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-xie-zuo-yu-yan-de-zhuan-bian",{"tags":156,"path":157},[6],"\u002Fblog\u002F2026\u002F2026-08-14-demystification-research",{"tags":159,"path":160},[95],"\u002Fblog\u002F2026\u002F2026-08-19-yan-jiu-guan-xi-de-san-zhong-shi-jiao",{"tags":162,"path":163},[95],"\u002Fblog\u002F2026\u002F2026-08-22-are-local-minima-rare-in-high-dimensions",[165,172,178,184,190,196,202,209,215,221,227,233,239,245,251,257,263,269,275,281,287,293,299,305,311,317,323,330,336,342,348,354,360,366,372,378,384,390,396,402,408,414,420,426,432,438,443,448,454],{"title":166,"summary":167,"image":168,"time":169,"tags":170,"path":108,"id":171},"f-散度族及其推论","f-散度族（f-divergence）用一个凸函数 f 统一刻画两个概率分布之间的差异，KL、JS、全变差、卡方、Hellinger、α-散度都是它的特例。","","2026-10-17T04:47:08+08:00",[76,38],"blog\u002Fblog\u002F2026\u002F0011-about-the-f-divergence.md",{"title":173,"summary":174,"image":168,"time":175,"tags":176,"path":105,"id":177},"克劳德·香农小传","从密歇根小镇那根架在铁丝围栏上的电报线，到贝尔实验室走廊里的独轮车，再到麻省理工那间堆满零件的办公室。他给「信息」下了数学定义，自己却一辈子只对有意思的东西负责。","2026-10-16T22:03:15+08:00",[6],"blog\u002Fblog\u002F2026\u002F0010-biography-of-claude-shannon.md",{"title":179,"summary":180,"image":168,"time":181,"tags":182,"path":102,"id":183},"Dirichlet 分布与证据深度学习","Dirichlet 是单纯形上的分布、多项分布的共轭先验，也是「关于概率的概率」这一二阶对象的自然载体。本文先给出它在定义、矩结构、共轭更新与分裂构造上的完整形式化，神经网络的输出重解释为证据并参数化迪利克雷分布，推导证据深度学习的对数损失等应用。","2026-10-01T18:52:06+08:00",[76,95],"blog\u002Fblog\u002F2026\u002F0007-dirichlet-distribution-and-evidential-deep-learning.md",{"title":185,"summary":186,"image":168,"time":187,"tags":188,"path":99,"id":189},"Markdown 并不适合科学写作","写作的格式工具会悄悄影响到你的行文组织方式。Markdown 与其说「不适合写科学内容」，不如说它的抽象层级主要是「轻量文档标记」，而科学写作本质上更接近「结构化知识建模」。","2026-09-22T22:53:33+08:00",[6],"blog\u002Fblog\u002F2026\u002F0006-markdown-ke-xue-xie-zuo-tong-dian-wen-ti.md",{"title":191,"summary":192,"image":168,"time":193,"tags":194,"path":96,"id":195},"因果结构模型简论","为什么概率论不足以回答因果问题？本文以 Judea Pearl 的因果推断阶梯为线索，依次展开因果图、结构因果模型与结构方程这三层层层递进的形式化工具，进而讨论因果发现、中介分析、do-演算与前门准则，并对照潜在结果框架与传统结构方程模型，梳理这一体系成立所依赖的假设与适用边界。","2026-09-20T23:05:13+08:00",[95],"blog\u002Fblog\u002F2026\u002F0005-yin-guo-jie-gou-mo-xing-jian-lun.md",{"title":197,"summary":198,"image":168,"time":199,"tags":200,"path":92,"id":201},"冯 · 诺依曼小传","从 1903 年布达佩斯的银行家之子，到 1957 年华盛顿病床上的原子能委员。