5388 lines
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向量
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矩阵
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统计学
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概率论
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机器学习
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计算语言学
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计算机视觉
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音频与语音
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多模态学习
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自主系统
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图神经网络
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计算机与操作系统
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数据结构与算法
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生产级软件工程
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概率论
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机器学习
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深度学习
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强化学习
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分布式深度学习
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</span>
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计算语言学
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文本处理与经典 NLP
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</span>
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</a>
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嵌入与序列模型
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高级文本生成
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目标检测与分割
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ViT 与生成模型
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</span>
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</a>
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视频与 3D 视觉
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</span>
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音频与语音
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<span class="md-nav__icon md-icon"></span>
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<span class="md-ellipsis">
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数字信号处理
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</span>
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</a>
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自动语音识别
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</span>
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</a>
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<span class="md-ellipsis">
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语音合成
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</span>
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</a>
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<span class="md-ellipsis">
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说话人与音频分析
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</span>
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</a>
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</li>
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<span class="md-ellipsis">
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源分离与降噪
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</span>
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</a>
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</ul>
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</nav>
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<span class="md-ellipsis">
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多模态学习
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</span>
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<span class="md-nav__icon md-icon"></span>
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</label>
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<span class="md-nav__icon md-icon"></span>
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多模态学习
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</label>
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<span class="md-ellipsis">
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多模态表征
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</span>
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</a>
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视觉语言模型
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<span class="md-ellipsis">
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图像与视频 Token 化
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<span class="md-ellipsis">
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跨模态生成
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter%2010%3A%20multimodal%20learning/05.%20unified%20multimodal%20architectures/" class="md-nav__link">
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<span class="md-ellipsis">
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统一多模态架构
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</span>
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
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<span class="md-ellipsis">
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自主系统
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</span>
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<span class="md-nav__icon md-icon"></span>
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</label>
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<span class="md-nav__icon md-icon"></span>
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自主系统
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
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感知
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<span class="md-ellipsis">
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机器人学习
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</span>
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</a>
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</li>
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<span class="md-ellipsis">
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视觉-语言-动作模型
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter%2011%3A%20autonomous%20systems/04.%20self-driving/" class="md-nav__link">
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<span class="md-ellipsis">
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自动驾驶
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter%2011%3A%20autonomous%20systems/05.%20space%20and%20extreme%20robotics/" class="md-nav__link">
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<span class="md-ellipsis">
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太空与极端机器人
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SIMD 与 GPU 编程
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ARM 与 NEON
