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‎docs/categories/index.md‎

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<div class="landing-page-marker" aria-hidden="true"></div>
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# 分类
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先选择要学习的方向，再进入对应分类的文章目录。
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<div class="category-directory">
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<a class="category-directory__card" href="math-post-training/">
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<span class="category-directory__count">2 篇</span>
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<strong>从数学讲清后训练</strong>
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<span>从目标函数、概率分布与优化过程出发，理解后训练算法为什么成立。</span>
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<em>进入分类目录 →</em>
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</a>
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<a class="category-directory__card" href="post-training-basics/">
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<span class="category-directory__count">1 篇</span>
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<strong>后训练基础</strong>
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<span>补齐模型结构、训练链路与实现基础，为具体后训练算法建立统一底座。</span>
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<em>进入分类目录 →</em>
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</a>
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</div>

‎docs/categories/math-post-training.md‎

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# 从数学讲清后训练
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---
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这个分类从目标函数、概率分布与优化过程出发，重点回答后训练算法中的公式为什么成立，以及这些公式最终如何改变模型的生成分布。
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<div class="landing-page-marker" aria-hidden="true"></div>
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## 收录内容
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# 从数学讲清后训练
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### [在分布视角下理解语言模型后训练](../post-training/distributional-view.md)
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这个分类从目标函数、概率分布与优化过程出发，重点回答后训练算法中的公式为什么成立，以及这些公式最终如何改变模型的生成分布。
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从“语言模型是一个序列分布”出发，将生成过程展开成自回归概率树，并在同一视角下理解 SFT、RL 与 OPD。
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[← 返回全部分类](index.md)
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### [DPO 为什么只做偏好分类，却“自带” KL 约束？](../post-training/dpo-implicit-kl.md)
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<div class="directory-list">
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<article class="directory-item">
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<div class="directory-item__meta">
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<time datetime="2026-07-14">2026.07.14</time>
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<span>分布视角</span>
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</div>
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<h2><a href="../../post-training/distributional-view/">在分布视角下理解语言模型后训练</a></h2>
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<p>从“语言模型是一个序列分布”出发，将生成过程展开成自回归概率树，并在同一视角下理解 SFT、RL 与 OPD。</p>
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<a href="../../post-training/distributional-view/">阅读文章 →</a>
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</article>
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从 KL-Regularized Reward Maximization 出发，推导最优策略、Reward 表达与 DPO Loss 之间的关系。
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<article class="directory-item">
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<div class="directory-item__meta">
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<time datetime="2026-07-14">2026.07.14</time>
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<span>DPO</span>
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</div>
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<h2><a href="../../post-training/dpo-implicit-kl/">DPO 为什么只做偏好分类，却“自带” KL 约束？</a></h2>
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<p>从 KL-Regularized Reward Maximization 出发，推导最优策略、Reward 表达与 DPO Loss 之间的关系。</p>
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<a href="../../post-training/dpo-implicit-kl/">阅读文章 →</a>
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</article>
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</div>

‎docs/categories/post-training-basics.md‎

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# 后训练基础
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这个分类整理进入 SFT、DPO、PPO、GRPO 等后训练方法之前，需要先掌握的模型结构、训练链路与实现基础。
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## 收录内容
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### [PyTorch 训练底层与 CausalLM 手撕](../post-training-basics/pytorch-training-causallm.md)
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[← 返回全部分类](index.md)
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从 Tensor、计算图、梯度与 AdamW 出发，串起 CausalLM 的 Logprob、Loss 和参数更新，并进一步手写最小 Llama 风格 Transformer。
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<time datetime="2026-07-15">2026.07.15</time>
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<span>PyTorch / CausalLM</span>
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</div>
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<h2><a href="../../post-training-basics/pytorch-training-causallm/">PyTorch 训练底层与 CausalLM 手撕</a></h2>
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<p>从 Tensor、计算图、梯度与 AdamW 出发，串起 CausalLM 的 Logprob、Loss 和参数更新，并进一步手写最小 Llama 风格 Transformer。</p>
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<a href="../../post-training-basics/pytorch-training-causallm/">阅读文章 →</a>
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</article>
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</div>

