[{"data":1,"prerenderedAt":5711},["ShallowReactive",2],{"post-\u002Fblog\u002F2026\u002F2026-08-14-demystification-research":3,"i-boxicons:location":5703,"i-mingcute:time-line":5707,"i-ci:tag":5709},{"post":4,"nextPost":287,"prevPost":5539},{"id":5,"title":6,"body":7,"description":13,"draft":273,"enableComment":274,"extension":275,"image":264,"important":273,"location":276,"meta":277,"navigation":274,"ogImage":278,"path":279,"seo":280,"stem":281,"summary":282,"tags":283,"time":285,"__hash__":286},"blog\u002Fblog\u002F2026\u002F2026-08-14-demystification-research.md","祛魅科研，每个研究生的必修课",{"type":8,"value":9,"toc":263},"minimark",[10,14,17,21,24,27,30,41,44,47,50,53,56,59,62,65,68,71,75,78,81,84,91,99,102,105,108,111,114,120,123,126,129,132,137,140,143,146,149,155,158,161,168,171,174,177,180,183,186,192,195,198,201,204,207,210,213,216,219,226,230,237,242,245,248,251,254,257,260],[11,12,13],"p",{},"从 2025 年开始入学读研，到现在已经有一个年头了，不知不觉已经研二了。在过去的一年的研究生学习中，我发现我的心态、世界观经历了一次完整的、打击性的重塑。如果说之前我的心态是中规中矩，那么现在则是满心失落。自从经历过完整的科研训练，调研课题、找 idea，做实验、处理数据、撰写论文、修改文章、等投稿、写 Rebuttal、拒稿再转投、论文改版等一系列流程完整经历过后，只剩下满心苦涩。一度怀疑，我们搞的这个所谓的「科研」的价值和意义。😇",[11,15,16],{},"因为笔者读的研究生是计算机工程类专业，对于其他理工科领域、文科领域，笔者不是很熟悉，所以以下观点体验仅适用于该专业。",[18,19,20],"h2",{"id":20},"草台班子",[11,22,23],{},"第一个对我的改变就是对学术成果的怀疑。学术圈的科研，其实并没有那么高端，可以说是草台班子。",[11,25,26],{},"在读研之前，我一直认为学术论文其实是非常高端的东西，至少是可信度很高的参考。但是读研之后，这个想法被改变了：绝大多数论文，他们的观点、数据、实验，看看就好，不必认真。",[11,28,29],{},"一篇论文的结论，往往只有作者自己的机器上成立。审稿人不会复现，编辑不会复现，引用者也不会复现。大家都默认了这个不可验证的游戏潜规则。论文并不是经过验证的知识，而是一个经过美化的故事。",[11,31,32,33,40],{},"有人专门对被 ICML 收录的 Oral 论文进行了复现，并给出了",[34,35,39],"a",{"href":36,"rel":37},"https:\u002F\u002Fx.com\u002FChenhaoTan\u002Fstatus\u002F2079969545629118737",[38],"nofollow","论文的报告信息","。结果发现，在 105 篇完整的复现论文中，只有 27 篇复现了超过 40% 的声称效果，剩余的几乎无法复现，要么效果不达标。原因包括代码无法运行、文件缺失以及模型已弃用等等。",[11,42,43],{},"复现困难确实是机器学习领域长期存在的问题。因为，CUDA 版本、显卡型号、CPU 型号、PyTorch 框架版本，可能都有大量隐蔽的细节差异，如果再组合起来，那么效果就完全无法验证。实验中的很多关键 Hack（比如特定的随机种子、数据预处理的微妙顺序、超参数的精细调节）可能只存在于作者的实验笔记或潜意识里。这些隐性经验很难通过文字传递，导致复现者像在黑暗中摸索。",[11,45,46],{},"甚至如果作者的代码里有 Bug，也很可能会造成完全错误的结论。我曾经跑过前人的基线实验，发现一篇论文，他的某个指标又非常虚高。最后才发现，作者对数据集根本没有清洗干净，也就是说，这份成绩是假的。",[11,48,49],{},"但问题是，这个论文已经被大量后人引用且作为基线了，后人想要再投稿，那么他的成绩必须要比这个假成绩更高，但是你根本比不过这假成绩，怎么办呢？你只能偷偷摸摸用点魔法手段，万不可认真，否则反而会显得像是你做错了，审稿人不接受。后来的研究者反而成了受害者。这不就是难为后人么？",[11,51,52],{},"所以，后人也只能不得不逼着也参与这种数字游戏，偷偷使用手段。结果就是，学术论文逐渐沦为一场“数字通胀”。每一篇新论文都在前人的数字泡沫上再吹一层泡沫，直到某个数据集上的准确率达到 99.9%，然后这个方向就“死掉”了——因为没人能再超越了，而大家都知道那个 99.9% 是假的，但谁都不想捅破。",[11,54,55],{},"这已经超出了学术不端的范畴，演变成了一种系统性的「囚徒困境」，很遗憾，这种困境，在学术圈里几乎无解。",[11,57,58],{},"无法复现不一定是作者故意有造假意向，而是因为深度学习本身就是一个巨大的黑盒，可验证性、可解释性非常差。很多错误，作者不一定能及时发现，审稿人也不一定能发现，于是，“只要能 work 就能发文”。当审稿人面对一篇充满“惊艳”实验数据的论文时，他既没有算力去复现，也没有理论工具去证伪其内部的混沌过程。于是，审稿的标准退化为：“只要故事逻辑自洽，且结果看起来比 SOTA（当前最优）高，我就信。”这就给出了巨大的浑水摸鱼的空间。",[11,60,61],{},"这种无法复现的现象，也会给自己带来很多的麻烦：如果你的文章需要依赖前人的工作，但是前人的工作本身就有问题，那么你的工作就几乎不可能顺利下去。你只能花大把时间来反思、调试，最后还很可能一无所获。",[11,63,64],{},"最后被浪费大把的时间和精力。这种消耗是精神凌迟。后续工作往往不得不替它买单。",[11,66,67],{},"有时候，我也甚至怀疑作者是故意在开源里缺斤少两，删减关键代码和文件或者埋入 Bug，或者论文被 Accept 后立即下架数据集，极力避免复现。😇要知道，审稿人通常只有 2-3 位，他们在几周内免费审稿，不可能复现你的实验，也无法验证你的原始数据。他们主要检查的是逻辑是否顺畅和方法是否看起来合理，而不是结论是否绝对正确。",[11,69,70],{},"学术论文它的首要目标是发表，而不是传世。为了发表，作者必须讲一个完整且自洽的故事。他们会突出最漂亮的数据，而弱化不支持的“噪音”结果。所以，他们会在讨论部分夹带私货，把故事讲得更有吸引力。它也确实是痛苦的。因为这意味着你失去了一个可以无条件信任的知识权威。",[18,72,74],{"id":73},"ai-审稿危机","AI 审稿危机",[11,76,77],{},"读研起到现在，我已经投稿了三篇文章，这点我是有亲身体会的。",[11,79,80],{},"另一种尴尬是 AI 时代的审稿危机。AI 时代的恶果就是，论文灌水越来越容易。往常，写一篇论文很可能需要一学期、大半年的时间，要辛辛苦苦做实验、分析结果、画图表、斟酌写作。但是现在不一样了，利用自动化学术 Agent 如 AutoResearch，只要输入合适的提示词和模糊的想法再交给 Agent，它两天时间就可以编出一篇像模像样的论文，自动编写程序做实验，自动画图表，一个人一个月就能编写出 10 篇论文，直接投到顶会轰炸。",[11,82,83],{},"AAAI 在 2026 年收到了五万多份取号，几乎是 2025 年的两倍。而前年 2024 年才不过九千多份，短短两年时间就增长了五倍！其实不止 AAAI，其他的计算机会议的投稿量也是几乎翻倍增长。假设每篇论文标准配备 3 名审稿人，组委会将需要管理 120,000 份独立审稿意见：",[11,85,86],{},[87,88],"img",{"alt":89,"src":90},"计算机顶会近五年投稿量。自从 2025 年后，大多数投稿量都是翻倍式增长","https:\u002F\u002Fimage-assets.dreams.plus\u002F202608111219721.jpg",[11,92,93,94,98],{},"这就会导致一个后果：劣币驱逐良币。审稿体系正在加速崩溃。就算你辛辛苦苦完成了心血，设计实验，写好文章，",[95,96,97],"strong",{},"审稿人也几乎不会认真看你的文章，而是直接交给 LLM 敷衍。"," 因为审稿人压根无法区分哪篇论文是 AI 写得，哪篇不是。更糟糕的是，学术领域是高度分化的，审稿人极有可能也不熟悉、也不理解你的研究领域。所以，他也只能同样一股脑交给 AI 审稿。",[11,100,101],{},"在这种情况下，灌水零成本，中间大量灌水的作者和敷衍的审稿人占多数。认真的审稿人和认真的作者只能被动深受其害。受害的永远只是认真搞学术的你。在这种情况下，审稿工作还能正常进行下去吗？",[11,103,104],{},"而 LLM 审稿本身就有很大的问题，AI 并不会理解你的文章，LLM 的幻觉问题众所周知。它会用非常刁钻的角度在你的文章里挑刺，哪怕是没有问题也会制造出一些问题。这是因为 LLM 在训练、SFT 偏好微调的时候，天生就倾向于给你打低分。LLM 并不真正拥有论文作者的研究上下文。它尤其容易犯一种很危险的错误：把“我没理解”转换成“作者的方法存在问题”。",[11,106,107],{},"LLM 模型学习到的统计规律是：“审稿”这个动作的语义空间，几乎完全由“批评性词汇”构成。因此，即使一篇论文毫无瑕疵，模型根据概率分布生成的“审稿风格”文本，天然就带有负面倾向。SFT 微调的时候，宽松的论文意见并不受欢迎，为了要尽可能压榨 LLM 能力，在微调的时候会特意设计出非常严苛的训练案例。这种奖惩机制直接塑造了模型的“人格”：它必须“生产批评”来证明自己的价值。哪怕没有真实缺陷，它也会启动“防御性挑刺”模式，利用模式匹配强行构造出看似合理的问题。",[11,109,110],{},"我的文章被拒稿过一次，三个 Reviewer 里两人给出的意见，明显就是 AI 复制粘贴的。😅 但是你不能抗议，你还要捏着鼻子忍着恶心，在 rebuttal 里面假模假样地感谢审稿人，再假模假样地写 rebuttal，跪求他赏赐一口饭吃。😅",[11,112,113],{},"审稿体系存在一个非常明显的权力不对称。Reviewer 可以随意评价“The novelty is insufficient.”而作者很难说：“你根本没读懂我的论文。”因为作者没有证据。另外，Reviewer 可以洋洋洒洒写出几千字的审稿意见，没有字数限制，而作者给的 Rebuttal 却严格限制在几百字以内。这也是最恶心的一点😅",[11,115,116],{},[87,117],{"alt":118,"src":119},"如图，是几个 LLM 在审稿 ArXiv 计算机学科论文时给出的平均得分（10 分制）","https:\u002F\u002Fimage-assets.dreams.plus\u002F202608111210591.png",[11,121,122],{},"试过把 21-23 年，GPT 出来以前的三大顶会里，已经发表收录的论文随机爬下来，投给 AI 审，50 篇里 30 多个 weak reject，10 多个 weak accept，剩下的全部都是 reject。一篇 accept 都没有。后 AI 时代所谓的顶会论文已经变成笑话哩。",[11,124,125],{},"审稿人因为反驳文太长而疲惫，作者因为审稿人固执而绝望。当作者知道审稿人是 AI，审稿人知道作者用了 AI 时，作者 - 审稿人 - 编辑三方之间的这场学术对话，就彻底沦为了一场荒诞剧。这就造成了非常滑稽的景象，AI 写 AI 审：",[11,127,128],{},"用 AI 写论文、写代码，再用 AI 初审，根据 AI 的意见修改，完成初稿。审稿人拿到初稿，再交给 AI 审稿，用 AI 的意见给出 review 意见，作者拿到 AI 写的意见后再交给 AI 写 rebuttal。审稿人再用 AI 根据 rebuttal 做出决定。堪称学术出版领域正在逼近的赛博朋克式奇观。",[11,130,131],{},"在三方中，编辑\u002F主席的地位最为尴尬。当所有文字意见如审稿、反驳都由 AI 生成时，编辑失去了判断学术创新性的任何抓手。他唯一能做的，就是检查流程是否走完：AI 是否提了 3 个问题？作者是否逐条回复？回复长度是否达标？只要格式合规，就可以按下接受键。学术判断的权力，在此刻已完全让渡给了硅基算法。",[11,133,134],{},[95,135,136],{},"所以，能否发顶会、顶刊，实际上已经越来越像摸彩票中奖的运气、概率问题，跟你的文章质量、工作效果已经几乎没有什么关系了。",[18,138,139],{"id":139},"手艺人",[11,141,142],{},"硕博生这个身份曾经是不少人引以为傲的根本。但是真正体验过他们的生活，也会发现他们本质上和流水线的螺丝工人相差无几，这种生活状态其实是非常压抑的，如果过这种日子，那只能用「熬」来形容。",[11,144,145],{},"硕博生本质上也是出卖高强度脑力劳动换取生存资格的劳动者。跟工地上抗水泥的农民工、顶着大太阳湿透衣服的清洁工没有本质区别。",[11,147,148],{},"对于理工科研究生，996 是常态，实验室的灯永远亮着。每天睁眼闭眼就是要面对屏幕上密密麻麻的实验数据、代码和仪器。高强度脑力劳动后，带给身心的除了疲劳还是疲劳。日子久了，精气神会被消磨掉，慢慢丧失对这个世界的好奇心和一切欲望，不想谈恋爱，不想出去旅游，哪怕是手里的游戏，日子久了玩起来也没意思。",[150,151,152],"blockquote",{},[11,153,154],{},"到周末后，只想在床上躺着，啥也不干。脑一旦被单一的高强度任务长期占据，负责发散思维、感受情绪、产生欲望的脑区就会被持续抑制。只像一个漂浮在数据海洋里的意识，拖着一具沉重而麻木的肉体，犹如冢中枯骨而已。",[11,156,157],{},"这是最致命的。当你看清你所做的研究可能只是学术游戏里的一个废棋，对外部世界毫无影响时，熬就变成了一种精神上的凌迟。不禁会问，「我做的这一切，受了那么多折磨，到底有什么意义？」",[11,159,160],{},"工人进厂时，起码能自知之明、清醒地知道这是出卖身体，用劳动换生存。但硕博生被社会、被家人、被曾经的自己赋予了天子骄子、知识精英的光环。当现实变成日复一日地跑数据、伺候仪器时，日子久了你会有这样一种感觉：自己并不是一个人，而是一个庞大机器中的一颗零件。",[11,162,163,164,167],{},"硕士生（Master）也不是大师。博士生也不博学。他的知识广度，甚至还可能不如一个高中生。",[95,165,166],{},"读研后，你的视角只会被限制在高度狭窄且专业的小领域里。"," 在自己的学术孤岛里自娱自乐。",[11,169,170],{},"中世纪的经院哲学家热衷于争论「一个针尖上能站几个天使」，而今天的学术圈，大量精力被消耗在维护主流范式上。正如前文所提到的，学术论文本身也是高度固定化的、范式的。有时候你不会感觉自己「在创造一个想法」，而是「完成一个八股文」。",[11,172,173],{},"如果要比喻硕博生这个群体的身份，它更像是一个高度程序化的手艺人、螺丝工。搞科研的流程本身就是高度固定化、流水线化的。调研、idea、实验、写作、改稿、Rebuttal。这一圈下来，恭喜你，你已经是一名合格的劳工！",[18,175,176],{"id":176},"学术圈",[11,178,179],{},"曾经对学术圈的浪漫想象，至少代表了知识的前沿、先进的生产力和思想文化，具有进步性。我其实对科研领域内的学者，高校里的教授、教师等群体，长期是存在敬仰的，认为他们或多或少都是代表了人类开拓认知知识、征服星辰大海的一批人，在心里也会敬三分。",[11,181,182],{},"现在才知道，学术圈其实是高度封闭的。因为知识本身就有很强的入门壁垒，当人类认知突破到一定边界时，工具、术语和范式的复杂度必然形成门槛，学术方向往往会走向高度分化、隔行如隔山的细碎分支，各个分支又会高度壁垒。这就造成了学术圈的高度封闭性。",[11,184,185],{},"其实，越是高度封闭的圈子，越容易产生高度固化的权力结构，行事作风越是封建化、越是讲政治。😅其实现在的学术圈其实跟欧洲中世纪的经学院教派之争、西藏喇嘛们的辩经并没有什么区别。那些专家，领域学者，头衔看得是挺唬人，但做的无非在极度封闭的圈子里，用只有内部人能懂的黑话，争论着对外部世界影响甚微的问题，而决定胜负的常常不是真理，而是资历、人脉和对经典的诠释权。",[11,187,188,191],{},[95,189,190],{},"学术圈，其实比大多数人想象的还要小。"," 因为现代学科已经进入高度分化、高度专业化的时代了。如果细分下去，全中国十四亿人里，同一个领域的研究同行很可能不超过百人，甚至十几人。在一个村落里，任何小动作，全落在这几十个低头不见抬头见的人手里。这里没法对事不对人，因为在结构上，所有的事，最终都是人的事。",[11,193,194],{},"然而，现在的学术圈是零和博弈，资源是极其有限的。这个在申请基金、文章版面、学术交流等等活动中，只要有人胜出，必然会有人落选。这也就意味着，你的小圈子里，可能到处都在「树敌」。这并不意味着本人有错，而是你的存在，本身就是威胁。",[11,196,197],{},"所以遇到同行暗中使绊子，也是常见的事。你的审稿人很可能跟你的导师有竞争或者过节，就直接轻松 Reject 你的心血。即使现在的审稿制度大多是双盲制，在一个领域只有几十上百人的圈子里，根本不存在真正的双向匿名。看研究问题、看方法、看引用的文献，审稿人闭着眼都能猜到这篇稿子出自哪个课题组。",[11,199,200],{},"对一个埋头苦干的学生来说，这是最深的打击。你相信公正，相信学术质量至上。然后，一堵由学派、人情、资源争夺构成的墙，悄无声息地挡在你面前，将你的心血轻松驳回。你甚至没有一个明确的敌人去质问抗争，你甚至不知道你的敌人是谁，又得罪了谁，只剩下无尽的无力感和被戏弄的愤怒。这种被暗算的体验会深刻腐蚀对学术共同体的信任。",[11,202,203],{},"像中世纪的领主分封土地一样，大牛导师和顶尖实验室把持着顶级期刊的版面、重大项目的经费和学阀圈子的话语权。你想在他的领地上发文章，就得遵循他的范式、引他的文章、甚至拜他的码头。学术圈的游戏规则是，正确不等于接受。