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GPU 架构与 CUDA
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Triton、TPU 与 Pallas
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Vulkan Compute 与跨平台 GPU
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AI 推理
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AI 推理
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量化
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服务与批处理
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边缘推理
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扩缩与部署
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ML 系统设计
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ML 系统设计
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系统设计基础
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云计算
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</span>
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</a>
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大规模基础设施
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ML 系统设计
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</span>
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</a>
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ML 设计案例
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</span>
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</a>
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应用 AI
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应用 AI
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AI 金融
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</span>
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</a>
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<span class="md-ellipsis">
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蛋白质设计
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</span>
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</a>
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<a href="chapter%2019%3A%20applied%20AI/03.%20drug%20discovery/" class="md-nav__link">
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<span class="md-ellipsis">
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药物发现
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</span>
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</a>
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<li class="md-nav__item">
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<a href="chapter%2019%3A%20applied%20AI/04.%20agentic%20systems/" class="md-nav__link">
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<span class="md-ellipsis">
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智能体系统
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</span>
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</a>
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</li>
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<a href="chapter%2019%3A%20applied%20AI/05.%20healthcare/" class="md-nav__link">
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<span class="md-ellipsis">
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医疗健康
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前沿 AI
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前沿 AI
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<span class="md-ellipsis">
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量子机器学习
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神经形态计算
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太空数据中心
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去中心化 AI
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脑机接口
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</span>
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<div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
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目录
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概述
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<a href="#_3" class="md-nav__link">
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<span class="md-ellipsis">
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背景
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</span>
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</a>
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</li>
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<a href="#mcp" class="md-nav__link">
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MCP 服务器
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</span>
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</a>
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<li class="md-nav__item">
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<a href="#_4" class="md-nav__link">
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<span class="md-ellipsis">
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内容大纲
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</span>
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</a>
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<a href="#_5" class="md-nav__link">
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前言
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</a>
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<li class="md-nav__item">
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<a href="#_6" class="md-nav__link">
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<span class="md-ellipsis">
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如何更好地学习
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</span>
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</a>
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<a href="#_7" class="md-nav__link">
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关于作者
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</a>
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<a href="#_8" class="md-nav__link">
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<span class="md-ellipsis">
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引用
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</span>
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</a>
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</li>
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</ul>
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</div>
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<h1 id="_1">数学、计算机科学与人工智能纲要<a class="headerlink" href="#_1" title="Permanent link">¶</a></h1>
|
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<p><img src="images/logo.png" alt="Logo" style="border-radius: 30px; width: 100%;"></p>
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<p><strong>在线阅读</strong>: <a href="https://henryndubuaku.github.io/maths-cs-ai-compendium/">henryndubuaku.github.io/maths-cs-ai-compendium</a></p>
