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已经展示了以图像为条件生成文字。接下来把问题推进到更多输出：训练怎样学习条件下的多种可能，使用时怎样产生其中一个样本？第四讲将比较生成路线；本讲的多解算例提供共同起点。","sha256":"bb88024bd9a3dd691ade320d1d149d5dca6435e4185f6b62d23f1050f66df517","chapter":{"id":"III","title":"视觉与语言"},"unit":{"id":"generation-many-possible-results","title":"一个条件怎样容纳多种合理结果？"},"page":{"id":"generation-mean-versus-sample","title":"算出最优平均值，再检查它是不是可能样本","number":1},"sectionTitle":"算出最优平均值，再检查它是不是可能样本","currentQuestion":"条件均值、合理样本与生成过程为什么是不同目标？","sourceSlides":["l3-r2-p67","l3-r2-p68"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-e4a40b9c2e16ff4169eda5f9","nextBlock":"b-bb605cd222d7a3aafc0fc567","prerequisites":[{"id":"b-e4a40b9c2e16ff4169eda5f9","url":"#b-e4a40b9c2e16ff4169eda5f9","role":"section-title"}],"relatedBlocks":[{"id":"b-bb605cd222d7a3aafc0fc567","url":"#b-bb605cd222d7a3aafc0fc567","relation":"figure-and-explanation"}]},{"id":"b-bb605cd222d7a3aafc0fc567","type":"figure","scope":"document","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p68.html#b-bb605cd222d7a3aafc0fc567","content":"图内标签与数值：同一条件，可以有多种合理结果；学习可能性；产生一个样本；x ∼ pθ(x | c)；第四讲的比较入口；GAN；VAE；Diffusion；自回归；图像　·　文字　·　视频　·　3D；逼真，是否意味着理解了规律？\n\n同条件的三幅红杯图，连接学习可能性和产生样本两个问题；下方只列第四讲四类方法入口。\n\n- 同一条件，可以有多种合理结果\n- 学习可能性\n- 产生一个样本\n- x ∼ pθ(x | c)\n- 第四讲的比较入口\n- GAN\n- VAE\n- Diffusion\n- 自回归\n- 图像 · 文字 · 视频 · 3D\n- 逼真，是否意味着理解了规律？同条件的三幅红杯图，连接学习可能性和产生样本两个问题；下方只列第四讲四类方法入口。 [查看对应图解状态](/#/l3-r2-p68/0)[查看完整图解](/course/figures/l3-r2-p68-0.html)","sha256":"7b2603dfb745ff05400739d2b76d33ce2e307e203295e10d07a92bdfdf89b24e","chapter":{"id":"III","title":"视觉与语言"},"unit":{"id":"generation-many-possible-results","title":"一个条件怎样容纳多种合理结果？"},"page":{"id":"generation-mean-versus-sample","title":"算出最优平均值，再检查它是不是可能样本","number":1},"sectionTitle":"算出最优平均值，再检查它是不是可能样本","currentQuestion":"条件均值、合理样本与生成过程为什么是不同目标？","sourceSlides":["l3-r2-p67","l3-r2-p68"],"knowledgeBlock":null,"formulas":[],"figure":{"caption":"同条件的三幅红杯图，连接学习可能性和产生样本两个问题；下方只列第四讲四类方法入口。 查看对应图解状态","labels":["同一条件，可以有多种合理结果","学习可能性","产生一个样本","x ∼ pθ(x | 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查看对应图解状态","images":[{"src":"/assets/display/9a66faeae8dd2c354bc56482.webp","alt":""},{"src":"/assets/display/2e37eb55c23251072aa0d535.webp","alt":""},{"src":"/assets/display/6a8758227350d5d202325c45.webp","alt":""}]},"previousBlock":"b-7e7cafabad86cfaa09b21138","nextBlock":"b-c165c53268ec67c0f74503f6","prerequisites":[{"id":"b-e4a40b9c2e16ff4169eda5f9","url":"#b-e4a40b9c2e16ff4169eda5f9","role":"section-title"},{"id":"b-7e7cafabad86cfaa09b21138","url":"#b-7e7cafabad86cfaa09b21138","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-c165c53268ec67c0f74503f6","type":"h2","scope":"narrative","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p68.html#b-c165c53268ec67c0f74503f6","content":"## 课堂讲述","sha256":"786ce10a6b32a492259a3dccd0a54e61cd41d28a34382fb7b5386c5f03b7ad69","chapter":{"id":"III","title":"视觉与语言"},"unit":{"id":"generation-many-possible-results","title":"一个条件怎样容纳多种合理结果？"