‎docs/download.md‎

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# 获取笔记
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## 下载完整内容
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<span class="rem-hero__eyebrow">REM'S LLM NOTES</span>
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## 内容分类
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<div class="grid cards" markdown>
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## 快速入口
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- **从数学讲清后训练**
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从目标函数、概率分布与优化过程出发，理解后训练算法为什么成立。
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[进入分类](categories/math-post-training.md)
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<nav class="portal-grid" aria-label="站点主要入口">
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<a class="portal-card portal-card--current" href="#rem-hero-title">
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<span class="portal-card__index">01</span>
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<strong>简介</strong>
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<span>了解这个站点记录什么，以及笔记的整理方式。</span>
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</a>
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<a class="portal-card" href="categories/">
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<span class="portal-card__index">02</span>
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<strong>分类</strong>
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<span>先选择学习方向，再进入该分类的文章目录。</span>
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</a>
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<a class="portal-card" href="updates/">
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<span class="portal-card__index">03</span>
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<strong>最新更新</strong>
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<span>按发布日期查看更新，并直接进入具体文章。</span>
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</a>
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<a class="portal-card" href="download/">
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<span class="portal-card__index">04</span>
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<strong>下载入口</strong>
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<span>下载完整仓库、单篇 Markdown 原稿与相关图片。</span>
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</a>
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</nav>
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- **后训练基础**
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## 最新更新
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补齐模型结构、训练链路与实现基础，为后续学习 SFT、DPO、PPO、GRPO 建立统一底座。
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<div class="updates-list">
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<article class="latest-note-card">
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<div class="latest-note-card__meta">
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<time datetime="2026-07-15">2026.07.15</time>
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<span>后训练基础</span>
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</div>
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<h3><a href="post-training-basics/pytorch-training-causallm/">PyTorch 训练底层与 CausalLM 手撕</a></h3>
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<p>从 Tensor、计算图和 AdamW 开始，串起 CausalLM 的前向传播、Loss、反向传播与参数更新。</p>
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<a class="latest-note-card__link" href="post-training-basics/pytorch-training-causallm/">直接阅读 →</a>
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</article>
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[进入分类](categories/post-training-basics.md)
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<article class="latest-note-card">
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<div class="latest-note-card__meta">
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<time datetime="2026-07-14">2026.07.14</time>
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<span>从数学讲清后训练</span>
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</div>
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<h3><a href="post-training/dpo-implicit-kl/">DPO 为什么只做偏好分类，却“自带” KL 约束？</a></h3>
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<p>从 KL-Regularized RL 出发，推导最优策略、Reward 表达与 DPO Loss 之间的关系。</p>
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<a class="latest-note-card__link" href="post-training/dpo-implicit-kl/">直接阅读 →</a>
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</article>
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<article class="latest-note-card">
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<div class="latest-note-card__meta">
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<time datetime="2026-07-14">2026.07.14</time>
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<span>从数学讲清后训练</span>
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</div>
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<h3><a href="post-training/distributional-view/">在分布视角下理解语言模型后训练</a></h3>
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<p>从序列分布与自回归概率树出发，在同一视角下理解 SFT、RL 与 OPD。</p>
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<a class="latest-note-card__link" href="post-training/distributional-view/">直接阅读 →</a>
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## 最新收录
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<span>后训练基础</span>
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<h3><a href="post-training-basics/pytorch-training-causallm/">PyTorch 训练底层与 CausalLM 手撕</a></h3>
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<p>从 Tensor、Parameter、计算图和 AdamW 开始，串起 CausalLM 的前向传播、Loss、反向传播与参数更新，并进一步手写最小 Llama 风格 Transformer。</p>
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<a class="latest-note-card__link" href="post-training-basics/pytorch-training-causallm/">阅读文章 →</a>
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<p class="section-more"><a href="updates/">查看全部更新记录 →</a></p>
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## 获取原文
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## 下载入口
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- [查看 GitHub 仓库](https://github.com/kaining-never-stop/llm-learning-notes)
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- [查看全部 Markdown 原文](https://github.com/kaining-never-stop/llm-learning-notes/tree/main/docs)
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Markdown 原稿、数学公式和文章图片均保留在 GitHub 仓库中。
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更多下载方式见[获取笔记](download.md)。
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[前往下载页面](download.md){ .md-button .md-button--primary }

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