他留下的不是一尊天才的神像，而是一道冷峻的背影——一个快得让时代跟不上的头脑，一个把理性用到极致、也走到理性尽头的人。","2026-09-02T02:45:47+08:00",[6],"blog\u002Fblog\u002F2026\u002F0002-brief-biography-of-von-neumann.md",{"title":203,"summary":204,"image":205,"time":206,"tags":207,"path":163,"id":208},"高维非凸优化的「鞍点主导」","高维空间中的局部极小值极为罕见——因为一个真正的局部极小值要求所有方向都向上弯曲，也就是 Hessian 矩阵的所有特征值都必须为正。而高维空间里，随机的临界点几乎总有某个方向可以向下走，也就是鞍点。这正是为什么神经网络训练更像是「逃离鞍点」的游戏，而不是「跳出局部最优」的游戏。",null,"2026-08-22T14:32:17+08:00",[95],"blog\u002Fblog\u002F2026\u002F2026-08-22-are-local-minima-rare-in-high-dimensions.md",{"title":210,"summary":211,"image":168,"time":212,"tags":213,"path":160,"id":214},"研究关系的三种视角","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。","2026-08-19T00:00:00+08:00",[95],"blog\u002Fblog\u002F2026\u002F2026-08-19-yan-jiu-guan-xi-de-san-zhong-shi-jiao.md",{"title":216,"summary":217,"image":168,"time":218,"tags":219,"path":157,"id":220},"祛魅科研，每个研究生的必修课","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。","2026-08-14T00:00:00+08:00",[6],"blog\u002Fblog\u002F2026\u002F2026-08-14-demystification-research.md",{"title":222,"summary":223,"image":168,"time":224,"tags":225,"path":154,"id":226},"写作语言的转变","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。","2026-08-13T00:00:00+08:00",[6],"blog\u002Fblog\u002F2026\u002F2026-08-13-xie-zuo-yu-yan-de-zhuan-bian.md",{"title":228,"summary":229,"image":168,"time":230,"tags":231,"path":151,"id":232},"大语言模型中的表征流形","将 LLM 的表征流形形式化：以度量空间定义特征，证明余弦相似度编码了特征之间的测地距离，并在颜色、日期与年份三类数据上实证验证了同胚性与等距性。","2026-08-04T00:00:00+08:00",[95,141],"blog\u002Fblog\u002F2026\u002F2026-08-04-the-representations-in-llm.md",{"title":234,"summary":235,"image":168,"time":236,"tags":237,"path":148,"id":238},"对角线论证：改变数学与计算机的证明方法","对角线论证由康托尔于 1891 年提出，通过构造一个能逃脱任何「完备列表或映射」的对象，证明某些无穷严格大于另一些无穷。这一自指技巧同样蕴含于康托尔定理、图灵停机问题与哥德尔不完备定理之中——一个统一了集合论、可计算性与逻辑学的思想。","2026-07-31T00:00:00+08:00",[38,53],"blog\u002Fblog\u002F2026\u002F2026-07-31-the-diagonal-argument-en.md",{"title":240,"summary":241,"image":168,"time":242,"tags":243,"path":145,"id":244},"在开始 AGI 之前，先定义它","AGI 研究仍停留在经验层面，缺乏基础性的理论框架。计算主义与不可判定问题之间存在核心张力，AIXI 正是一个例证。作者提出，与环境保持连续的因果耦合可能是缺失的公理，并呼吁寻找能约束任何物理可实现智能的根本性约束原理。","2026-07-30T00:00:00+08:00",[141,6],"blog\u002Fblog\u002F2026\u002F2026-07-30-what-agi-needs-may-not-be-a-larger-model-but-a-set-of-theories.md",{"title":246,"summary":247,"image":168,"time":248,"tags":249,"path":142,"id":250},"涌现是幻象吗？","Schaeffer 等人表明，LLM 的「涌现能力」往往只是不连续的指标掩盖了平滑的能力增长。