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notes/2025/mvp/chapters/4-nn.tex
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25 changes: 25 additions & 0 deletions docs/superpowers/specs/2026-07-11-a5-chinese-notes-design.md
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# A5 中文讲义副本设计

## 目标

在不修改现有 A4 中文版 `notes/2025/mvp-cn` 的前提下,创建独立的 A5 竖版副本 `notes/2025/mvp-cn-a5`。A5 版必须保留完整内容、公式、插图、标签与交叉引用,并形成可直接阅读和打印的 PDF。

## 选定版式

采用用户确认的“均衡版”:纸张尺寸为 A5(148 × 210 mm),正文约 10 pt,页边距约 13–14 mm。目标是在小开本上保持舒适阅读,同时避免紧凑版的拥挤感和大字版过多的分页。

## 实现方式

完整复制当前中文版本,然后只在新副本中调整主文档的纸张和页面几何参数。正文必须由 LaTeX 针对 A5 页面重新换行和分页,不采用把 A4 PDF 等比例缩小的方式。封面缩放到 A5 页面;章节源码和本地化插图默认保持不变。

如果完整构建发现超宽公式、表格、算法或插图,仅在 A5 副本中做局部、最小化的版式修正。修正不得删改内容、改变数学含义或反向影响 A4 中文版。

## 文件边界

源版本为 `notes/2025/mvp-cn`,目标版本为 `notes/2025/mvp-cn-a5`。A4 中文版、英文版、2024 notes 和 slides 均不在修改范围内。

## 验证标准

使用 XeLaTeX/latexmk 完整构建 A5 主文档。最终 PDF 的页面尺寸必须由 `pdfinfo` 验证为 A5;构建日志不得包含 LaTeX 错误、未定义引用、缺字或超出版心。渲染并视觉检查封面、目录、各章首页、公式密集页、算法页与插图页,确保无裁切、重叠、过小文字或孤立标题。

源版与 A5 版的 LaTeX 环境、标签、引用和插图集合必须保持一致;允许的差异仅限页面几何和必要的 A5 局部排版命令。
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4 changes: 4 additions & 0 deletions notes/2025/mvp/appendix/1-la.tex
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\documentclass[../main]{subfiles}
\begin{document}
\chapter{Linear Algebra}
\end{document}
4 changes: 4 additions & 0 deletions notes/2025/mvp/appendix/2-info.tex
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\documentclass[../main]{subfiles}
\begin{document}
\chapter{Information Theory}
\end{document}
4 changes: 4 additions & 0 deletions notes/2025/mvp/appendix/3-convex.tex
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\documentclass[../main]{subfiles}
\begin{document}
\chapter{Convex Analysis}
\end{document}
4 changes: 4 additions & 0 deletions notes/2025/mvp/appendix/4-diffgeo.tex
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\documentclass[../main]{subfiles}
\begin{document}
\chapter{Differential Geometry}
\end{document}
4 changes: 4 additions & 0 deletions notes/2025/mvp/appendix/5-lie.tex
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\documentclass[../main]{subfiles}
\begin{document}
\chapter{Lie Groups and Lie Algebras}
\end{document}
4 changes: 4 additions & 0 deletions notes/2025/mvp/appendix/6-mt.tex
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\documentclass[../main]{subfiles}
\begin{document}
\chapter{Measure Theory}
\end{document}
4 changes: 4 additions & 0 deletions notes/2025/mvp/appendix/7-pt.tex
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\documentclass[../main]{subfiles}
\begin{document}
\chapter{Probability Theory}
\end{document}
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\documentclass[../main]{subfiles}
\begin{document}
\chapter{Stochastic Optimization and Stochastic Differential Equations}
\end{document}
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\documentclass[../main]{subfiles}
\begin{document}
\chapter{Concentration Inequalities}
\end{document}
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Expand Up @@ -15,12 +15,10 @@ \section{Basic Knowledge of Linear Regression}
\item Dataset: $D=\{(x_i,y_i)\}_{i=1}^n$, where $x_i\in\mathbb{R}^d$ and $y_i\in\mathbb{R}$.
Here, $y_i$ denotes the regression target, while $x_i$ represents the input features used to predict $y_i$.

\item Linear Model: $f(x)=w^{\top}x+b$, with weight $w\in\mathbb{R}^d$ and bias $b\in\mathbb{R}$.
\item Linear Model: $f(x)=w^{\top}x+b$, with weight $w\in\mathbb{R}^d$ and bias $b\in\mathbb{R}$.
\begin{note}
This definition is equivalent to an inner product:
$\hat y = w^{\top}x+b.$
$\hat y = w^{\top}x+b.$
\end{note}

\begin{definition}[Learnable / Trainable Parameters]
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