-p10"],"knowledgeBlock":null,"formulas":[],"figure":{"caption":"三候选相似度1、0.5、0经过温度0.5缩放成2、1、0，概率0.665、0.245、0.090，指定正项损失0.408。 查看对应图解状态","labels":["三候选教学算例 · 指定第 1 项为正例","相似度 s","除以温度 τ = 0.5","归一化概率 p","k⁺","1","2","0.665","k₁","0.5","1","0.245","k₂","0","0","0.090","pⱼ = exp(sⱼ / τ) / Σₗ exp(sₗ / τ)","L = −ln p⁺ = 0.408"],"description":"三候选相似度1、0.5、0经过温度0.5缩放成2、1、0，概率0.665、0.245、0.090，指定正项损失0.408。三候选教学算例 · 指定第 1 项为正例相似度 s除以温度 τ = 0.5归一化概率 pk⁺120.665k₁0.510.245k₂000.090pⱼ = exp(sⱼ / τ) / Σₗ exp(sₗ / τ)L = −ln p⁺ = 0.408","evidenceIdentity":"三候选相似度1、0.5、0经过温度0.5缩放成2、1、0，概率0.665、0.245、0.090，指定正项损失0.408。 查看对应图解状态","images":[]},"previousBlock":"b-dbf9f62230b4bdff27af2c34","nextBlock":"b-cfffa6d30c1d18701b711cde","prerequisites":[{"id":"b-901ef17381bd7e373e02cf5c","url":"#b-901ef17381bd7e373e02cf5c","role":"section-title"},{"id":"b-dbf9f62230b4bdff27af2c34","url":"#b-dbf9f62230b4bdff27af2c34","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-cfffa6d30c1d18701b711cde","type":"h2","scope":"narrative","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p10.html#b-cfffa6d30c1d18701b711cde","content":"## 课堂讲述","sha256":"786ce10a6b32a492259a3dccd0a54e61cd41d28a34382fb7b5386c5f03b7ad69","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-view-objective","title":"视图关系怎样成为学习目标，又会牺牲什么？"},"page":{"id":"h-i-contrastive-choice","title":"从三个候选算出一次选择损失","number":1},"sectionTitle":"从三个候选算出一次选择损失","currentQuestion":"视图关系怎样成为学习目标，又会牺牲什么？","sourceSlides":["l3-r2-p10"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-c3db11a480c42febc9a33fe3","nextBlock":"b-0ba7b2d4c162f83220e3d1b5","prerequisites":[{"id":"b-901ef17381bd7e373e02cf5c","url":"#b-901ef17381bd7e373e02cf5c","role":"section-title"},{"id":"b-dbf9f62230b4bdff27af2c34","url":"#b-dbf9f62230b4bdff27af2c34","role":"problem-context"}],"relatedBlocks":[{"id":"b-c3db11a480c42febc9a33fe3","url":"#b-c3db11a480c42febc9a33fe3","relation":"figure-and-explanation"}]},{"id":"b-0ba7b2d4c162f83220e3d1b5","type":"p","scope":"narrative","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p10.html#b-0ba7b2d4c162f83220e3d1b5","content":"现在用三个候选算一次。我们设它们与查询的相似度分别是 1、0.5、0，第一项是正例。经过温度缩放和归一化，模型给正例的概率约为 0.665。训练希望这个指定对应获得更高的相对分数。\n这里的“答案”不是狗或猫，而是：这一组候选里，哪一项与查询对应。负对数损失把这个选择变成可以优化的数值。温度会改变分数差距转换成概率后的尖锐程度，并进一步影响梯度。\n不需要把公式背下来，但要能够指着图回答：谁是查询，谁是正例，谁进入比较，误差从哪里来。这四件事清楚以后，对比学习就不再只是散点图上“拉近一点、推远一点”的动画。","sha256":"239378bd7c486c10c2232e008bb79b63f795b19bee91f16af0f11835140f4d39","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-view-objective","title":"视图关系怎样成为学习目标，又会牺牲什么？"