但 grokking、归纳头以及居里点式的转变都证明，真实的相变确实存在。","2026-06-30T00:00:00+08:00",[141,95,6],"blog\u002Fblog\u002F2026\u002F2026-06-30-about-the-emergency.md",{"title":252,"summary":253,"image":168,"time":254,"tags":255,"path":138,"id":256},"最大似然估计视角下的神经网络","从统计学习的视角看，现代神经网络确实可以理解为一个大规模的最大似然估计（MLE）过程。具体而言，神经网络是一个参数化函数，而最常见的训练方式正是在数据上做最大似然估计。","2026-06-08T00:00:00+08:00",[38,95,76],"blog\u002Fblog\u002F2026\u002F2026-06-08-explanation-of-neural-network-from-maximum-likelihood-estimation.md",{"title":258,"summary":259,"image":168,"time":260,"tags":261,"path":135,"id":262},"魏尔斯特拉斯理论下的 UAT 证明","UAT（通用逼近定理）的核心要旨是：神经网络能逼近任何连续函数，而连续函数又可用多项式逼近（魏尔斯特拉斯定理）。","2026-06-06T00:00:00+08:00",[95,38],"blog\u002Fblog\u002F2026\u002F2026-06-06-proof-of-the-uat-by-weierstrass-theory.md",{"title":264,"summary":265,"image":168,"time":266,"tags":267,"path":132,"id":268},"张量 Tensor 简述","向量是箭头，对偶向量是标尺——它们的配对产生不变的标量。张量是带多个可填充槽位的线性机器，化解了「向量进向量出」与「输出标量」之间的悖论。度量张量连接二者，使长度与能量保持坐标不变。","2026-05-30T00:00:00+08:00",[38,95],"blog\u002Fblog\u002F2026\u002F2026-05-30-about-the-tensor.md",{"title":270,"summary":271,"image":168,"time":272,"tags":273,"path":129,"id":274},"The Messianic Narrative of Anthropic","The theatrics of Anthropic, led by Dario Amodei, exhibit the quintessential characteristics of the Judaic Messianic narrative, whose structure typically proceeds as follows: the world confronts an immense crisis of which the majority remains unaware; only a select few prophets perceive the danger; these prophets must be entrusted with authority; and they shall deliver salvation to the world.","2026-05-26T00:00:00+08:00",[6],"blog\u002Fblog\u002F2026\u002F2026-05-26-the-messianic-narrative-of-anthropic.md",{"title":276,"summary":277,"image":168,"time":278,"tags":279,"path":126,"id":280},"暗淡蓝点","所有的战争与和平，爱恨与悲欢，都在这颗名为「地球」的微尘上，日复一日地上演。","2026-05-13T00:00:00+08:00",[6],"blog\u002Fblog\u002F2026\u002F2026-05-13-the-pale-blue-dot.md",{"title":282,"summary":283,"image":168,"time":284,"tags":285,"path":123,"id":286},"Fréchet 均值原型","Fréchet 均值原型是度量空间中使到所有数据点距离平方和最小的中心点。它将求平均的运算从平坦向量空间推广到任意弯曲空间或复杂对象。","2026-04-25T00:00:00+08:00",[38,95],"blog\u002Fblog\u002F2026\u002F2026-04-25-the-frechet-mean-prototype.md",{"title":288,"summary":289,"image":168,"time":290,"tags":291,"path":120,"id":292},"函数变化：梯度、雅可比和海塞矩阵","三者递进关系体现在：海塞矩阵是梯度的雅可比矩阵。即先对函数求一阶得梯度，再将梯度视为新的向量函数求一阶雅可比，自然就得到了二阶海塞。