投稿像一场赌博，审稿人的口味、当期版面、甚至运气，都比你那篇精心打磨的论文权重更高。",[18,205,206],{"id":206},"事业意义",[11,208,209],{},"虽然小时候有「长大要当科学家」这种理想，但是，个人认为「学术」这条路并不适合像我这样的平民子弟。没有充裕的家底和财力作为后盾，吃学术这碗饭，也是一种高风险职业。",[11,211,212],{},"我觉得那些在学术圈里搞研究的人，其实也挺可悲的。自己把大量的青春，时间，精力投入到自己的课题里，勉强能讨得经费，靠这个饭碗。因为，选择某个研究领域，在初期往往带有偶然性。但一旦投入，就成了无法回头的豪赌。赌的是这个方向在几十年内不被证伪、不被超越、不被认为是死胡同、不会没落。他用的是几十年的青春和精力做赌注，用最严谨的头脑，从事着一项本质上充满不确定性的高风险事业。",[11,214,215],{},"如果有人突然跳出来用新理论、新范式挑战他，或者推翻了他的观点课题，这无异于把他降维打击成了一块废品，弃之如敝履，这不是嘲讽，而是真实的悲剧。在高度职业化的学术圈里，一个人的身份、地位、自尊，都深深扎根于他那一亩三分地的研究课题。",[11,217,218],{},"当他的理论被推翻，在外人看来不过是一个观点被证伪。但对他而言，无异于整个学术人格被判处了死刑，在这个圈子里，会被迅速边缘化，从而判了死刑。他毕生构建的意义大厦，瞬间崩塌为一座废墟。这就是一种存在主义危机。",[11,220,221,222,225],{},"大多数普通人活下去本身就很难。因为 ",[95,223,224],{},"他们的人生，还有其他责任"," 。若压制住七情六欲，寒窗几十年，去碰学术圈，也未免太委屈了。如果一个人 25 岁读博士，30 岁左右博士毕业，然后经历博士后、非升即走、青年项目竞争，他可能在四十岁前都处于高度竞争状态。而同期进入工业界的人，可能已经积累了财富、住房和职业资本。",[18,227,229],{"id":228},"破局功利化读研","破局：功利化读研",[11,231,232,233,236],{},"在中国，虽然知识分子往往被冠以社会期待的光环，但是这也是一种负担和枷锁。请记住：我们是普通人尤其是出身平民家庭，我们首要目标是生存。在生存生计成为问题的时候，我们 ",[95,234,235],{},"没有义务背负太多期待","。",[150,238,239],{},[11,240,241],{},"沧浪之水清兮，可以濯吾缨；沧浪之水浊兮，可以濯吾足。",[11,243,244],{},"请卸下你的「学术羞耻感」。把研究生学历视为一份职业准入资格证，而非学术朝圣。学术职业是一种高风险选择，而不是所有人都必须承担的使命。",[11,246,247],{},"如何破局——功利化读研不失为一种出路。研究生必须思考：我读研的目的是为了什么？获得更好的就业门槛，暂时避开竞争激烈的就业市场，获得更多选择权。这完全是一种合理的人生规划。",[11,249,250],{},"首要的当然是毕业、混文凭，获得硕博的身份————这也是最现实、也最重要的一条。所以，在读研前期，你的一切目标是，必须以尽可能短的时间，完成最低毕业要求。大量水论文、蹭项目就足矣，不需要尽善尽美。科研嘛，也就那样，随便搞搞就行。",[11,252,253],{},"这是功利化读研真正的溢价所在。既然科研只求及格，那你必须把多出来的精力毫无愧疚地投入生存技能的构建。",[11,255,256],{},"在当前的环境下，「包装」比「做事」更重要，「数量」比「质量」更重要。不要把自己的全部人生价值绑定在学术成果上。科研如此，创业如此，艺术如此，很多长期主义事业都是如此。我不需要证明自己是英雄，我只需要把自己的人生过好。知识值得敬畏，但人的生命也值得敬畏。学术可以是人生的一部分，但不必成为人生的全部。",[11,258,259],{},"希望研究生们，不必神化科研、不必自我内耗、不必绑定学术理想，认清行业真相后，依然可以清醒活着、务实成长。",[11,261,262],{},"到最后，这种「虽千万人，吾往矣」，本身就有壮士断腕的秋风式悲凉，不是吗？😮‍💨",{"title":264,"searchDepth":265,"depth":265,"links":266},"",2,[267,268,269,270,271,272],{"id":20,"depth":265,"text":20},{"id":73,"depth":265,"text":74},{"id":139,"depth":265,"text":139},{"id":176,"depth":265,"text":176},{"id":206,"depth":265,"text":206},{"id":228,"depth":265,"text":229},false,true,"md","河南郑州",{},null,"\u002Fblog\u002F2026\u002F2026-08-14-demystification-research",{"title":6,"description":13},"blog\u002F2026\u002F2026-08-14-demystification-research","自 2025 年入学至今，一年光阴悄然而逝，我已步入研二。回望这一年的研究生生活，我的心态与世界观经历了一场彻底而沉重的重塑——曾经的从容平实，如今已被挥之不去的失落感取代。",[284],"thoughts","2026-08-14T00:00:00+08:00","utt_zVmdYpEoW-2HkgNeH6tsTcym6PstUAxslVH-wUE",{"id":288,"title":289,"body":290,"description":294,"draft":273,"enableComment":274,"extension":275,"image":264,"important":273,"location":278,"meta":5530,"navigation":274,"ogImage":278,"path":5531,"seo":5532,"stem":5533,"summary":5534,"tags":5535,"time":5537,"__hash__":5538},"blog\u002Fblog\u002F2026\u002F2026-08-19-yan-jiu-guan-xi-de-san-zhong-shi-jiao.md","研究关系的三种视角",{"type":8,"value":291,"toc":5522},[292,295,298,301,305,308,576,1255,1450,1454,1457,1858,1862,1865,2342,2620,3433,3436,3439,3499,3845,3940,4215,4218,4221,4224,4335,4723,4726,4729,4802,4805,5516,5519],[11,293,294],{},"哲学里有一种命题：「存在即关系」，在数理研究中同样也有很深的体现。听起来很抽象，但它其实是对世界本质是什么的一种深刻回答。理解事物不是先存在、再去建立关系，而是事物在建立关系的过程中，才得以成为事物。它最著名的提出者是 20 世纪法国哲学家怀特海（过程哲学），但其思想渊源可以追溯到德国哲学家莱布尼茨（单子论）和古希腊的赫拉克利特（万物流动）。",[11,296,297],{},"所以，研究「存在」也是研究「关系」。而关系通常有三种视角：几何、拓扑和因果。",[11,299,300],{},"拓扑提供稳健的骨架，几何赋予精细的尺度，因果指明干预的方向。三者共同构成智能系统理解世界的先验地基。更准确的说法或许是：几何和拓扑是关于「关系的静态结构」（分别是度量化的和非度量化的），而因果是关于「关系的动态\u002F生成机制」，它回答的不是「这两者如何关联」，而是「如果我改变一个，另一个会怎样」。",[18,302,304],{"id":303},"几何度量结构","几何（度量结构）",[11,306,307],{},"几何关注的是「测量」。基本问题是多接近、多相似，或者一个具体的度量数值。——它需要一个度量结构（距离、内积、相似度函数），通常要求满足对称性、三角不等式等公理。典型例子：嵌入空间里两个向量的余弦相似度、社会心理学里的「亲密度量表」。研究的是关系的强度。几何关系是最重的——信息量最大，但也最脆弱，度量方式一变，结论可能就变。",[11,309,310,311,394,395,575],{},"一个度量空间是二元组 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\\tau",[312,1603,1605,1633],{"className":1604,"ariaHidden":342},[358],[312,1606,1608,1612,1615,1618,1621,1624,1627,1630],{"className":1607},[362],[312,1609],{"className":1610,"style":1611},[366],"height:0.9444em;vertical-align:-0.1944em;",[312,1613,1589],{"className":1614},[375],[312,1616,343],{"className":1617},[381],[312,1619],{"className":1620,"style":386},[385],[312,1622,339],{"className":1623,"style":377},[375,376],[312,1625],{"className":1626,"style":457},[385],[312,1628,1596],{"className":1629},[461],[312,1631],{"className":1632,"style":457},[385],[312,1634,1636,1639],{"className":1635},[362],[312,1637],{"className":1638,"style":1541},[366],[312,1640,1480],{"className":1641,"style":1510},[375,376],"。拓扑结构不需要度量：任何度量空间都能诱导出一个拓扑（用开球生成开集），但反过来不成立——拓扑空间不一定可度量化。关键的不变量是在",[95,1644,1645],{},"同胚","（连续双射且逆映射也连续）下保持不变的性质，比如连通性、紧致性、亏格（洞的个数）。用代数拓扑的语言，贝蒂数 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数的是 ",[312,1725,1727,1740],{"className":1726,"translate":316},[315],[312,1728,1730],{"className":1729},[320],[322,1731,1732],{"xmlns":324},[326,1733,1734,1738],{},[329,1735,1736],{},[337,1737,1666],{},[351,1739,1666],{"encoding":353},[312,1741,1743],{"className":1742,"ariaHidden":342},[358],[312,1744,1746,1749],{"className":1745},[362],[312,1747],{"className":1748,"style":450},[366],[312,1750,1666],{"className":1751,"style":1710},[375,376]," 维「洞」的个数，这是持久同调（persistent homology）在数据分析里常用的工具——它告诉你数据云的「形状骨架」，而完全不关心具体的尺度参数。这解释了为什么拓扑比几何「轻」：它是几何结构经过遗忘函子 ",[312,1754,1756,1797],{"className":1755,"translate":316},[315],[312,1757,1759],{"className":1758},[320],[322,1760,1761],{"xmlns":324},[326,1762,1763,1794],{},[329,1764,1765,1768,1770,1782,1784],{},[337,1766,1767],{},"U",[332,1769,411],{},[329,1771,1772,1776,1779],{},[337,1773,1775],{"mathvariant":1774},"bold","M",[337,1777,1778],{"mathvariant":1774},"e",[337,1780,1781],{"mathvariant":1774},"t",[332,1783,421],{},[329,1785,1786,1789,1792],{},[337,1787,1788],{"mathvariant":1774},"T",[337,1790,1791],{"mathvariant":1774},"o",[337,1793,11],{"mathvariant":1774},[351,1795,1796],{"encoding":353},"U: \\mathbf{Met} \\to \\mathbf{Top}",[312,1798,1800,1819,1843],{"className":1799,"ariaHidden":342},[358],[312,1801,1803,1806,1810,1813,1816],{"className":1802},[362],[312,1804],{"className":1805,"style":492},[366],[312,1807,1767],{"className":1808,"style":1809},[375,376],"margin-right:0.109em;",[312,1811],{"className":1812,"style":457},[385],[312,1814,411],{"className":1815},[461],[312,1817],{"className":1818,"style":457},[385],[312,1820,1822,1826,1834,1837,1840],{"className":1821},[362],[312,1823],{"className":1824,"style":1825},[366],"height:0.6861em;",[312,1827,1829],{"className":1828},[375],[312,1830,1833],{"className":1831},[375,1832],"mathbf","Met",[312,1835],{"className":1836,"style":457},[385],[312,1838,421],{"className":1839},[461],[312,1841],{"className":1842,"style":457},[385],[312,1844,1846,1850],{"className":1845},[362],[312,1847],{"className":1848,"style":1849},[366],"height:0.8805em;vertical-align:-0.1944em;",[312,1851,1853],{"className":1852},[375],[312,1854,1856],{"className":1855},[375,1832],"Top"," 投影之后剩下的东西。",[18,1859,1861],{"id":1860},"因果约束结构","因果（约束结构）",[11,1863,1864],{},"因果关注的是「约束」。这一支和前两支有本质区别：几何和拓扑通常是对称的（A 到 B 的距离=B 到 A 的距离；A 连着 B 等价于 B 连着 A），而因果关系本质上是非对称的——「X 决定\u002F限制 Y 的取值范围」不等于反过来成立。因果结构需要额外的信息才能识别（干预、反事实、时间先后），单纯的相关性数据（哪怕是几何或拓扑意义上完整的）不足以确定因果方向。这也是 Pearl 那套 do-calculus 要解决的问题。在 ML 中，几何\u002F拓扑模型在独立同分布（i.i.d.）下表现很好，但只要测试分布变了（协变量偏移），它们就会崩。而因果结构（比如有向无环图 DAG）告诉你的是「机制」——只要干预机制不变，哪怕输入分布变了，模型依然能泛化。