},"page":{"id":"h-i-contrastive-choice","title":"从三个候选算出一次选择损失","number":1},"sectionTitle":"从三个候选算出一次选择损失","currentQuestion":"视图关系怎样成为学习目标，又会牺牲什么？","sourceSlides":["l3-r2-p10"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-cfffa6d30c1d18701b711cde","nextBlock":"b-f23732826278250aca148020","prerequisites":[{"id":"b-cfffa6d30c1d18701b711cde","url":"#b-cfffa6d30c1d18701b711cde","role":"section-title"},{"id":"b-dbf9f62230b4bdff27af2c34","url":"#b-dbf9f62230b4bdff27af2c34","role":"problem-context"}],"relatedBlocks":[{"id":"b-c3db11a480c42febc9a33fe3","url":"#b-c3db11a480c42febc9a33fe3","relation":"figure-and-explanation"}]},{"id":"b-f23732826278250aca148020","type":"h3","scope":"infonce-as-candidate-choice","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p10.html#b-f23732826278250aca148020","content":"### 把对比损失算成一道选择题","sha256":"ff7915af8cf854e49b355f358c36a219a3421ba8f845747a30ff3b21d2168573","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-view-objective","title":"视图关系怎样成为学习目标，又会牺牲什么？"},"page":{"id":"h-i-contrastive-choice","title":"从三个候选算出一次选择损失","number":1},"sectionTitle":"把对比损失算成一道选择题","currentQuestion":"视图关系怎样成为学习目标，又会牺牲什么？","sourceSlides":["l3-r2-p10"],"knowledgeBlock":"infonce-as-candidate-choice","formulas":[],"previousBlock":"b-0ba7b2d4c162f83220e3d1b5","nextBlock":"b-5040613cdb85475c767121f2","prerequisites":[{"id":"b-cfffa6d30c1d18701b711cde","url":"#b-cfffa6d30c1d18701b711cde","role":"section-title"},{"id":"b-dbf9f62230b4bdff27af2c34","url":"#b-dbf9f62230b4bdff27af2c34","role":"problem-context"}],"relatedBlocks":[{"id":"b-c3db11a480c42febc9a33fe3","url":"#b-c3db11a480c42febc9a33fe3","relation":"figure-and-explanation"},{"id":"b-5040613cdb85475c767121f2","url":"#b-5040613cdb85475c767121f2","relation":"same-reasoning"},{"id":"b-44fb6083adfc5d3e3b71d95a","url":"#b-44fb6083adfc5d3e3b71d95a","relation":"same-reasoning"},{"id":"b-60da8e6f827fa4f6a042f397","url":"#b-60da8e6f827fa4f6a042f397","relation":"same-reasoning"}]},{"id":"b-5040613cdb85475c767121f2","type":"p","scope":"infonce-as-candidate-choice","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p10.html#b-5040613cdb85475c767121f2","content":"设查询的三个候选logit为2、1、0，第一项是已知正例。这些是**温度缩放后的分数**，不是三个原始余弦值。softmax分母为 $e^2+e^1+e^0\\approx11.107$，概率约为 $(0.6652,0.2447,0.0900)$，正例损失 $-\\ln0.6652\\approx0.4076$。","sha256":"9c85b2a94e12be025a25906ccd3086fd9e23b04cd418d9dae7558fa656dda707","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-view-objective","title":"视图关系怎样成为学习目标，又会牺牲什么？"},"page":{"id":"h-i-contrastive-choice","title":"从三个候选算出一次选择损失","number":1},"sectionTitle":"把对比损失算成一道选择题","currentQuestion":"视图关系怎样成为学习目标，又会牺牲什么？","sourceSlides":["l3-r2-p10"],"knowledgeBlock":"infonce-as-candidate-choice","formulas":[{"latex":"e^2+e^1+e^0\\approx11.107","definitionContext":"设查询的三个候选logit为2、1、0，第一项是已知正例。这些是**温度缩放后的分数**，不是三个原始余弦值。softmax分母为 $e^2+e^1+e^0\\approx11.107$，概率约为 $(0.6652,0.2447,0.0900)$，正例损失 $-\\ln0.6652\\approx0.4076$。\n一般式为 $L=-\\log\\{\\exp(s_+/\\tau)/\\sum_j\\exp(s_j/\\tau)\\}$，分母包含正例。提高正例相对分数会降低损失；把所有分数同时加一个常数不会改变概率，所以目标关注相对选择而非绝对分数大。\n实际训练中分数由图像经编码器算出，损失反传到参数。手算这一行只解释目标，不是模型实验。接到LAB 07时，应沿真实图像→两视图→向量→logit→loss→参数变化逐项找到对应对象。"},{"latex":"(0.6652,0.2447,0.0900)","definitionContext":"设查询的三个候选logit为2、1、0，第一项是已知正例。