> For the complete documentation index, see [llms.txt](https://yeasy.gitbook.io/llm_internals/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://yeasy.gitbook.io/llm_internals/di-si-bu-fen-mo-xing-yu-qian-yan-pian/appendix.md).

# 附录

本附录提供数学基础、实现示例、模型参数与参考资料。实践按两层组织：[A.6](/llm_internals/di-si-bu-fen-mo-xing-yu-qian-yan-pian/appendix/a6_practice_path.md) 用无需下载模型的 CPU 实验验证计算和状态；[A.7](/llm_internals/di-si-bu-fen-mo-xing-yu-qian-yan-pian/appendix/a7_framework_recipes.md) 将这些检查迁移到开源训练框架与推理服务。两者分别说明运行条件、验收要求和未覆盖的边界。