这也是为什么说因果是稳健性的终极来源。",[11,1866,1867,1868,394,1958,1986,1987,2165,2166,2341],{},"结构因果模型（SCM）是一个三元组 ",[312,1869,1871,1903],{"className":1870,"translate":316},[315],[312,1872,1874],{"className":1873},[320],[322,1875,1876],{"xmlns":324},[326,1877,1878,1900],{},[329,1879,1880,1882,1884,1886,1888,1890,1893,1895,1898],{},[337,1881,1775],{},[332,1883,648],{},[332,1885,1278],{"stretchy":334},[337,1887,1767],{},[332,1889,343],{"separator":342},[337,1891,1892],{},"V",[332,1894,343],{"separator":342},[337,1896,1897],{},"F",[332,1899,1288],{"stretchy":334},[351,1901,1902],{"encoding":353},"M = \\langle U, V, F \\rangle",[312,1904,1906,1924],{"className":1905,"ariaHidden":342},[358],[312,1907,1909,1912,1915,1918,1921],{"className":1908},[362],[312,1910],{"className":1911,"style":492},[366],[312,1913,1775],{"className":1914,"style":1809},[375,376],[312,1916],{"className":1917,"style":457},[385],[312,1919,648],{"className":1920},[461],[312,1922],{"className":1923,"style":457},[385],[312,1925,1927,1930,1933,1936,1939,1942,1945,1948,1951,1955],{"className":1926},[362],[312,1928],{"className":1929,"style":367},[366],[312,1931,1278],{"className":1932},[371],[312,1934,1767],{"className":1935,"style":1809},[375,376],[312,1937,343],{"className":1938},[381],[312,1940],{"className":1941,"style":386},[385],[312,1943,1892],{"className":1944,"style":478},[375,376],[312,1946,343],{"className":1947},[381],[312,1949],{"className":1950,"style":386},[385],[312,1952,1897],{"className":1953,"style":1954},[375,376],"margin-right:0.1389em;",[312,1956,1288],{"className":1957},[393],[312,1959,1961,1974],{"className":1960,"translate":316},[315],[312,1962,1964],{"className":1963},[320],[322,1965,1966],{"xmlns":324},[326,1967,1968,1972],{},[329,1969,1970],{},[337,1971,1767],{},[351,1973,1767],{"encoding":353},[312,1975,1977],{"className":1976,"ariaHidden":342},[358],[312,1978,1980,1983],{"className":1979},[362],[312,1981],{"className":1982,"style":492},[366],[312,1984,1767],{"className":1985,"style":1809},[375,376]," 是外生变量，",[312,1988,1990,2032],{"className":1989,"translate":316},[315],[312,1991,1993],{"className":1992},[320],[322,1994,1995],{"xmlns":324},[326,1996,1997,2029],{},[329,1998,1999,2001,2003,2005,2012,2014,2017,2019,2026],{},[337,2000,1892],{},[332,2002,648],{},[332,2004,595],{"stretchy":334},[423,2006,2007,2009],{},[337,2008,1892],{},[435,2010,2011],{},"1",[332,2013,343],{"separator":342},[332,2015,2016],{},"…",[332,2018,343],{"separator":342},[423,2020,2021,2023],{},[337,2022,1892],{},[337,2024,2025],{},"n",[332,2027,2028],{"stretchy":334},"}",[351,2030,2031],{"encoding":353},"V = \\{V_1, \\dots, V_n\\}",[312,2033,2035,2053],{"className":2034,"ariaHidden":342},[358],[312,2036,2038,2041,2044,2047,2050],{"className":2037},[362],[312,2039],{"className":2040,"style":492},[366],[312,2042,1892],{"className":2043,"style":478},[375,376],[312,2045],{"className":2046,"style":457},[385],[312,2048,648],{"className":2049},[461],[312,2051],{"className":2052,"style":457},[385],[312,2054,2056,2059,2062,2103,2106,2109,2112,2115,2118,2121,2162],{"className":2055},[362],[312,2057],{"className":2058,"style":367},[366],[312,2060,595],{"className":2061},[371],[312,2063,2065,2068],{"className":2064},[375],[312,2066,1892],{"className":2067,"style":478},[375,376],[312,2069,2071],{"className":2070},[522],[312,2072,2074,2095],{"className":2073},[526,527],[312,2075,2077,2092],{"className":2076},[531],[312,2078,2080],{"className":2079,"style":536},[535],[312,2081,2083,2086],{"style":2082},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[312,2084],{"className":2085,"style":544},[543],[312,2087,2089],{"className":2088},[548,549,550,551],[312,2090,2011],{"className":2091},[375,551],[312,2093,565],{"className":2094},[564],[312,2096,2098],{"className":2097},[531],[312,2099,2101],{"className":2100,"style":1720},[535],[312,2102],{},[312,2104,343],{"className":2105},[381],[312,2107],{"className":2108,"style":386},[385],[312,2110,2016],{"className":2111},[787],[312,2113],{"className":2114,"style":386},[385],[312,2116,343],{"className":2117},[381],[312,2119],{"className":2120,"style":386},[385],[312,2122,2124,2127],{"className":2123},[375],[312,2125,1892],{"className":2126,"style":478},[375,376],[312,2128,2130],{"className":2129},[522],[312,2131,2133,2154],{"className":2132},[526,527],[312,2134,2136,2151],{"className":2135},[531],[312,2137,2140],{"className":2138,"style":2139},[535],"height:0.1514em;",[312,2141,2142,2145],{"style":2082},[312,2143],{"className":2144,"style":544},[543],[312,2146,2148],{"className":2147},[548,549,550,551],[312,2149,2025],{"className":2150},[375,376,551],[312,2152,565],{"className":2153},[564],[312,2155,2157],{"className":2156},[531],[312,2158,2160],{"className":2159,"style":1720},[535],[312,2161],{},[312,2163,2028],{"className":2164},[393]," 是内生变量，",[312,2167,2169,2208],{"className":2168,"translate":316},[315],[312,2170,2172],{"className":2171},[320],[322,2173,2174],{"xmlns":324},[326,2175,2176,2205],{},[329,2177,2178,2180,2182,2184,2191,2193,2195,2197,2203],{},[337,2179,1897],{},[332,2181,648],{},[332,2183,595],{"stretchy":334},[423,2185,2186,2189],{},[337,2187,2188],{},"f",[435,2190,2011],{},[332,2192,343],{"separator":342},[332,2194,2016],{},[332,2196,343],{"separator":342},[423,2198,2199,2201],{},[337,2200,2188],{},[337,2202,2025],{},[332,2204,2028],{"stretchy":334},[351,2206,2207],{"encoding":353},"F = \\{f_1, \\dots, f_n\\}",[312,2209,2211,2229],{"className":2210,"ariaHidden":342},[358],[312,2212,2214,2217,2220,2223,2226],{"className":2213},[362],[312,2215],{"className":2216,"style":492},[366],[312,2218,1897],{"className":2219,"style":1954},[375,376],[312,2221],{"className":2222,"style":457},[385],[312,2224,648],{"className":2225},[461],[312,2227],{"className":2228,"style":457},[385],[312,2230,2232,2235,2238,2280,2283,2286,2289,2292,2295,2298,2338],{"className":2231},[362],[312,2233],{"className":2234,"style":367},[366],[312,2236,595],{"className":2237},[371],[312,2239,2241,2245],{"className":2240},[375],[312,2242,2188],{"className":2243,"style":2244},[375,376],"margin-right:0.1076em;",[312,2246,2248],{"className":2247},[522],[312,2249,2251,2272],{"className":2250},[526,527],[312,2252,2254,2269],{"className":2253},[531],[312,2255,2257],{"className":2256,"style":536},[535],[312,2258,2260,2263],{"style":2259},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[312,2261],{"className":2262,"style":544},[543],[312,2264,2266],{"className":2265},[548,549,550,551],[312,2267,2011],{"className":2268},[375,551],[312,2270,565],{"className":2271},[564],[312,2273,2275],{"className":2274},[531],[312,2276,2278],{"className":2277,"style":1720},[535],[312,2279],{},[312,2281,343],{"className":2282},[381],[312,2284],{"className":2285,"style":386},[385],[312,2287,2016],{"className":2288},[787],[312,2290],{"className":2291,"style":386},[385],[312,2293,343],{"className":2294},[381],[312,2296],{"className":2297,"style":386},[385],[312,2299,2301,2304],{"className":2300},[375],[312,2302,2188],{"className":2303,"style":2244},[375,376],[312,2305,2307],{"className":2306},[522],[312,2308,2310,2330],{"className":2309},[526,527],[312,2311,2313,2327],{"className":2312},[531],[312,2314,2316],{"className":2315,"style":2139},[535],[312,2317,2318,2321],{"style":2259},[312,2319],{"className":2320,"style":544},[543],[312,2322,2324],{"className":2323},[548,549,550,551],[312,2325,2025],{"className":2326},[375,376,551],[312,2328,565],{"className":2329},[564],[312,2331,2333],{"className":2332},[531],[312,2334,2336],{"className":2335,"style":1720},[535],[312,2337],{},[312,2339,2028],{"className":2340},[393]," 是一组函数，满足",[312,2343,2345],{"className":2344,"translate":316},[579],[312,2346,2348,2406],{"className":2347,"translate":316},[315],[312,2349,2351],{"className":2350},[320],[322,2352,2353],{"xmlns":324,"display":588},[326,2354,2355,2403],{},[329,2356,2357,2364,2366,2368,2374,2376,2383,2385,2391,2393,2395,2401],{},[423,2358,2359,2361],{},[337,2360,1892],{},[337,2362,2363],{},"i",[332,2365,411],{},[332,2367,648],{},[423,2369,2370,2372],{},[337,2371,2188],{},[337,2373,2363],{},[332,2375,335],{"stretchy":334},[329,2377,2378,2381],{},[337,2379,2380],{"mathvariant":1363},"P",[337,2382,34],{"mathvariant":1363},[332,2384,335],{"stretchy":334},[423,2386,2387,2389],{},[337,2388,1892],{},[337,2390,2363],{},[332,2392,349],{"stretchy":334},[332,2394,343],{"separator":342},[423,2396,2397,2399],{},[337,2398,1767],{},[337,2400,2363],{},[332,2402,349],{"stretchy":334},[351,2404,2405],{"encoding":353},"V_i := f_i(\\mathrm{Pa}(V_i), U_i)",[312,2407,2409,2467],{"className":2408,"ariaHidden":342},[358],[312,2410,2412,2416,2457,2460,2464],{"className":2411},[362],[312,2413],{"className":2414,"style":2415},[366],"height:0.8333em;vertical-align:-0.15em;",[312,2417,2419,2422],{"className":2418},[375],[312,2420,1892],{"className":2421,"style":478},[375,376],[312,2423,2425],{"className":2424},[522],[312,2426,2428,2449],{"className":2427},[526,527],[312,2429,2431,2446],{"className":2430},[531],[312,2432,2435],{"className":2433,"style":2434},[535],"height:0.3117em;",[312,2436,2437,2440],{"style":2082},[312,2438],{"className":2439,"style":544},[543],[312,2441,2443],{"className":2442},[548,549,550,551],[312,2444,2363],{"className":2445},[375,376,551],[312,2447,565],{"className":2448},[564],[312,2450,2452],{"className":2451},[531],[312,2453,2455],{"className":2454,"style":1720},[535],[312,2456],{},[312,2458],{"className":2459,"style":457},[385],[312,2461,2463],{"className":2462},[461],":=",[312,2465],{"className":2466,"style":457},[385],[312,2468,2470,2473,2513,2516,2524,2527,2567,2570,2573,2576,2617],{"className":2469},[362],[312,2471],{"className":2472,"style":367},[366],[312,2474,2476,2479],{"className":2475},[375],[312,2477,2188],{"className":2478,"style":2244},[375,376],[312,2480,2482],{"className":2481},[522],[312,2483,2485,2505],{"className":2484},[526,527],[312,2486,2488,2502],{"className":2487},[531],[312,2489,2491],{"className":2490,"style":2434},[535],[312,2492,2493,2496],{"style":2259},[312,2494],{"className":2495,"style":544},[543],[312,2497,2499],{"className":2498},[548,549,550,551],[312,2500,2363],{"className":2501},[375,376,551],[312,2503,565],{"className":2504},[564],[312,2506,2508],{"className":2507},[531],[312,2509,2511],{"className":2510,"style":1720},[535],[312,2512],{},[312,2514,335],{"className":2515},[371],[312,2517,2519],{"className":2518},[375],[312,2520,2523],{"className":2521},[375,2522],"mathrm","Pa",[312,2525,335],{"className":2526},[371],[312,2528,2530,2533],{"className":2529},[375],[312,2531,1892],{"className":2532,"style":478},[375,376],[312,2534,2536],{"className":2535},[522],[312,2537,2539,2559],{"className":2538},[526,527],[312,2540,2542,2556],{"className":2541},[531],[312,2543,2545],{"className":2544,"style":2434},[535],[312,2546,2547,2550],{"style":2082},[312,2548],{"className":2549,"style":544},[543],[312,2551,2553],{"className":2552},[548,549,550,551],[312,2554,2363],{"className":2555},[375,376,551],[312,2557,565],{"className":2558},[564],[312,2560,2562],{"className":2561},[531],[312,2563,2565],{"className":2564,"style":1720},[535],[312,2566],{},[312,2568,349],{"className":2569},[393],[312,2571,343],{"className":2572},[381],[312,2574],{"className":2575,"style":386},[385],[312,2577,2579,2582],{"className":2578},[375],[312,2580,1767],{"className":2581,"style":1809},[375,376],[312,2583,2585],{"className":2584},[522],[312,2586,2588,2609],{"className":2587},[526,527],[312,2589,2591,2606],{"className":2590},[531],[312,2592,2594],{"className":2593,"style":2434},[535],[312,2595,2597,2600],{"style":2596},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[312,2598],{"className":2599,"style":544},[543],[312,2601,2603],{"className":2602},[548,549,550,551],[312,2604,2363],{"className":2605},[375,376,551],[312,2607,565],{"className":2608},[564],[312,2610,2612],{"className":2611},[531],[312,2613,2615],{"className":2614,"style":1720},[535],[312,2616],{},[312,2618,349],{"className":2619},[393],[11,2621,2622,2623,2653,2654,2683,2684,2687,2688,2717,2718,2855,2856,3011,3012,3064,3065,3175,3176,3204,3205,3233,3234,3262,3263,3351,3352,3403,3404,3432],{},"赋值符号 ",[312,2624,2626,2641],{"className":2625,"translate":316},[315],[312,2627,2629],{"className":2628},[320],[322,2630,2631],{"xmlns":324},[326,2632,2633,2639],{},[329,2634,2635,2637],{},[332,2636,411],{},[332,2638,648],{},[351,2640,2463],{"encoding":353},[312,2642,2644],{"className":2643,"ariaHidden":342},[358],[312,2645,2647,2650],{"className":2646},[362],[312,2648],{"className":2649,"style":1541},[366],[312,2651,2463],{"className":2652},[461],"（而非 ",[312,2655,2657,2670],{"className":2656,"translate":316},[315],[312,2658,2660],{"className":2659},[320],[322,2661,2662],{"xmlns":324},[326,2663,2664,2668],{},[329,2665,2666],{},[332,2667,648],{},[351,2669,648],{"encoding":353},[312,2671,2673],{"className":2672,"ariaHidden":342},[358],[312,2674,2676,2680],{"className":2675},[362],[312,2677],{"className":2678,"style":2679},[366],"height:0.3669em;",[312,2681,648],{"className":2682},[461],"）是关键——它表示这是一个",[95,2685,2686],{},"机制","，不是一个可逆的代数等式。这组机制天然诱导一张有向无环图（DAG）",[312,2689,2691,2705],{"className":2690,"translate":316},[315],[312,2692,2694],{"className":2693},[320],[322,2695,2696],{"xmlns":324},[326,2697,2698,2703],{},[329,2699,2700],{},[337,2701,2702],{},"G",[351,2704,2702],{"encoding":353},[312,2706,2708],{"className":2707,"ariaHidden":342},[358],[312,2709,2711,2714],{"className":2710},[362],[312,2712],{"className":2713,"style":492},[366],[312,2715,2702],{"className":2716},[375,376],"，边 ",[312,2719,2721,2748],{"className":2720,"translate":316},[315],[312,2722,2724],{"className":2723},[320],[322,2725,2726],{"xmlns":324},[326,2727,2728,2745],{},[329,2729,2730,2737,2739],{},[423,2731,2732,2734],{},[337,2733,1892],{},[337,2735,2736],{},"j",[332,2738,421],{},[423,2740,2741,2743],{},[337,2742,1892],{},[337,2744,2363],{},[351,2746,2747],{"encoding":353},"V_j \\to V_i",[312,2749,2751,2809],{"className":2750,"ariaHidden":342},[358],[312,2752,2754,2758,2800,2803,2806],{"className":2753},[362],[312,2755],{"className":2756,"style":2757},[366],"height:0.9694em;vertical-align:-0.2861em;",[312,2759,2761,2764],{"className":2760},[375],[312,2762,1892],{"className":2763,"style":478},[375,376],[312,2765,2767],{"className":2766},[522],[312,2768,2770,2791],{"className":2769},[526,527],[312,2771,2773,2788],{"className":2772},[531],[312,2774,2776],{"className":2775,"style":2434},[535],[312,2777,2778,2781],{"style":2082},[312,2779],{"className":2780,"style":544},[543],[312,2782,2784],{"className":2783},[548,549,550,551],[312,2785,2736],{"className":2786,"style":2787},[375,376,551],"margin-right:0.0572em;",[312,2789,565],{"className":2790},[564],[312,2792,2794],{"className":2793},[531],[312,2795,2798],{"className":2796,"style":2797},[535],"height:0.2861em;",[312,2799],{},[312,2801],{"className":2802,"style":457},[385],[312,2804,421],{"className":2805},[461],[312,2807],{"className":2808,"style":457},[385],[312,2810,2812,2815],{"className":2811},[362],[312,2813],{"className":2814,"style":2415},[366],[312,2816,2818,2821],{"className":2817},[375],[312,2819,1892],{"className":2820,"style":478},[375,376],[312,2822,2824],{"className":2823},[522],[312,2825,2827,2847],{"className":2826},[526,527],[312,2828,2830,2844],{"className":2829},[531],[312,2831,2833],{"className":2832,"style":2434},[535],[312,2834,2835,2838],{"style":2082},[312,2836],{"className":2837,"style":544},[543],[312,2839,2841],{"className":2840},[548,549,550,551],[312,2842,2363],{"className":2843},[375,376,551],[312,2845,565],{"className":2846},[564],[312,2848,2850],{"className":2849},[531],[312,2851,2853],{"className":2852,"style":1720},[535],[312,2854],{}," 存在当且仅当 ",[312,2857,2859,2895],{"className":2858,"translate":316},[315],[312,2860,2862],{"className":2861},[320],[322,2863,2864],{"xmlns":324},[326,2865,2866,2892],{},[329,2867,2868,2874,2876,2882,2884,2890],{},[423,2869,2870,2872],{},[337,2871,1892],{},[337,2873,2736],{},[332,2875,1596],{},[329,2877,2878,2880],{},[337,2879,2380],{"mathvariant":1363},[337,2881,34],{"mathvariant":1363},[332,2883,335],{"stretchy":334},[423,2885,2886,2888],{},[337,2887,1892],{},[337,2889,2363],{},[332,2891,349],{"stretchy":334},[351,2893,2894],{"encoding":353},"V_j \\in \\mathrm{Pa}(V_i)",[312,2896,2898,2953],{"className":2897,"ariaHidden":342},[358],[312,2899,2901,2904,2944,2947,2950],{"className":2900},[362],[312,2902],{"className":2903,"style":2757},[366],[312,2905,2907,2910],{"className":2906},[375],[312,2908,1892],{"className":2909,"style":478},[375,376],[312,2911,2913],{"className":2912},[522],[312,2914,2916,2936],{"className":2915},[526,527],[312,2917,2919,2933],{"className":2918},[531],[312,2920,2922],{"className":2921,"style":2434},[535],[312,2923,2924,2927],{"style":2082},[312,2925],{"className":2926,"style":544},[543],[312,2928,2930],{"className":2929},[548,549,550,551],[312,2931,2736],{"className":2932,"style":2787},[375,376,551],[312,2934,565],{"className":2935},[564],[312,2937,2939],{"className":2938},[531],[312,2940,2942],{"className":2941,"style":2797},[535],[312,2943],{},[312,2945],{"className":2946,"style":457},[385],[312,2948,1596],{"className":2949},[461],[312,2951],{"className":2952,"style":457},[385],[312,2954,2956,2959,2965,2968,3008],{"className":2955},[362],[312,2957],{"className":2958,"style":367},[366],[312,2960,2962],{"className":2961},[375],[312,2963,2523],{"className":2964},[375,2522],[312,2966,335],{"className":2967},[371],[312,2969,2971,2974],{"className":2970},[375],[312,2972,1892],{"className":2973,"style":478},[375,376],[312,2975,2977],{"className":2976},[522],[312,2978,2980,3000],{"className":2979},[526,527],[312,2981,2983,2997],{"className":2982},[531],[312,2984,2986],{"className":2985,"style":2434},[535],[312,2987,2988,2991],{"style":2082},[312,2989],{"className":2990,"style":544},[543],[312,2992,2994],{"className":2993},[548,549,550,551],[312,2995,2363],{"className":2996},[375,376,551],[312,2998,565],{"className":2999},[564],[312,3001,3003],{"className":3002},[531],[312,3004,3006],{"className":3005,"style":1720},[535],[312,3007],{},[312,3009,349],{"className":3010},[393],"。