},"page":{"id":"generation-mean-versus-sample","title":"算出最优平均值，再检查它是不是可能样本","number":1},"sectionTitle":"算出最优平均值，再检查它是不是可能样本","currentQuestion":"条件均值、合理样本与生成过程为什么是不同目标？","sourceSlides":["l3-r2-p67","l3-r2-p68"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-bb605cd222d7a3aafc0fc567","nextBlock":"b-c7d6211731094e96b78281ae","prerequisites":[{"id":"b-e4a40b9c2e16ff4169eda5f9","url":"#b-e4a40b9c2e16ff4169eda5f9","role":"section-title"},{"id":"b-7e7cafabad86cfaa09b21138","url":"#b-7e7cafabad86cfaa09b21138","role":"problem-context"}],"relatedBlocks":[{"id":"b-bb605cd222d7a3aafc0fc567","url":"#b-bb605cd222d7a3aafc0fc567","relation":"figure-and-explanation"}]},{"id":"b-c7d6211731094e96b78281ae","type":"p","scope":"narrative","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p68.html#b-c7d6211731094e96b78281ae","content":"第四讲会比较 GAN、VAE、Diffusion 等路线，也会把已经见过的自回归生成放进同一张问题图。它们不是严格的前后替代史，关键是训练信号、表示方式和产生样本的过程各有什么不同。\n图像、文字、视频和三维数据又提出不同要求：文字有离散单位，视频要处理时间关系，三维还要考虑空间和多视角的一致性。这些会在生成问题中逐步进入，不在今天再开启四个专题。Transformer 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一个可算的多解例子：最小均方误差为何给出不存在的结果","sha256":"eba5c775920285641f715d644da1e68aa3801bae7a362a232c4661fe7a917071","chapter":{"id":"III","title":"视觉与语言"},"unit":{"id":"generation-many-possible-results","title":"一个条件怎样容纳多种合理结果？"},"page":{"id":"generation-mean-versus-sample","title":"算出最优平均值，再检查它是不是可能样本","number":1},"sectionTitle":"一个可算的多解例子：最小均方误差为何给出不存在的结果","currentQuestion":"条件均值、合理样本与生成过程为什么是不同目标？","sourceSlides":["l3-r2-p67","l3-r2-p68"],"knowledgeBlock":"conditional-mean-is-not-sample","formulas":[],"previousBlock":"b-c7d6211731094e96b78281ae","nextBlock":"b-7b95e6194298f996c03ce289","prerequisites":[{"id":"b-c165c53268ec67c0f74503f6","url":"#b-c165c53268ec67c0f74503f6","role":"section-title"},{"id":"b-7e7cafabad86cfaa09b21138","url":"#b-7e7cafabad86cfaa09b21138","role":"problem-context"}],"relatedBlocks":[{"id":"b-bb605cd222d7a3aafc0fc567","url":"#b-bb605cd222d7a3aafc0fc567","relation":"figure-and-explanation"},{"id":"b-7b95e6194298f996c03ce289","url":"#b-7b95e6194298f996c03ce289","relation":"same-reasoning"},{"id":"b-66e82751f4aa6cbcd4d995d6","url":"#b-66e82751f4aa6cbcd4d995d6","relation":"same-reasoning"},{"id":"b-61aced1e0be6e98242b14813","url":"#b-61aced1e0be6e98242b14813","relation":"same-reasoning"},{"id":"b-98e2ca2b5398e674587110c5","url":"#b-98e2ca2b5398e674587110c5","relation":"same-reasoning"},{"id":"b-b42f01a2ca36c674fb393a8b","url":"#b-b42f01a2ca36c674fb393a8b","relation":"same-reasoning"}]},{"id":"b-7b95e6194298f996c03ce289","type":"p","scope":"conditional-mean-is-not-sample","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p68.html#b-7b95e6194298f996c03ce289","content":"给定同一条件 $c$，真实结果 $X$ 等概率取 $-1$ 或 $+1$。若模型只能给一个确定数 $a$，并最小化平均平方误差，","sha256":"929af997fc6bdbbd04b73346162aeb9058b628b892a26dfe166ebc101a2b4eb9","chapter":{"id":"III","title":"视觉与语言"},"unit":{"id":"generation-many-possible-results","title":"一个条件怎样容纳多种合理结果？"},"page":{"id":"generation-mean-versus-sample","title":"算出最优平均值，再检查它是不是可能样本","number":1},"sectionTitle":"一个可算的多解例子：最小均方误差为何给出不存在的结果","currentQuestion":"条件均值、合理样本与生成过程为什么是不同目标？","sourceSlides":["l3-r2-p67","l3-r2-p68"],"knowledgeBlock":"conditional-mean-is-not-sample","formulas":[{"latex":"c","definitionContext":"给定同一条件 $c$，真实结果 $X$ 等概率取 $-1$ 或 $+1$。若模型只能给一个确定数 $a$，并最小化平均平方误差，\n$\\mathbb E[(X-a)^2\\mid c]=\\tfrac12(-1-a)^2+\\tfrac12(1-a)^2=1+a^2.$\n最优值是 $a=0$，误差为 1；但真实分布从不产生 0。模型给出了最好的条件均值，却没有给出一个真实可能样本。对应图像的直观例子是杯子可能在左或右，逐像素平均可能出现模糊或重影，而不是某一次合理摆放。\n再设生成器正确地随机输出 $-1$ 或 $+1$，与一份独立抽出的真值比较，二者一半相同、一半差 2，期望平方误差是 $0.5\\times0+0.5\\times4=2$。生成器符合真实分布，却在这种独立配对 MSE 上比输出 0 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