从这个角度看，雅可比是求导算子的矩阵化，而海塞是这一过程的二次应用。","2026-04-23T20:45:13+08:00",[38,95],"blog\u002Fblog\u002F2026\u002F2026-04-23-shu-de-bian-hua-ti-du-ya-ke-bi-ju-zhen-he-hai-sai-ju-zhen.md",{"title":294,"summary":295,"image":168,"time":296,"tags":297,"path":117,"id":298},"零曲率与正曲率空间中的维数灾难","维数灾难并非某种特定的几何结构，而是由高维空间内在性质所引发的一类现象。","2026-04-10T00:00:00+08:00",[38,95],"blog\u002Fblog\u002F2026\u002F2026-04-10-dimension-curse-on-zero-and-positive-curvature-space.md",{"title":300,"summary":301,"image":168,"time":302,"tags":303,"path":114,"id":304},"超球面上的 vMF 分布简介","von Mises–Fisher 分布（vMF）通常被视为正态分布在超球面上的对应物，因为它刻画了在单位超球面上围绕某一平均方向聚集的数据。","2026-04-09T00:00:00+08:00",[95,38],"blog\u002Fblog\u002F2026\u002F2026-04-09-introduction-of-v-mf-distribution-on-hypersphere.md",{"title":306,"summary":307,"image":168,"time":308,"tags":309,"path":111,"id":310},"非线性与激活函数","线性要求满足可加性与齐次性，但神经网络需要非线性才能摆脱简单的仿射变换。仿射层只能对数据进行拉伸和旋转，而不改变其拓扑结构；激活函数则能实现复杂的形变，使网络能够解开数据流形，有效地学习复杂模式。","2026-04-06T00:00:00+08:00",[38,95],"blog\u002Fblog\u002F2026\u002F2026-04-06-nonlinearity-with-activations.md",{"title":312,"summary":313,"image":205,"time":314,"tags":315,"path":89,"id":316},"斯特林公式","斯特林公式揭示了当 n 趋向无穷大时 n!、nⁿ 与 eⁿ 之间的关系。","2025-09-18T00:00:00+08:00",[38],"blog\u002Fblog\u002F2025\u002F2025-09-18-the-stirling-formula.md",{"title":318,"summary":319,"image":205,"time":320,"tags":321,"path":86,"id":322},"可叹的程序员们","许多软件工程师和程序员常常陷入一种困境：他们对自己所掌握的技术细节沾沾自喜，却很少意识到生活中几乎没有什么事情与代码有关。","2025-08-17T00:00:00+08:00",[6],"blog\u002Fblog\u002F2025\u002F2025-08-17-the-lamentable-programmers.md",{"title":324,"summary":325,"image":326,"time":327,"tags":328,"path":83,"id":329},"考上了，但似乎也没有那么开心","2025 年研招已经落幕，考上了，但似乎也并没有那么开心。日后，救赎之道仍待探索，毕竟，人生是旷野嘛。","https:\u002F\u002Fimage-assets.dreams.plus\u002F20250507130209622.png","2025-05-07T00:00:00+08:00",[6],"blog\u002Fblog\u002F2025\u002F2025-05-07-kao-shang-le.md",{"title":331,"summary":332,"image":205,"time":333,"tags":334,"path":80,"id":335},"计算机科学专业的学生应当学习大学物理吗","中国的计算机科学教育因历史与体制的惯性而显得过时，常常包含物理这类不相关的科目。","2025-01-11T00:00:00+08:00",[6],"blog\u002Fblog\u002F2025\u002F2025-01-11-should-computer-science-majors-learn-college-physics.md",{"title":337,"summary":338,"image":205,"time":339,"tags":340,"path":77,"id":341},"苏格拉底：寻找最大的麦穗的故事","本文介绍了博弈论中经典的 37% 法则及其数学推导过程。","2024-09-21T00:00:00+08:00",[76,49],"blog\u002Fblog\u002F2024\u002F2024-09-21-the-37-rules-in-making-choice.md",{"title":343,"summary":344,"image":205,"time":345,"tags":346,"path":73,"id":347},"Box-Muller 变换","Box-Muller 