因果推断的核心操作是 ",[312,3013,3015,3039],{"className":3014,"translate":316},[315],[312,3016,3018],{"className":3017},[320],[322,3019,3020],{"xmlns":324},[326,3021,3022,3036],{},[329,3023,3024,3030,3032,3034],{},[329,3025,3026,3028],{},[337,3027,346],{"mathvariant":1363},[337,3029,1791],{"mathvariant":1363},[332,3031,335],{"stretchy":334},[332,3033,1281],{},[332,3035,349],{"stretchy":334},[351,3037,3038],{"encoding":353},"\\mathrm{do}(\\cdot)",[312,3040,3042],{"className":3041,"ariaHidden":342},[358],[312,3043,3045,3048,3055,3058,3061],{"className":3044},[362],[312,3046],{"className":3047,"style":367},[366],[312,3049,3051],{"className":3050},[375],[312,3052,3054],{"className":3053},[375,2522],"do",[312,3056,335],{"className":3057},[371],[312,3059,1281],{"className":3060},[375],[312,3062,349],{"className":3063},[393]," 算子：",[312,3066,3068,3108],{"className":3067,"translate":316},[315],[312,3069,3071],{"className":3070},[320],[322,3072,3073],{"xmlns":324},[326,3074,3075,3105],{},[329,3076,3077,3079,3081,3084,3087,3093,3095,3097,3099,3101,3103],{},[337,3078,2380],{},[332,3080,335],{"stretchy":334},[337,3082,3083],{},"Y",[332,3085,3086],{},"∣",[329,3088,3089,3091],{},[337,3090,346],{"mathvariant":1363},[337,3092,1791],{"mathvariant":1363},[332,3094,335],{"stretchy":334},[337,3096,339],{},[332,3098,648],{},[337,3100,638],{},[332,3102,349],{"stretchy":334},[332,3104,349],{"stretchy":334},[351,3106,3107],{"encoding":353},"P(Y \\mid \\mathrm{do}(X=x))",[312,3109,3111,3135,3162],{"className":3110,"ariaHidden":342},[358],[312,3112,3114,3117,3120,3123,3126,3129,3132],{"className":3113},[362],[312,3115],{"className":3116,"style":367},[366],[312,3118,2380],{"className":3119,"style":1954},[375,376],[312,3121,335],{"className":3122},[371],[312,3124,3083],{"className":3125,"style":478},[375,376],[312,3127],{"className":3128,"style":457},[385],[312,3130,3086],{"className":3131},[461],[312,3133],{"className":3134,"style":457},[385],[312,3136,3138,3141,3147,3150,3153,3156,3159],{"className":3137},[362],[312,3139],{"className":3140,"style":367},[366],[312,3142,3144],{"className":3143},[375],[312,3145,3054],{"className":3146},[375,2522],[312,3148,335],{"className":3149},[371],[312,3151,339],{"className":3152,"style":377},[375,376],[312,3154],{"className":3155,"style":457},[385],[312,3157,648],{"className":3158},[461],[312,3160],{"className":3161,"style":457},[385],[312,3163,3165,3168,3171],{"className":3164},[362],[312,3166],{"className":3167,"style":367},[366],[312,3169,638],{"className":3170},[375,376],[312,3172,3174],{"className":3173},[393],"))"," 表示「把 ",[312,3177,3179,3192],{"className":3178,"translate":316},[315],[312,3180,3182],{"className":3181},[320],[322,3183,3184],{"xmlns":324},[326,3185,3186,3190],{},[329,3187,3188],{},[337,3189,339],{},[351,3191,339],{"encoding":353},[312,3193,3195],{"className":3194,"ariaHidden":342},[358],[312,3196,3198,3201],{"className":3197},[362],[312,3199],{"className":3200,"style":492},[366],[312,3202,339],{"className":3203,"style":377},[375,376]," 的赋值机制替换为常数 ",[312,3206,3208,3221],{"className":3207,"translate":316},[315],[312,3209,3211],{"className":3210},[320],[322,3212,3213],{"xmlns":324},[326,3214,3215,3219],{},[329,3216,3217],{},[337,3218,638],{},[351,3220,638],{"encoding":353},[312,3222,3224],{"className":3223,"ariaHidden":342},[358],[312,3225,3227,3230],{"className":3226},[362],[312,3228],{"className":3229,"style":1541},[366],[312,3231,638],{"className":3232},[375,376],"，切断它与所有父节点的连接」之后 ",[312,3235,3237,3250],{"className":3236,"translate":316},[315],[312,3238,3240],{"className":3239},[320],[322,3241,3242],{"xmlns":324},[326,3243,3244,3248],{},[329,3245,3246],{},[337,3247,3083],{},[351,3249,3083],{"encoding":353},[312,3251,3253],{"className":3252,"ariaHidden":342},[358],[312,3254,3256,3259],{"className":3255},[362],[312,3257],{"className":3258,"style":492},[366],[312,3260,3083],{"className":3261,"style":478},[375,376]," 的分布，这与条件概率 ",[312,3264,3266,3294],{"className":3265,"translate":316},[315],[312,3267,3269],{"className":3268},[320],[322,3270,3271],{"xmlns":324},[326,3272,3273,3291],{},[329,3274,3275,3277,3279,3281,3283,3285,3287,3289],{},[337,3276,2380],{},[332,3278,335],{"stretchy":334},[337,3280,3083],{},[332,3282,3086],{},[337,3284,339],{},[332,3286,648],{},[337,3288,638],{},[332,3290,349],{"stretchy":334},[351,3292,3293],{"encoding":353},"P(Y \\mid X=x)",[312,3295,3297,3321,3339],{"className":3296,"ariaHidden":342},[358],[312,3298,3300,3303,3306,3309,3312,3315,3318],{"className":3299},[362],[312,3301],{"className":3302,"style":367},[366],[312,3304,2380],{"className":3305,"style":1954},[375,376],[312,3307,335],{"className":3308},[371],[312,3310,3083],{"className":3311,"style":478},[375,376],[312,3313],{"className":3314,"style":457},[385],[312,3316,3086],{"className":3317},[461],[312,3319],{"className":3320,"style":457},[385],[312,3322,3324,3327,3330,3333,3336],{"className":3323},[362],[312,3325],{"className":3326,"style":492},[366],[312,3328,339],{"className":3329,"style":377},[375,376],[312,3331],{"className":3332,"style":457},[385],[312,3334,648],{"className":3335},[461],[312,3337],{"className":3338,"style":457},[385],[312,3340,3342,3345,3348],{"className":3341},[362],[312,3343],{"className":3344,"style":367},[366],[312,3346,638],{"className":3347},[375,376],[312,3349,349],{"className":3350},[393],"——「观察到 ",[312,3353,3355,3373],{"className":3354,"translate":316},[315],[312,3356,3358],{"className":3357},[320],[322,3359,3360],{"xmlns":324},[326,3361,3362,3370],{},[329,3363,3364,3366,3368],{},[337,3365,339],{},[332,3367,648],{},[337,3369,638],{},[351,3371,3372],{"encoding":353},"X=x",[312,3374,3376,3394],{"className":3375,"ariaHidden":342},[358],[312,3377,3379,3382,3385,3388,3391],{"className":3378},[362],[312,3380],{"className":3381,"style":492},[366],[312,3383,339],{"className":3384,"style":377},[375,376],[312,3386],{"className":3387,"style":457},[385],[312,3389,648],{"className":3390},[461],[312,3392],{"className":3393,"style":457},[385],[312,3395,3397,3400],{"className":3396},[362],[312,3398],{"className":3399,"style":1541},[366],[312,3401,638],{"className":3402},[375,376]," 之后 ",[312,3405,3407,3420],{"className":3406,"translate":316},[315],[312,3408,3410],{"className":3409},[320],[322,3411,3412],{"xmlns":324},[326,3413,3414,3418],{},[329,3415,3416],{},[337,3417,3083],{},[351,3419,3083],{"encoding":353},[312,3421,3423],{"className":3422,"ariaHidden":342},[358],[312,3424,3426,3429],{"className":3425},[362],[312,3427],{"className":3428,"style":492},[366],[312,3430,3083],{"className":3431,"style":478},[375,376]," 的分布」——一般是不相等的。两者的差异，正是相关不等于因果的形式化版本。",[18,3434,3435],{"id":3435},"因果与拓扑",[11,3437,3438],{},"一个自然的问题是：几何遗忘度量得到拓扑，那因果是不是遗忘更多东西之后剩下的更轻的骨架？答案是否定的。",[11,3440,3441,3442,3445,3446,3449,3450,3453,3454,3498],{},"几何到拓扑的「变轻」是",[95,3443,3444],{},"同一个信息维度上的压缩","——都是对称关系，只是分辨率从「连续的数值」降到了「是否连通」的二值\u002F离散判断。但因果结构引入了一个几何和拓扑都没有的新维度：",[95,3447,3448],{},"方向性\u002F非对称性","，并且这个方向性原则上",[95,3451,3452],{},"不能","从纯观测的联合分布 ",[312,3455,3457,3477],{"className":3456,"translate":316},[315],[312,3458,3460],{"className":3459},[320],[322,3461,3462],{"xmlns":324},[326,3463,3464,3474],{},[329,3465,3466,3468,3470,3472],{},[337,3467,2380],{},[332,3469,335],{"stretchy":334},[337,3471,1892],{},[332,3473,349],{"stretchy":334},[351,3475,3476],{"encoding":353},"P(V)",[312,3478,3480],{"className":3479,"ariaHidden":342},[358],[312,3481,3483,3486,3489,3492,3495],{"className":3482},[362],[312,3484],{"className":3485,"style":367},[366],[312,3487,2380],{"className":3488,"style":1954},[375,376],[312,3490,335],{"className":3491},[371],[312,3493,1892],{"className":3494,"style":478},[375,376],[312,3496,349],{"className":3497},[393]," 中单独用几何或拓扑手段识别出来。这就是可识别性问题（identifiability）：",[150,3500,3501],{},[11,3502,3503,3506,3507,3550,3551,3608,3609,3660,3661,3660,3712,3788,3789,236],{},[95,3504,3505],{},"命题（因果不可从观测唯一识别）。"