这些是**温度缩放后的分数**，不是三个原始余弦值。softmax分母为 $e^2+e^1+e^0\\approx11.107$，概率约为 $(0.6652,0.2447,0.0900)$，正例损失 $-\\ln0.6652\\approx0.4076$。\n一般式为 $L=-\\log\\{\\exp(s_+/\\tau)/\\sum_j\\exp(s_j/\\tau)\\}$，分母包含正例。提高正例相对分数会降低损失；把所有分数同时加一个常数不会改变概率，所以目标关注相对选择而非绝对分数大。\n实际训练中分数由图像经编码器算出，损失反传到参数。手算这一行只解释目标，不是模型实验。接到LAB 07时，应沿真实图像→两视图→向量→logit→loss→参数变化逐项找到对应对象。"},{"latex":"-\\ln0.6652\\approx0.4076","definitionContext":"设查询的三个候选logit为2、1、0，第一项是已知正例。这些是**温度缩放后的分数**，不是三个原始余弦值。softmax分母为 $e^2+e^1+e^0\\approx11.107$，概率约为 $(0.6652,0.2447,0.0900)$，正例损失 $-\\ln0.6652\\approx0.4076$。\n一般式为 $L=-\\log\\{\\exp(s_+/\\tau)/\\sum_j\\exp(s_j/\\tau)\\}$，分母包含正例。提高正例相对分数会降低损失；把所有分数同时加一个常数不会改变概率，所以目标关注相对选择而非绝对分数大。\n实际训练中分数由图像经编码器算出，损失反传到参数。手算这一行只解释目标，不是模型实验。接到LAB 07时，应沿真实图像→两视图→向量→logit→loss→参数变化逐项找到对应对象。"}],"previousBlock":"b-f23732826278250aca148020","nextBlock":"b-44fb6083adfc5d3e3b71d95a","prerequisites":[{"id":"b-f23732826278250aca148020","url":"#b-f23732826278250aca148020","role":"section-title"},{"id":"b-dbf9f62230b4bdff27af2c34","url":"#b-dbf9f62230b4bdff27af2c34","role":"problem-context"}],"relatedBlocks":[{"id":"b-c3db11a480c42febc9a33fe3","url":"#b-c3db11a480c42febc9a33fe3","relation":"figure-and-explanation"},{"id":"b-f23732826278250aca148020","url":"#b-f23732826278250aca148020","relation":"same-reasoning"},{"id":"b-44fb6083adfc5d3e3b71d95a","url":"#b-44fb6083adfc5d3e3b71d95a","relation":"same-reasoning"},{"id":"b-60da8e6f827fa4f6a042f397","url":"#b-60da8e6f827fa4f6a042f397","relation":"same-reasoning"}]},{"id":"b-44fb6083adfc5d3e3b71d95a","type":"p","scope":"infonce-as-candidate-choice","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p10.html#b-44fb6083adfc5d3e3b71d95a","content":"一般式为 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图示条件与公式约定","sha256":"ef7f915c1ae63ed67bd23fecf050249273ba0efa8965d2c8d1c1c6b2d3178122","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-view-objective","title":"视图关系怎样成为学习目标，又会牺牲什么？"},"page":{"id":"h-i-contrastive-choice","title":"从三个候选算出一次选择损失","number":1},"sectionTitle":"从三个候选算出一次选择损失","currentQuestion":"视图关系怎样成为学习目标，又会牺牲什么？","sourceSlides":["l3-r2-p10"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-60da8e6f827fa4f6a042f397","nextBlock":"b-53300e421b0b4b117e246bc7","prerequisites":[{"id":"b-f23732826278250aca148020","url":"#b-f23732826278250aca148020","role":"section-title"},{"id":"b-dbf9f62230b4bdff27af2c34","url":"#b-dbf9f62230b4bdff27af2c34","role":"problem-context"}],"relatedBlocks":[{"id":"b-c3db11a480c42febc9a33fe3","url":"#b-c3db11a480c42febc9a33fe3","relation":"figure-and-explanation"}]},{"id":"b-53300e421b0b4b117e246bc7","type":"p","scope":"document","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p10.html#b-53300e421b0b4b117e246bc7","content":"教学设定 s=[1,.5,0]，τ=.5，logits=[2,1,0]；p=[.6652409558,.2447284711,.0900305732]；−ln 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