变换是一种利用服从均匀分布的随机变量构造服从高斯分布的随机变量的方法。","2024-09-12T00:00:00+08:00",[38],"blog\u002Fblog\u002F2024\u002F2024-09-12-box-muller-transformation.md",{"title":349,"summary":350,"image":205,"time":351,"tags":352,"path":70,"id":353},"线性同余伪随机数","线性同余法是一种基于确定性数学算法生成随机数序列的伪随机数生成方法。","2024-09-11T00:00:00+08:00",[38,69],"blog\u002Fblog\u002F2024\u002F2024-09-11-linear-congruential-for-psedurandom-number.md",{"title":355,"summary":356,"image":205,"time":357,"tags":358,"path":66,"id":359},"行列式的 Laplace 定理","行列式中 Laplace 定理及其应用","2024-08-27T00:00:00+08:00",[38],"blog\u002Fblog\u002F2024\u002F2024-08-27-the-laplace-theorem-for-determinant.md",{"title":361,"summary":362,"image":205,"time":363,"tags":364,"path":63,"id":365},"Bernoulli 数入门","Bernoulli 数的介绍、推导与证明","2024-04-23T00:00:00+08:00",[38],"blog\u002Fblog\u002F2024\u002F2024-04-23-introduction-to-bernoulli-number.md",{"title":367,"summary":368,"image":205,"time":369,"tags":370,"path":60,"id":371},"Taylor 公式、Taylor 定理、Taylor 级数与 Taylor 展开","本文主要介绍 Taylor 公式、Taylor 定理、Taylor 级数与 Taylor 展开这四个概念的内容及其相互联系。","2024-03-06T00:00:00+08:00",[38],"blog\u002Fblog\u002F2024\u002F2024-03-06-taylor-formula-taylor-theorem-taylor-series-taylor-expansion.md",{"title":373,"summary":374,"image":205,"time":375,"tags":376,"path":57,"id":377},"Faulhaber 公式的证明","Faulhaber 公式提供了一种计算前 n 个正整数 p 次方之和的方法。","2024-03-05T00:00:00+08:00",[38],"blog\u002Fblog\u002F2024\u002F2024-03-05-proof-of-faulhabers-formula.md",{"title":379,"summary":380,"image":205,"time":381,"tags":382,"path":54,"id":383},"时间复杂度主定理","本文用数学方法对分治算法的时间复杂度建模，分析其渐近性质，并给出三种计算方法。","2023-12-18T00:00:00+08:00",[42,38,53],"blog\u002Fblog\u002F2023\u002F2023-12-18-The-Master-Theroy-For-Time-Complexity.md",{"title":385,"summary":386,"image":205,"time":387,"tags":388,"path":50,"id":389},"巴什博弈","一堆石子，两人轮流取，至少取 1 颗、至多取 2 颗，取到最后一颗石子的人输。","2023-12-14T00:00:00+08:00",[42,49],"blog\u002Fblog\u002F2023\u002F2023-12-14-the-bash-game.md",{"title":391,"summary":392,"image":205,"time":393,"tags":394,"path":46,"id":395},"快速平方根倒数算法","本文介绍一种名为快速平方根倒数（Fast Inverse Square Root）的算法，用于快速计算浮点数的平方根倒数。","2023-12-08T00:00:00+08:00",[38,42],"blog\u002Fblog\u002F2023\u002F2023-12-08-Fast-Inverse-Square-Root.md",{"title":397,"summary":398,"image":205,"time":399,"tags":400,"path":43,"id":401},"计算机如何计算对数函数","从数值分析的角度，分析计算机中对数函数的底层实现。","2023-12-07T00:00:00+08:00",[42,38],"blog\u002Fblog\u002F2023\u002F2023-12-07-How-do-computer-calculate-the-log-function.md",{"title":403,"summary":404,"image":205,"time":405,"tags":406,"path":39,"id":407},"用矩阵法与差分方程法推导斐波那契通项公式","本文给出两种推导斐波那契数列的方法：矩阵法与差分方程法。","2023-11-20T00:00:00+08:00",[38],"blog\u002Fblog\u002F2023\u002F2023-11-20-conduct-the-fibonacci.md",{"title":409,"summary":410,"image":205,"time":411,"tags":412,"path":35,"id":413},"C\u002FC++ 跨平台编译宏","在编译跨平台程序时，我们难免会遇到  win32、  linux 等编译器或编译环境宏。