docs(chapter4): 修正奖励模型公式中的数学符号和格式错误

修复公式中的数学符号显示问题，包括 KL 散度计算和奖励函数中的点乘符号

.gitignore

@@ -0,0 +1,162 @@
+# Byte-compiled / optimized / DLL files
+__pycache__/
+*.py[cod]
+*$py.class
+.idea/
+# C extensions
+*.so
+
+# Distribution / packaging
+.Python
+build/
+develop-eggs/
+dist/
+downloads/
+eggs/
+.eggs/
+lib/
+lib64/
+parts/
+sdist/
+var/
+wheels/
+share/python-wheels/
+*.egg-info/
+.installed.cfg
+*.egg
+MANIFEST
+
+# PyInstaller
+#  Usually these files are written by a python script from a template
+#  before PyInstaller builds the exe, so as to inject date/other infos into it.
+*.manifest
+*.spec
+
+# Installer logs
+pip-log.txt
+pip-delete-this-directory.txt
+
+# Unit test / coverage reports
+htmlcov/
+.tox/
+.nox/
+.coverage
+.coverage.*
+.cache
+nosetests.xml
+coverage.xml
+*.cover
+*.py,cover
+.hypothesis/
+.pytest_cache/
+cover/
+
+# Translations
+*.mo
+*.pot
+
+# Django stuff:
+*.log
+local_settings.py
+db.sqlite3
+db.sqlite3-journal
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+# Flask stuff:
+instance/
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+target/
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+profile_default/
+ipython_config.py
+
+# pyenv
+#   For a library or package, you might want to ignore these files since the code is
+#   intended to run in multiple environments; otherwise, check them in:
+# .python-version
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+# pipenv
+#   According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
+#   However, in case of collaboration, if having platform-specific dependencies or dependencies
+#   having no cross-platform support, pipenv may install dependencies that don't work, or not
+#   install all needed dependencies.
+#Pipfile.lock
+
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+#   Similar to Pipfile.lock, it is generally recommended to include poetry.lock in version control.
+#   This is especially recommended for binary packages to ensure reproducibility, and is more
+#   commonly ignored for libraries.
+#   https://python-poetry.org/docs/basic-usage/#commit-your-poetrylock-file-to-version-control
+#poetry.lock
+
+# pdm
+#   Similar to Pipfile.lock, it is generally recommended to include pdm.lock in version control.
+#pdm.lock
+#   pdm stores project-wide configurations in .pdm.toml, but it is recommended to not include it
+#   in version control.
+#   https://pdm.fming.dev/#use-with-ide
+.pdm.toml
+
+# PEP 582; used by e.g. github.com/David-OConnor/pyflow and github.com/pdm-project/pdm
+__pypackages__/
+
+# Celery stuff
+celerybeat-schedule
+celerybeat.pid
+
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+*.sage.py
+
+# Environments
+.env
+.venv
+env/
+venv/
+ENV/
+env.bak/
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+#  option (not recommended) you can uncomment the following to ignore the entire idea folder.
+#.idea/
+.DS_Store
+.obsidian

docs/chapter4/第四章 大语言模型.md

@@ -339,9 +339,9 @@ RM，Reward Model，即奖励模型。RM 是用于拟合人类偏好，来给 LL
 
 1. 从 SFT 之后的 LLM 初始化两个模型分别作为 Actor Model 和 Ref Model；从训练的 RM 初始化两个模型分别作为 Reward Model 和 Critic Model；
 2. 输入一个 Prompt，Actor Model 和 Ref Model 分别就 Prompt 生成回复；
-3. Actor Response 和 Ref Response 计算 KL 散度：$r_{KL} = -\theta_{KL}D_{KL}(\pi_{PPO}(y|x)||\pi_{base}(y|x))$其中，$\pi_{PPO}(y|x)$即为 Actor Model 的输出，而 $\pi_{base}(y|x)$即为 Ref Model 的输出，$theta_{KL}D_{KL}$即是计算 KL 散度的方法；
+3. Actor Response 和 Ref Response 计算 KL 散度：$r_{KL} = -\theta_{KL}D_{KL}(\pi_{PPO}(y|x)||\pi_{base}(y|x))$其中，$\pi_{PPO}(y|x)$即为 Actor Model 的输出，而 $\pi_{base}(y|x)$即为 Ref Model 的输出，$\theta_{KL}D_{KL}$即是计算 KL 散度的方法；
 4. Actor Response 分别输入到 Reward Model 和 Critic Model 进行打分，其中，Reward Model 输出的是回复对应的标量奖励，Critic Model 还会输出累加奖励（即从i位置到最后的累积奖励）；
-5. 计算的 KL 散度、两个模型的打分均输入到奖励函数中，计算奖励：$loss = -(kl_{ctl}*r_{KL} + \gamma * V_{t+1} - V_{t})logP(A_t|V_t)$，这里的 $kl_{ctl}是控制 KL 散度对结果影响的权重参数，$\gamma$ 是控制下一个时间（也就是样本）打分对结果影响的权重参数，$V_t$ 是 Critic Model 的打分输出，$A_t$ 则是 Reward Model 的打分输出;
+5. 计算的 KL 散度、两个模型的打分均输入到奖励函数中，计算奖励：$loss = -(kl_{ctl} \cdot r_{KL} + \gamma \cdot V_{t+1} - V_{t}) \log P(A_t|V_t)$，这里的 $kl_{ctl}$ 是控制 KL 散度对结果影响的权重参数，$\gamma$ 是控制下一个时间（也就是样本）打分对结果影响的权重参数，$V_t$ 是 Critic Model 的打分输出，$A_t$ 则是 Reward Model 的打分输出;
 6. 根据奖励函数分别计算出的 actor loss 和 critic loss，更新 Actor Model 的参数和 Critic Model 的参数；注意，Actor Model 和 Critic Model 的参数更新方法是不同的，此处就不再一一赘述了，感兴趣的读者可以深入研究强化学习的相关理论。
 
 在上述过程中，因为要使用到四个模型，显存占用会数倍于 SFT。例如，如果我们 RM 和 LLM 都是用 7B 的体量，PPO 过程中大概需要 240G（4张 80G A100，每张卡占用 60G）显存来进行模型加载。那么，为什么我们需要足足四个模型呢？Actor Model 和 Critic Model 较为容易理解，而之所以我们还需要保持原参数不更新的 Ref Model 和 Reward Model，是为了限制模型的更新不要过于偏离原模型以至于丢失了 Pretrain 和 SFT 赋予的能力。