," 对于两个变量 ",[312,3508,3510,3528],{"className":3509,"translate":316},[315],[312,3511,3513],{"className":3512},[320],[322,3514,3515],{"xmlns":324},[326,3516,3517,3525],{},[329,3518,3519,3521,3523],{},[337,3520,339],{},[332,3522,343],{"separator":342},[337,3524,3083],{},[351,3526,3527],{"encoding":353},"X, Y",[312,3529,3531],{"className":3530,"ariaHidden":342},[358],[312,3532,3534,3538,3541,3544,3547],{"className":3533},[362],[312,3535],{"className":3536,"style":3537},[366],"height:0.8778em;vertical-align:-0.1944em;",[312,3539,339],{"className":3540,"style":377},[375,376],[312,3542,343],{"className":3543},[381],[312,3545],{"className":3546,"style":386},[385],[312,3548,3083],{"className":3549,"style":478},[375,376],"，仅凭观测联合分布 ",[312,3552,3554,3578],{"className":3553,"translate":316},[315],[312,3555,3557],{"className":3556},[320],[322,3558,3559],{"xmlns":324},[326,3560,3561,3575],{},[329,3562,3563,3565,3567,3569,3571,3573],{},[337,3564,2380],{},[332,3566,335],{"stretchy":334},[337,3568,339],{},[332,3570,343],{"separator":342},[337,3572,3083],{},[332,3574,349],{"stretchy":334},[351,3576,3577],{"encoding":353},"P(X,Y)",[312,3579,3581],{"className":3580,"ariaHidden":342},[358],[312,3582,3584,3587,3590,3593,3596,3599,3602,3605],{"className":3583},[362],[312,3585],{"className":3586,"style":367},[366],[312,3588,2380],{"className":3589,"style":1954},[375,376],[312,3591,335],{"className":3592},[371],[312,3594,339],{"className":3595,"style":377},[375,376],[312,3597,343],{"className":3598},[381],[312,3600],{"className":3601,"style":386},[385],[312,3603,3083],{"className":3604,"style":478},[375,376],[312,3606,349],{"className":3607},[393],"，一般无法在 ",[312,3610,3612,3630],{"className":3611,"translate":316},[315],[312,3613,3615],{"className":3614},[320],[322,3616,3617],{"xmlns":324},[326,3618,3619,3627],{},[329,3620,3621,3623,3625],{},[337,3622,339],{},[332,3624,421],{},[337,3626,3083],{},[351,3628,3629],{"encoding":353},"X \\to Y",[312,3631,3633,3651],{"className":3632,"ariaHidden":342},[358],[312,3634,3636,3639,3642,3645,3648],{"className":3635},[362],[312,3637],{"className":3638,"style":492},[366],[312,3640,339],{"className":3641,"style":377},[375,376],[312,3643],{"className":3644,"style":457},[385],[312,3646,421],{"className":3647},[461],[312,3649],{"className":3650,"style":457},[385],[312,3652,3654,3657],{"className":3653},[362],[312,3655],{"className":3656,"style":492},[366],[312,3658,3083],{"className":3659,"style":478},[375,376],"、",[312,3662,3664,3682],{"className":3663,"translate":316},[315],[312,3665,3667],{"className":3666},[320],[322,3668,3669],{"xmlns":324},[326,3670,3671,3679],{},[329,3672,3673,3675,3677],{},[337,3674,3083],{},[332,3676,421],{},[337,3678,339],{},[351,3680,3681],{"encoding":353},"Y \\to X",[312,3683,3685,3703],{"className":3684,"ariaHidden":342},[358],[312,3686,3688,3691,3694,3697,3700],{"className":3687},[362],[312,3689],{"className":3690,"style":492},[366],[312,3692,3083],{"className":3693,"style":478},[375,376],[312,3695],{"className":3696,"style":457},[385],[312,3698,421],{"className":3699},[461],[312,3701],{"className":3702,"style":457},[385],[312,3704,3706,3709],{"className":3705},[362],[312,3707],{"className":3708,"style":492},[366],[312,3710,339],{"className":3711,"style":377},[375,376],[312,3713,3715,3739],{"className":3714,"translate":316},[315],[312,3716,3718],{"className":3717},[320],[322,3719,3720],{"xmlns":324},[326,3721,3722,3736],{},[329,3723,3724,3726,3729,3732,3734],{},[337,3725,339],{},[332,3727,3728],{},"←",[337,3730,3731],{},"Z",[332,3733,421],{},[337,3735,3083],{},[351,3737,3738],{"encoding":353},"X \\leftarrow Z \\to Y",[312,3740,3742,3760,3779],{"className":3741,"ariaHidden":342},[358],[312,3743,3745,3748,3751,3754,3757],{"className":3744},[362],[312,3746],{"className":3747,"style":492},[366],[312,3749,339],{"className":3750,"style":377},[375,376],[312,3752],{"className":3753,"style":457},[385],[312,3755,3728],{"className":3756},[461],[312,3758],{"className":3759,"style":457},[385],[312,3761,3763,3766,3770,3773,3776],{"className":3762},[362],[312,3764],{"className":3765,"style":492},[366],[312,3767,3731],{"className":3768,"style":3769},[375,376],"margin-right:0.0715em;",[312,3771],{"className":3772,"style":457},[385],[312,3774,421],{"className":3775},[461],[312,3777],{"className":3778,"style":457},[385],[312,3780,3782,3785],{"className":3781},[362],[312,3783],{"className":3784,"style":492},[366],[312,3786,3083],{"className":3787,"style":478},[375,376],"（混杂）等因果结构之间做出唯一判定——它们可以诱导出完全相同的 ",[312,3790,3792,3815],{"className":3791,"translate":316},[315],[312,3793,3795],{"className":3794},[320],[322,3796,3797],{"xmlns":324},[326,3798,3799,3813],{},[329,3800,3801,3803,3805,3807,3809,3811],{},[337,3802,2380],{},[332,3804,335],{"stretchy":334},[337,3806,339],{},[332,3808,343],{"separator":342},[337,3810,3083],{},[332,3812,349],{"stretchy":334},[351,3814,3577],{"encoding":353},[312,3816,3818],{"className":3817,"ariaHidden":342},[358],[312,3819,3821,3824,3827,3830,3833,3836,3839,3842],{"className":3820},[362],[312,3822],{"className":3823,"style":367},[366],[312,3825,2380],{"className":3826,"style":1954},[375,376],[312,3828,335],{"className":3829},[371],[312,3831,339],{"className":3832,"style":377},[375,376],[312,3834,343],{"className":3835},[381],[312,3837],{"className":3838,"style":386},[385],[312,3840,3083],{"className":3841,"style":478},[375,376],[312,3843,349],{"className":3844},[393],[11,3846,3847,3848,3882,3883,1514,3911,3939],{},"要打破这种不可识别性，需要额外的信息源：随机对照实验（真正的 ",[312,3849,3851,3867],{"className":3850,"translate":316},[315],[312,3852,3854],{"className":3853},[320],[322,3855,3856],{"xmlns":324},[326,3857,3858,3864],{},[329,3859,3860,3862],{},[337,3861,346],{"mathvariant":1363},[337,3863,1791],{"mathvariant":1363},[351,3865,3866],{"encoding":353},"\\mathrm{do}",[312,3868,3870],{"className":3869,"ariaHidden":342},[358],[312,3871,3873,3876],{"className":3872},[362],[312,3874],{"className":3875,"style":450},[366],[312,3877,3879],{"className":3878},[375],[312,3880,3054],{"className":3881},[375,2522],"）、时间先后顺序、结构假设（如可加噪声模型、非高斯性，如 LiNGAM 方法利用非高斯噪声打破对称性）。这说明因果结构不是几何\u002F拓扑那条压缩链上的下一站，而是一个正交的轴——即便你拥有关于系统的完整几何信息（所有点对的精确距离）和完整拓扑信息（所有连通关系），你依然可能无法回答「如果我强行改变 ",[312,3884,3886,3899],{"className":3885,"translate":316},[315],[312,3887,3889],{"className":3888},[320],[322,3890,3891],{"xmlns":324},[326,3892,3893,3897],{},[329,3894,3895],{},[337,3896,339],{},[351,3898,339],{"encoding":353},[312,3900,3902],{"className":3901,"ariaHidden":342},[358],[312,3903,3905,3908],{"className":3904},[362],[312,3906],{"className":3907,"style":492},[366],[312,3909,339],{"className":3910,"style":377},[375,376],[312,3912,3914,3927],{"className":3913,"translate":316},[315],[312,3915,3917],{"className":3916},[320],[322,3918,3919],{"xmlns":324},[326,3920,3921,3925],{},[329,3922,3923],{},[337,3924,3083],{},[351,3926,3083],{"encoding":353},[312,3928,3930],{"className":3929,"ariaHidden":342},[358],[312,3931,3933,3936],{"className":3932},[362],[312,3934],{"className":3935,"style":492},[366],[312,3937,3083],{"className":3938,"style":478},[375,376]," 会怎样」这个问题。这正是 Pearl 提出因果之梯（Ladder of Causation）的意义所在：",[3941,3942,3943,3962],"table",{},[3944,3945,3946],"thead",{},[3947,3948,3949,3953,3956,3959],"tr",{},[3950,3951,3952],"th",{},"层级",[3950,3954,3955],{},"问题类型",[3950,3957,3958],{},"例子",[3950,3960,3961],{},"所需信息",[3963,3964,3965,4045,4143],"tbody",{},[3947,3966,3967,3971,3974,4042],{},[3968,3969,3970],"td",{},"1. 关联",[3968,3972,3973],{},"看见（seeing）",[3968,3975,3976],{},[312,3977,3979,4003],{"className":3978,"translate":316},[315],[312,3980,3982],{"className":3981},[320],[322,3983,3984],{"xmlns":324},[326,3985,3986,4000],{},[329,3987,3988,3990,3992,3994,3996,3998],{},[337,3989,2380],{},[332,3991,335],{"stretchy":334},[337,3993,3083],{},[332,3995,3086],{},[337,3997,339],{},[332,3999,349],{"stretchy":334},[351,4001,4002],{"encoding":353},"P(Y\\mid X)",[312,4004,4006,4030],{"className":4005,"ariaHidden":342},[358],[312,4007,4009,4012,4015,4018,4021,4024,4027],{"className":4008},[362],[312,4010],{"className":4011,"style":367},[366],[312,4013,2380],{"className":4014,"style":1954},[375,376],[312,4016,335],{"className":4017},[371],[312,4019,3083],{"className":4020,"style":478},[375,376],[312,4022],{"className":4023,"style":457},[385],[312,4025,3086],{"className":4026},[461],[312,4028],{"className":4029,"style":457},[385],[312,4031,4033,4036,4039],{"className":4032},[362],[312,4034],{"className":4035,"style":367},[366],[312,4037,339],{"className":4038,"style":377},[375,376],[312,4040,349],{"className":4041},[393],[3968,4043,4044],{},"观测数据即可，几何\u002F拓扑视角覆盖此层",[3947,4046,4047,4050,4053,4140],{},[3968,4048,4049],{},"2. 