它们向编译器指示当前平台环境的一些信息。","2023-11-05T00:00:00+08:00",[34],"blog\u002Fblog\u002F2023\u002F2023-11-05-platform-macros.md",{"title":415,"summary":416,"image":205,"time":417,"tags":418,"path":7,"id":419},"做开源应当无私吗？","记住，做开源重要的是为了自己，而不是为了别人，不要委屈自己。","2023-02-27T00:00:00+08:00",[6],"blog\u002Fblog\u002F2022\u002F2022-02-27-how-to-do-open-source-for-a-long-time.md",{"title":421,"summary":422,"image":205,"time":423,"tags":424,"path":31,"id":425},"送東陽馬生序","余朝京師，生以鄉人子謁余，譔長書以為贄，辭甚暢達；與之論辯，言和而色夷。自謂少時用心於學甚勞，是可謂善學者矣。其將歸見其親也，余故道為學之難以告之。謂余勉鄉人以學者，余之志也；詆我夸際遇之盛而驕鄉人者，豈知予者哉。","2022-12-07T00:00:00+08:00",[18],"blog\u002Fblog\u002F2022\u002F2022-12-07-A-Farewell-to-Ma-Junze-of-Dongyang.md",{"title":427,"summary":428,"image":205,"time":429,"tags":430,"path":28,"id":431},"操作系统笔记：多处理器调度的两种方法","介绍多处理器调度的两种方法：对称多处理与非对称多处理。","2022-12-05T00:00:00+08:00",[10],"blog\u002Fblog\u002F2022\u002F2022-12-05-multi-cpu-process-scheduling.md",{"title":433,"summary":434,"image":205,"time":435,"tags":436,"path":19,"id":437},"顏真卿傳 - 新唐書","顏真卿，字清臣，秘書監師古五世從孫。少孤，母殷躬加訓導。既長，博學工辭章，事親孝。","2022-09-16T00:00:00+08:00",[18],"blog\u002Fblog\u002F2022\u002F2022-09-14-yanzhenqing-bibiography.md",{"title":439,"summary":440,"image":205,"time":435,"tags":441,"path":22,"id":442},"蘭亭集序","永和九年，歲在癸丑，暮春之初，會於會稽山陰之蘭亭，修禊事也。群賢畢至，少長咸集。此地有崇山峻嶺，茂林修竹；又有清流激湍，映帶左右，引以為流觴曲水，列坐其次。雖無絲竹管弦之盛，一觴一詠，亦足以暢敘幽情。",[18],"blog\u002Fblog\u002F2022\u002F2022-09-15-lanting-prelude.md",{"title":444,"summary":445,"image":205,"time":435,"tags":446,"path":25,"id":447},"沈煉 楊繼盛傳 - 明史","煉爲人剛直，嫉惡如仇，然頗疎狂。毎飲酒輒箕踞笑傲，旁若無人。錦衣帥陸炳善遇之。炳與嚴嵩父子交至深，以故煉亦數從世蕃飲。世蕃以酒虐客，煉心不平，輒爲反之，世蕃憚不敢較。",[18],"blog\u002Fblog\u002F2022\u002F2022-09-16-biology-of-shen-lian-and-yang-jisheng.md",{"title":449,"summary":450,"image":205,"time":451,"tags":452,"path":15,"id":453},"JavaScript 中的闭包","给出 JavaScript 中闭包的定义，并通过示例来理解它。","2022-04-18T00:00:00+08:00",[14],"blog\u002Fblog\u002F2022\u002F2022-04-18-Closure-in-javascript.md",{"title":455,"summary":456,"image":205,"time":457,"tags":458,"path":11,"id":459},"并发中的资源锁","对自旋锁、乐观锁、悲观锁、读写锁、互斥锁等概念的分析及使用场景。","2022-04-15T00:00:00+08:00",[10],"blog\u002Fblog\u002F2022\u002F2022-04-15-Resource-Lock-in-Concurrency.md",1792183813801]