机器学习基础Machine Learning Foundations
六章、29 节，备齐现代机器人学习要用的整套工具：从数据中学习与网络架构讲怎样拟合、怎样求梯度、该搭什么样的网络，从逻辑回归走到 Transformer 和动作 token；自监督学习讲没有标签时怎样学到好的表示；生成模型讲怎样学会整个分布，从 VAE 一路走到扩散与 flow matching，也就是 Diffusion Policy 和 π0 的引擎；强化学习讲怎样从奖励里学策略，从 Bellman 方程走到 PPO、SAC 与离线 RL；专题讲微调、scaling law、不确定性与多任务。每一节都有在浏览器里现场运行的实验，大多是现场训练的小网络，例子都来自机器人。 Six chapters and 29 lessons that assemble the toolbox of modern robot learning: learning from data and network architectures cover how to fit, how to get gradients and which network to build, from logistic regression to transformers and action tokens; self-supervised learning covers learning good representations without labels; generative models cover learning a whole distribution, from VAEs to diffusion and flow matching, the engines of Diffusion Policy and π0; reinforcement learning covers learning a policy from rewards, from the Bellman equations to PPO, SAC and offline RL; special topics cover fine-tuning, scaling laws, uncertainty and multi-task learning. Every lesson has labs that run live in your browser, most of them small networks trained on the spot, on robot examples.
1六章之间的关系How the six chapters connect
第 16 章是其他各章的地基：损失、泛化和反向传播在后面几章里反复用到。架构（17 章）喂给自监督（18 章）和生成模型（19 章）；强化学习（20 章）主要建立在 Part I 的概率与动态规划之上，逆强化学习一节还借用了 GAN 的判别器。来自前面的部分主要是 Part I 的线性代数、微积分、概率与优化，另有 Part II 的构型空间和 Part IV 的状态空间模型。把鼠标放在（或点击）任意一个方块上：琥珀色是它依赖的部分，紫色是用到它的部分；虚线框是前面的章节或后续部分，本部分各章之间的依赖画成右侧的弧线。每一节具体依赖哪几节，见第 3 部分。
Chapter 16 is the foundation of the others: losses, generalization and backpropagation come back again and again in the later chapters. Architectures (chapter 17) feed self-supervised learning (chapter 18) and generative models (chapter 19); reinforcement learning (chapter 20) rests mainly on Part I's probability and dynamic programming, and its inverse-RL lesson borrows the discriminator of a GAN. From earlier parts come mainly Part I's linear algebra, calculus, probability and optimization, plus configuration space from Part II and the state-space model from Part IV. Hover (or tap) any box: amber shows what it builds on, purple shows what builds on it; dashed boxes are earlier chapters or later parts, and dependencies between this part's chapters are drawn as arcs on the right. Section 3 lists exactly which lessons each lesson builds on.
2各章一览The chapters
★ 标记的是核心节，点击标题即可进入（灰色的是尚未上线的节）。每章都会写出它的"一句话直觉"和在机器人中的主要用途。
★ marks core lessons; click a title to open it (greyed-out lessons are not live yet). Each chapter lists its one-line intuition and its main uses in robotics.
3逐节内容与前置Each lesson and what it builds on
每节一句话说明它讲什么，下面列出该节自己标注的前置节。青色边框的是本部分内的前置节，其余来自 Part I–IV；点击即可跳转。
Each lesson gets one line on what it covers, followed by the prerequisites the lesson itself lists. Prerequisites with a cyan border are inside this part; the rest come from Parts I–IV. Click one to jump there.
4按目标选路线Pick a route by goal
时间有限的话，可以按你的方向挑一条路线先走通，再回头补全。路线里跳过的节，遇到时看第 3 部分列出的前置即可。
Short on time? Pick the route that matches your direction, walk it end to end, then come back and fill in the rest. When a route skips a lesson you turn out to need, the prerequisites in section 3 show where to look.