干预",[3968,4051,4052],{},"行动（doing）",[3968,4054,4055],{},[312,4056,4058,4092],{"className":4057,"translate":316},[315],[312,4059,4061],{"className":4060},[320],[322,4062,4063],{"xmlns":324},[326,4064,4065,4089],{},[329,4066,4067,4069,4071,4073,4075,4081,4083,4085,4087],{},[337,4068,2380],{},[332,4070,335],{"stretchy":334},[337,4072,3083],{},[332,4074,3086],{},[329,4076,4077,4079],{},[337,4078,346],{"mathvariant":1363},[337,4080,1791],{"mathvariant":1363},[332,4082,335],{"stretchy":334},[337,4084,339],{},[332,4086,349],{"stretchy":334},[332,4088,349],{"stretchy":334},[351,4090,4091],{"encoding":353},"P(Y\\mid \\mathrm{do}(X))",[312,4093,4095,4119],{"className":4094,"ariaHidden":342},[358],[312,4096,4098,4101,4104,4107,4110,4113,4116],{"className":4097},[362],[312,4099],{"className":4100,"style":367},[366],[312,4102,2380],{"className":4103,"style":1954},[375,376],[312,4105,335],{"className":4106},[371],[312,4108,3083],{"className":4109,"style":478},[375,376],[312,4111],{"className":4112,"style":457},[385],[312,4114,3086],{"className":4115},[461],[312,4117],{"className":4118,"style":457},[385],[312,4120,4122,4125,4131,4134,4137],{"className":4121},[362],[312,4123],{"className":4124,"style":367},[366],[312,4126,4128],{"className":4127},[375],[312,4129,3054],{"className":4130},[375,2522],[312,4132,335],{"className":4133},[371],[312,4135,339],{"className":4136,"style":377},[375,376],[312,4138,3174],{"className":4139},[393],[3968,4141,4142],{},"需要实验或因果图假设",[3947,4144,4145,4148,4151,4212],{},[3968,4146,4147],{},"3. 反事实",[3968,4149,4150],{},"想象（imagining）",[3968,4152,4153,4154,4182,4183,4211],{},"若 ",[312,4155,4157,4170],{"className":4156,"translate":316},[315],[312,4158,4160],{"className":4159},[320],[322,4161,4162],{"xmlns":324},[326,4163,4164,4168],{},[329,4165,4166],{},[337,4167,339],{},[351,4169,339],{"encoding":353},[312,4171,4173],{"className":4172,"ariaHidden":342},[358],[312,4174,4176,4179],{"className":4175},[362],[312,4177],{"className":4178,"style":492},[366],[312,4180,339],{"className":4181,"style":377},[375,376]," 不同，",[312,4184,4186,4199],{"className":4185,"translate":316},[315],[312,4187,4189],{"className":4188},[320],[322,4190,4191],{"xmlns":324},[326,4192,4193,4197],{},[329,4194,4195],{},[337,4196,3083],{},[351,4198,3083],{"encoding":353},[312,4200,4202],{"className":4201,"ariaHidden":342},[358],[312,4203,4205,4208],{"className":4204},[362],[312,4206],{"className":4207,"style":492},[366],[312,4209,3083],{"className":4210,"style":478},[375,376]," 会怎样",[3968,4213,4214],{},"需要完整 SCM，包括外生噪声的联合分布",[11,4216,4217],{},"几何和拓扑视角，本质上被限制在第一层；只有引入因果结构，才能爬上第二、第三层。这也是为什么「因果关系需要额外信息才能识别」这句话不是技术细节，而是三种视角在存在论意义上的分界线。",[18,4219,4220],{"id":4220},"机器学习视角",[11,4222,4223],{},"回到机器学习的语境，三种视角之间的差异直接决定了模型在分布偏移下的表现。可以按「随分布变化保持不变的程度」给三者排一个序：",[312,4225,4227],{"className":4226,"translate":316},[579],[312,4228,4230,4264],{"className":4229,"translate":316},[315],[312,4231,4233],{"className":4232},[320],[322,4234,4235],{"xmlns":324,"display":588},[326,4236,4237,4261],{},[329,4238,4239,4242,4244,4247,4249,4252,4254,4256,4258],{},[652,4240,4241],{},"Geometry",[652,4243,654],{},[332,4245,4246],{},"≺",[652,4248,654],{},[652,4250,4251],{},"Topology Invariance",[652,4253,654],{},[332,4255,4246],{},[652,4257,654],{},[652,4259,4260],{},"Causality",[351,4262,4263],{"encoding":353},"\\text{Geometry} \\;\\prec\\; \\text{Topology Invariance} \\;\\prec\\; \\text{Causality}",[312,4265,4267,4295,4323],{"className":4266,"ariaHidden":342},[358],[312,4268,4270,4273,4280,4283,4286,4289,4292],{"className":4269},[362],[312,4271],{"className":4272,"style":3537},[366],[312,4274,4277],{"className":4275},[375,4276],"text",[312,4278,4241],{"className":4279},[375],[312,4281],{"className":4282,"style":457},[385],[312,4284],{"className":4285,"style":457},[385],[312,4287,4246],{"className":4288},[461],[312,4290],{"className":4291,"style":457},[385],[312,4293],{"className":4294,"style":457},[385],[312,4296,4298,4302,4308,4311,4314,4317,4320],{"className":4297},[362],[312,4299],{"className":4300,"style":4301},[366],"height:0.8889em;vertical-align:-0.1944em;",[312,4303,4305],{"className":4304},[375,4276],[312,4306,4251],{"className":4307},[375],[312,4309],{"className":4310,"style":457},[385],[312,4312],{"className":4313,"style":457},[385],[312,4315,4246],{"className":4316},[461],[312,4318],{"className":4319,"style":457},[385],[312,4321],{"className":4322,"style":457},[385],[312,4324,4326,4329],{"className":4325},[362],[312,4327],{"className":4328,"style":4301},[366],[312,4330,4332],{"className":4331},[375,4276],[312,4333,4260],{"className":4334},[375],[4336,4337,4338,4345,4395],"ul",{},[4339,4340,4341,4344],"li",{},[95,4342,4343],{},"几何层面的失败","：训练集和测试集哪怕只是特征做了不同的归一化，相似度排序就可能整体偏移——这是最脆弱的一层，任何非本质的表示变化都会渗透进度量数值本身。",[4339,4346,4347,4350,4351,4394],{},[95,4348,4349],{},"拓扑层面的稳健性","：持久同调等方法对噪声、尺度变化天然不敏感，因为它们本来就是在滤除度量细节之后提取「形状」。但拓扑结构依然是观测分布 ",[312,4352,4354,4373],{"className":4353,"translate":316},[315],[312,4355,4357],{"className":4356},[320],[322,4358,4359],{"xmlns":324},[326,4360,4361,4371],{},[329,4362,4363,4365,4367,4369],{},[337,4364,2380],{},[332,4366,335],{"stretchy":334},[337,4368,1892],{},[332,4370,349],{"stretchy":334},[351,4372,3476],{"encoding":353},[312,4374,4376],{"className":4375,"ariaHidden":342},[358],[312,4377,4379,4382,4385,4388,4391],{"className":4378},[362],[312,4380],{"className":4381,"style":367},[366],[312,4383,2380],{"className":4384,"style":1954},[375,376],[312,4386,335],{"className":4387},[371],[312,4389,1892],{"className":4390,"style":478},[375,376],[312,4392,349],{"className":4393},[393]," 的函数——一旦分布本身发生结构性改变（不只是尺度变化，而是变量间依赖关系变了），拓扑不变量也会随之改变，因为它仍然停留在因果之梯的第一层。",[4339,4396,4397,4400,4401,4451,4452,4592,4593,4637,4638,4722],{},[95,4398,4399],{},"因果层面的稳健性","：如果 ",[312,4402,4404,4421],{"className":4403,"translate":316},[315],[312,4405,4407],{"className":4406},[320],[322,4408,4409],{"xmlns":324},[326,4410,4411,4419],{},[329,4412,4413,4415,4417],{},[337,4414,339],{},[332,4416,421],{},[337,4418,3083],{},[351,4420,3629],{"encoding":353},[312,4422,4424,4442],{"className":4423,"ariaHidden":342},[358],[312,4425,4427,4430,4433,4436,4439],{"className":4426},[362],[312,4428],{"className":4429,"style":492},[366],[312,4431,339],{"className":4432,"style":377},[375,376],[312,4434],{"className":4435,"style":457},[385],[312,4437,421],{"className":4438},[461],[312,4440],{"className":4441,"style":457},[385],[312,4443,4445,4448],{"className":4444},[362],[312,4446],{"className":4447,"style":492},[366],[312,4449,3083],{"className":4450,"style":478},[375,376]," 的机制 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本身不随环境改变（这是很多领域里的物理假设——比如「重力加速度与颜色无关」），那么哪怕 ",[312,4594,4596,4616],{"className":4595,"translate":316},[315],[312,4597,4599],{"className":4598},[320],[322,4600,4601],{"xmlns":324},[326,4602,4603,4613],{},[329,4604,4605,4607,4609,4611],{},[337,4606,2380],{},[332,4608,335],{"stretchy":334},[337,4610,339],{},[332,4612,349],{"stretchy":334},[351,4614,4615],{"encoding":353},"P(X)",[312,4617,4619],{"className":4618,"ariaHidden":342},[358],[312,4620,4622,4625,4628,4631,4634],{"className":4621},[362],[312,4623],{"className":4624,"style":367},[366],[312,4626,2380],{"className":4627,"style":1954},[375,376],[312,4629,335],{"className":4630},[371],[312,4632,339],{"className":4633,"style":377},[375,376],[312,4635,349],{"className":4636},[393]," 的边际分布因为采样环境不同而剧烈变化，",[312,4639,4641,4674],{"className":4640,"translate":316},[315],[312,4642,4644],{"className":4643},[320],[322,4645,4646],{"xmlns":324},[326,4647,4648,4672],{},[329,4649,4650,4652,4654,4656,4658,4664,4666,4668,4670],{},[337,4651,2380],{},[332,4653,335],{"stretchy":334},[337,4655,3083],{},[332,4657,3086],{},[329,4659,4660,4662],{},[337,4661,346],{"mathvariant":1363},[337,4663,1791],{"mathvariant":1363},[332,4665,335],{"stretchy":334},[337,4667,339],{},[332,4669,349],{"stretchy":334},[332,4671,349],{"stretchy":334},[351,4673,4091],{"encoding":353},[312,4675,4677,4701],{"className":4676,"ariaHidden":342},[358],[312,4678,4680,4683,4686,4689,4692,4695,4698],{"className":4679},[362],[312,4681],{"className":4682,"style":367},[366],[312,4684,2380],{"className":4685,"style":1954},[375,376],[312,4687,335],{"className":4688},[371],[312,4690,3083],{"className":4691,"style":478},[375,376],[312,4693],{"className":4694,"style":457},[385],[312,4696,3086],{"className":4697},[461],[312,4699],{"className":4700,"style":457},[385],[312,4702,4704,4707,4713,4716,4719],{"className":4703},[362],[312,4705],{"className":4706,"style":367},[366],[312,4708,4710],{"className":4709},[375],[312,4711,3054],{"className":4712},[375,2522],[312,4714,335],{"className":4715},[371],[312,4717,339],{"className":4718,"style":377},[375,376],[312,4720,3174],{"className":4721},[393]," 这个机制仍然成立，模型依然可以泛化。这正是 Arjovsky 等人提出不变风险最小化方法的出发点：不去拟合在各个环境里都表现最好的相关性，而是寻找在所有环境下都保持不变的预测机制——本质上是把学习目标从「几何\u002F统计上的最优拟合」换成「因果机制上的不变性」。",[11,4724,4725],{},"用一句话概括：几何模型学的是「数据长什么样」，拓扑模型学的是「数据的骨架怎么连」，而因果模型学的是「数据为什么会长成这样、什么力量在背后生成它」。前两者是对现象的描述，后者试图逼近生成现象的机制——这也是为什么协变量偏移能摧毁前两者，却不一定能摧毁后者。",[18,4727,4728],{"id":4728},"递进的先验",[11,4730,4731,4732,4801],{},"如果用范畴论的语言简单勾勒一下三者的关系：存在遗忘函子 ",[312,4733,4735,4765],{"className":4734,"translate":316},[315],[312,4736,4738],{"className":4737},[320],[322,4739,4740],{"xmlns":324},[326,4741,4742,4762],{},[329,4743,4744,4752,4754],{},[329,4745,4746,4748,4750],{},[337,4747,1775],{"mathvariant":1774},[337,4749,1778],{"mathvariant":1774},[337,4751,1781],{"mathvariant":1774},[332,4753,421],{},[329,4755,4756,4758,4760],{},[337,4757,1788],{"mathvariant":1774},[337,4759,1791],{"mathvariant":1774},[337,4761,11],{"mathvariant":1774},[351,4763,4764],{"encoding":353},"\\mathbf{Met} \\to \\mathbf{Top}",[312,4766,4768,4789],{"className":4767,"ariaHidden":342},[358],[312,4769,4771,4774,4780,4783,4786],{"className":4770},[362],[312,4772],{"className":4773,"style":1825},[366],[312,4775,4777],{"className":4776},[375],[312,4778,1833],{"className":4779},[375,1832],[312,4781],{"className":4782,"style":457},[385],[312,4784,421],{"className":4785},[461],[312,4787],{"className":4788,"style":457},[385],[312,4790,4792,4795],{"className":4791},[362],[312,4793],{"className":4794,"style":1849},[366],[312,4796,4798],{"className":4797},[375],[312,4799,1856],{"className":4800},[375,1832],"，把度量空间的态射（等距同构）松弛成拓扑空间的态射（同胚），信息在这一步单调减少，但依然停留在「对称关系」的范畴里。因果结构则不在这条链上——它是在对象上额外加了一层有向、非对称的生成机制，这层机制无法通过对已有对称结构做进一步遗忘得到，只能通过引入新的认识论工具（干预、时间、结构假设）来「添加」。",[11,4803,4804],{},"所以更准确的图景不是一条线性的「由重到轻」的链条，而是：",[312,4806,4808],{"className":4807,"translate":316},[579],[312,4809,4811,4913],{"className":4810,"translate":316},[315],[312,4812,4814],{"className":4813},[320],[322,4815,4816],{"xmlns":324,"display":588},[326,4817,4818,4910],{},[597,4819,4822,4842,4859,4877,4892],{"rowspacing":4820,"columnalign":4821,"columnspacing":601},"0.16em","center",[603,4823,4824],{},[606,4825,4826],{},[609,4827,4828],{"scriptlevel":437,"displaystyle":334},[4829,4830,4831,4839],"munder",{},[4829,4832,4833,4836],{},[652,4834,4835],{},"几何",[332,4837,4838],{"stretchy":342},"⏟",[652,4840,4841],{},"对称，度量化，最重",[603,4843,4844],{},[606,4845,4846],{},[609,4847,4848],{"scriptlevel":437,"displaystyle":334},[329,4849,4850,4854],{},[332,4851,4853],{"fence":334,"stretchy":342,"minsize":4852,"maxsize":4852},"1.8em","↓",[609,4855,4856],{"scriptlevel":2011,"displaystyle":334},[652,4857,4858],{},"遗忘度量",[603,4860,4861],{},[606,4862,4863],{},[609,4864,4865],{"scriptlevel":437,"displaystyle":334},[4829,4866,4867,4874],{},[4829,4868,4869,4872],{},[652,4870,4871],{},"拓扑",[332,4873,4838],{"stretchy":342},[652,4875,4876],{},"对称，非度量化，中等",[603,4878,4879],{},[606,4880,4881],{},[609,4882,4883],{"scriptlevel":437,"displaystyle":334},[329,4884,4885,4887],{},[332,4886,4853],{"fence":334,"stretchy":342,"minsize":4852,"maxsize":4852},[609,4888,4889],{"scriptlevel":2011,"displaystyle":334},[652,4890,4891],{},"额外的干预\u002F时序信息",[603,4893,4894],{},[606,4895,4896],{},[609,4897,4898],{"scriptlevel":437,"displaystyle":334},[4829,4899,4900,4907],{},[4829,4901,4902,4905],{},[652,4903,4904],{},"因果",[332,4906,4838],{"stretchy":342},[652,4908,4909],{},"非对称，机制化，最稳健",[351,4911,4912],{"encoding":353},"\\begin{array}{c}\n\\underbrace{\\text{几何}}_{\\text{对称，度量化，最重}} \\\\[8pt]\n\\Big\\downarrow \\scriptstyle \\text{遗忘度量} \\\\[8pt]\n\\underbrace{\\text{拓扑}}_{\\text{对称，非度量化，中等}} \\\\[8pt]\n\\Big\\downarrow \\scriptstyle \\text{额外的干预\u002F时序信息} 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representation learning）想做的事情，正是把几何\u002F拓扑意义上学到的表示，进一步「提纯」出背后满足机制不变性的潜变量和因果图——这也是几何、拓扑、因果这三种视角在方法论上真正会师的地方。",{"title":264,"searchDepth":265,"depth":265,"links":5523},[5524,5525,5526,5527,5528,5529],{"id":303,"depth":265,"text":304},{"id":1452,"depth":265,"text":1453},{"id":1860,"depth":265,"text":1861},{"id":3435,"depth":265,"text":3435},{"id":4220,"depth":265,"text":4220},{"id":4728,"depth":265,"text":4728},{},"\u002Fblog\u002F2026\u002F2026-08-19-yan-jiu-guan-xi-de-san-zhong-shi-jiao",{"title":289,"description":294},"blog\u002F2026\u002F2026-08-19-yan-jiu-guan-xi-de-san-zhong-shi-jiao","研究「关系」有三种互补视角：几何，拓扑和因果。分别关注测量、连通和约束。它们不是并列的学科，而是看待「存在」的三个层层递进的维度。三者共同构成智能系统理解世界的先验地基。",[5536],"machine-learning","2026-08-19T00:00:00+08:00","A1vSrI3BiIRmUZD1R2c8bUvp1iXhI9JF4wAlPI7utpA",{"id":5540,"title":5541,"body":5542,"description":5546,"draft":273,"enableComment":274,"extension":275,"image":264,"important":273,"location":276,"meta":5695,"navigation":274,"ogImage":278,"path":5696,"seo":5697,"stem":5698,"summary":5699,"tags":5700,"time":5701,"__hash__":5702},"blog\u002Fblog\u002F2026\u002F2026-08-13-xie-zuo-yu-yan-de-zhuan-bian.md","写作语言的转变",{"type":8,"value":5543,"toc":5693},[5544,5547,5550,5553,5675,5678,5681,5684,5687,5690],[11,5545,5546],{},"长期以来，我对自己的博客定位从来不是分享，而更多是给自己看的「笔记」。很多情况是：记录一个刚刚搞懂的东西 → 写下来 → 以后自己查 → 写完就结束。我的博客基本都很短，基本三分钟以内就能读完。大约在 2023 年开始，同时为了学习英语，锻炼技术写作能力，我在疯狂背单词的同时，也可以保持用英语进行技术写作。现在坚持了快两年。所以长期以来，利用英语写作，对我来说压力并不大。写作时不需要追求完整论证，只需要把自己的思路编码下来。哪怕句子稍微生硬一点，只要自己以后能看懂，就已经达成目的。",[11,5548,5549],{},"过去两年的英语写作之所以轻松，是因为它服务于「笔记」功能——短、线性、结论明确。这种写作不需要复杂的逻辑嵌套，不需要反复回看和修改结构，英语的线性特征反而成了一种约束，帮你把想法压缩成清晰的短句。",[11,5551,5552],{},"但是后来，情况发生了变化，我的博客从「给自己看的笔记」的定位，开始转移到了「表达与推演」。当写作从记录变成表达与推演，语言就从工具变成了负担。写作负荷不是恒定的，它会随着结构复杂度和语言熟练度的乘积而非线性增长。",[11,5554,5555,5556,5674],{},"文章越来越长，关于技术写作的部分，有的文章我需要插入大量的 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公式、推导和演绎过程。此时再使用非母语进行技术写作时心智负担显著增大。短文里，一句话如果不知道怎么写，一般情况可以用简单句子绕一下，问题不大。但是到了长篇技术文章，可能连续几页都在描述一个复杂的思想。这时候需要同时控制数学符号、技术概念、论证结构、前后术语一致性、句法，还有段落之间的衔接。于是工作记忆里面同时跑着很多东西。",[11,5676,5677],{},"而且，长篇博客并不是一次写完的，很可能需要花上几个星期慢慢打磨，或者经常回顾我自己的博客的思想。写作的时候，我大多数时间都在思考：「这个理论到底应该怎么解释？」。但是，结果脑子里却不断出现：「这里应该用 which 还是 that？」、「这个东西应该叫 representation 还是 formulation？」、「这个词性是否合适，有没有对应的名词形式？」之类细枝末节的语法问题。久而久之，写作起来会非常累。在短文本写作里，这种差异几乎感觉不到。但当文本从几百字增长到几千、几万字以后，语言的视觉结构、信息密度、词法形态、定位效率和工作记忆负担都会开始成为写作系统的一部分。",[11,5679,5680],{},"另外一种原因，英文是线形文字，阅读效率天然就很低：想在长文中定位到某一块位置，必须要从每一段从头开始逐行扫过，无法像汉字那样逐块扫描。很多时候我在长文写作中，需要不断地往回头看。而英语的语法线性强，从句嵌套多了以后，读者和作者都容易迷失。因为汉字同时包含视觉图像和声音两种信息，它信息密度和视觉辨识特征，使中文文本非常适合视觉扫描。而英文单词之间存在大量空格，真正有语义重量的东西被拆成了很多视觉单元。所以当文章达到几千甚至上万字以后，回来看自己几周前写的东西，会出现一种很奇怪的体验：中文是在「看结构」，英文更容易变成「读句子」。所以，就导致语义单元和视觉单元不对齐——一个概念可能要三四个单词才能表达，视觉上要扫过更长的距离才能抓住一个完整意群。",[11,5682,5683],{},"其实不止是我，很多技术写作者都会遇到一个问题：语言不是中性的容器，它会反过来塑造你思考的形状。",[11,5685,5686],{},"笔记型写作的特点，思维已经完成。只是在编码一个已经清晰的结论，供未来的自己检索。表达与推演型写作则不同，写作本身就是思维过程。你在写的过程中推演、发现、修正。文字不是思维的镜像，而是思维的工具。当写作成为思考工具时，语言就不再只是输出端的问题，而是输入端的问题。非常需要语言来帮助你组织尚未成形的想法，来试探逻辑的边界，来连接不同的概念。",[11,5688,5689],{},"从此以后，我的博客功能，从以前的博客 externalized memory（外部记忆），到现在逐渐变成了 externalized thinking（外部化思考）。",[11,5691,5692],{},"也许从英语写作到中文写作，是在为思维本身让路。让认知资源从语言操作中解放出来，还给真正的思考。",{"title":264,"searchDepth":265,"depth":265,"links":5694},[],{},"\u002Fblog\u002F2026\u002F2026-08-13-xie-zuo-yu-yan-de-zhuan-bian",{"title":5541,"description":5546},"blog\u002F2026\u002F2026-08-13-xie-zuo-yu-yan-de-zhuan-bian","长期以来，为了学习英语并增强熟练度，在技术写作时，我都会刻意使用英语来写作。但是后来我发现使用英语的阅读和思考心智负担非常大。从笔记到表达与推演，写作目标发生变化后，认知资源也需要实现对应的重新分配。",[284],"2026-08-13T00:00:00+08:00","7ebbJ5U5Sd2pnIWInH_6aFeptiKE6s-ogM9nTwBT0EQ",{"left":5704,"top":5704,"width":5705,"height":5705,"rotate":5704,"vFlip":273,"hFlip":273,"body":5706},0,24,"\u003Cpath fill=\"currentColor\" d=\"M16 10c0-2.21-1.79-4-4-4s-4 1.79-4 4s1.79 4 4 4s4-1.79 4-4m-6 0c0-1.1.9-2 2-2s2 .9 2 2s-.9 2-2 2s-2-.9-2-2\"\u002F>\u003Cpath fill=\"currentColor\" d=\"M11.42 21.81c.17.12.38.19.58.19s.41-.06.58-.19c.3-.22 7.45-5.37 7.42-11.82c0-4.41-3.59-8-8-8s-8 3.59-8 8c-.03 6.44 7.12 11.6 7.42 11.82M12 4c3.31 0 6 2.69 6 6c.02 4.44-4.39 8.43-6 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