|
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<h2 id="_2">概述<a class="headerlink" href="#_2" title="Permanent link">¶</a></h2>
|
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<p>大多数教科书将好的思想埋没在密集的符号之下，跳过直觉，假设你已经掌握了一半的内容，并且在人工智能等快速发展的领域很快过时。这是一本开放、非传统的教科书，从零开始涵盖数学、计算机科学和人工智能。为那些希望深入理解知识、而不仅仅是为了通过考试或面试的好奇实践者而编写。</p>
|
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<h2 id="_3">背景<a class="headerlink" href="#_3" title="Permanent link">¶</a></h2>
|
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<p>在过去几年从事AI/ML工作的过程中，我用笔记本记录了数学、计算机科学和人工智能概念的直觉优先、结合实际、不打马虎眼的解释。2025年，几位朋友用这些笔记准备DeepMind、OpenAI、Nvidia等公司的面试。他们全部被录用，目前在工作中表现出色。而我去年也进入了Y Combinator。所以现在我把这些分享给所有人。</p>
|
|
<h2 id="mcp">MCP 服务器<a class="headerlink" href="#mcp" title="Permanent link">¶</a></h2>
|
|
<p>本仓库包含一个MCP服务器，允许任何AI助手（Claude Code、Cursor、VS Code等）将这本纲要作为知识库使用。它需要本地克隆该仓库。内置教育用途的工具和示例实现。</p>
|
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<h2 id="_4">内容大纲<a class="headerlink" href="#_4" title="Permanent link">¶</a></h2>
|
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<table>
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<thead>
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<tr>
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<th>#</th>
|
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<th>章节</th>
|
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<th>简介</th>
|
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<th>状态</th>
|
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</thead>
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<tbody>
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<tr>
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<td>01</td>
|
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<td><a href="chapter%2001%3A%20vectors/01.%20vector%20spaces/">向量</a></td>
|
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<td>空间、模长、方向、范数、度量、点积/叉积/外积、基、对偶性</td>
|
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<td>已完成</td>
|
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</tr>
|
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<tr>
|
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<td>02</td>
|
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<td><a href="chapter%2002%3A%20matrices/01.%20matrix%20properties/">矩阵</a></td>
|
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<td>性质、特殊类型、运算、线性变换、分解（LU、QR、SVD）</td>
|
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<td>已完成</td>
|
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</tr>
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<tr>
|
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<td>03</td>
|
|
<td><a href="chapter%2003%3A%20calculus/01.%20differential%20calculus/">微积分</a></td>
|
|
<td>导数、积分、多元微积分、泰勒近似、优化与梯度下降</td>
|
|
<td>已完成</td>
|
|
</tr>
|
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<tr>
|
|
<td>04</td>
|
|
<td><a href="chapter%2004%3A%20statistics/01.%20fundamentals/">统计学</a></td>
|
|
<td>描述性度量、抽样、中心极限定理、假设检验、置信区间</td>
|
|
<td>已完成</td>
|
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</tr>
|
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<tr>
|
|
<td>05</td>
|
|
<td><a href="chapter%2005%3A%20probability/01.%20counting/">概率论</a></td>
|
|
<td>计数、条件概率、分布、贝叶斯方法、信息论</td>
|
|
<td>已完成</td>
|
|
</tr>
|
|
<tr>
|
|
<td>06</td>
|
|
<td><a href="chapter%2006%3A%20machine%20learning/01.%20classical%20machine%20learning/">机器学习</a></td>
|
|
<td>经典机器学习、梯度方法、深度学习、强化学习、分布式训练</td>
|
|
<td>已完成</td>
|
|
</tr>
|
|
<tr>
|
|
<td>07</td>
|
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<td><a href="chapter%2007%3A%20computational%20linguistics/01.%20linguistic%20foundations/">计算语言学</a></td>
|
|
<td>句法学、语义学、语用学、自然语言处理、语言模型、RNN、CNN、注意力机制、Transformer、文本扩散、文本OCR、MoE、SSM、现代LLM架构、自然语言处理评估</td>
|
|
<td>已完成</td>
|
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</tr>
|
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<tr>
|
|
<td>08</td>
|
|
<td><a href="chapter%2008%3A%20computer%20vision/01.%20image%20fundamentals/">计算机视觉</a></td>
|
|
<td>图像处理、目标检测、分割、视频处理、SLAM、CNN、视觉Transformer、扩散模型、流匹配、VR/AR</td>
|
|
<td>已完成</td>
|
|
</tr>
|
|
<tr>
|
|
<td>09</td>
|
|
<td><a href="chapter%2009%3A%20audio%20and%20speech/01.%20digital%20signal%20processing/">音频与语音</a></td>
|
|
<td>数字信号处理、自动语音识别、文本转语音、语音与声学活动检测、说话人分离、源分离、主动降噪、WaveNet、Conformer</td>
|
|
<td>已完成</td>
|
|
</tr>
|
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<tr>
|
|
<td>10</td>
|
|
<td><a href="chapter%2010%3A%20multimodal%20learning/01.%20multimodal%20representations/">多模态学习</a></td>
|
|
<td>融合策略、对比学习、CLIP、视觉语言模型、图像/视频分词、跨模态生成、统一架构、世界模型</td>
|
|
<td>已完成</td>
|
|
</tr>
|
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<tr>
|
|
<td>11</td>
|
|
<td><a href="chapter%2011%3A%20autonomous%20systems/01.%20perception/">自主系统</a></td>
|
|
<td>感知、机器人学习、视觉-语言-动作模型、自动驾驶、太空机器人</td>
|
|
<td>已完成</td>
|
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</tr>
|
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<tr>
|
|
<td>12</td>
|
|
<td><a href="chapter%2012%3A%20graph%20neural%20networks/01.%20geometric%20deep%20learning/">图神经网络</a></td>
|
|
<td>几何深度学习、图论、GNN、图注意力机制、图Transformer、三维等变网络</td>
|
|
<td>已完成</td>
|
|
</tr>
|
|
<tr>
|
|
<td>13</td>
|
|
<td><a href="chapter%2013%3A%20computing%20and%20OS/01.%20discrete%20maths/">计算与操作系统</a></td>
|
|
<td>离散数学、计算机体系结构、操作系统、并发、并行、编程语言</td>
|
|
<td>已完成</td>
|
|
</tr>
|
|
<tr>
|
|
<td>14</td>
|
|
<td><a href="chapter%2014%3A%20data%20structures%20and%20algorithms/00.%20foundations/">数据结构与算法</a></td>
|
|
<td>大O表示法、递归、回溯、动态规划、数组、哈希、链表、栈、树、图、排序、二分查找</td>
|
|
<td>已完成</td>
|
|
</tr>
|
|
<tr>
|
|
<td>15</td>
|
|
<td><a href="chapter%2015%3A%20production%20software%20engineering/01.%20linux%20and%20CMD/">生产级软件工程</a></td>
|
|
<td>Linux、Git、代码库设计、测试、CI/CD、Docker、模型服务、MLOps、监控、使用编码代理的最佳实践</td>
|
|
<td>已完成</td>
|
|
</tr>
|
|
<tr>
|
|
<td>16</td>
|
|
<td><a href="chapter%2016%3A%20SIMD%20and%20GPU%20programming/00.%20why%20C%2B%2B%20and%20how%20ML%20frameworks%20work/">SIMD与GPU编程</a></td>
|
|
<td>面向机器学习的C++、框架工作原理、硬件基础、ARM NEON/I8MM/SME2、x86 AVX、GPU/CUDA、Triton、TPU、RISC-V、Vulkan、WebGPU</td>
|
|
<td>已完成</td>
|
|
</tr>
|
|
<tr>
|
|
<td>17</td>
|
|
<td><a href="chapter%2017%3A%20AI%20inference/01.%20quantisation/">AI推理</a></td>
|
|
<td>量化、高效架构、服务与批处理、边缘推理、推测解码、成本优化</td>
|
|
<td>已完成</td>
|
|
</tr>
|
|
<tr>
|
|
<td>18</td>
|
|
<td><a href="chapter%2018%3A%20ML%20systems%20design/01.%20systems%20design%20fundamentals/">ML系统设计</a></td>
|
|
<td>系统基础、云计算、分布式系统、ML生命周期、特征存储、A/B测试、推荐/搜索/广告/欺诈设计实例</td>
|
|
<td>已完成</td>
|
|
</tr>
|
|
<tr>
|
|
<td>19</td>
|
|
<td>应用人工智能</td>
|
|
<td>金融、医疗健康、蛋白质、药物发现中的人工智能</td>
|
|
<td>待完成</td>
|
|
</tr>
|
|
<tr>
|
|
<td>20</td>
|
|
<td>前沿人工智能</td>
|
|
<td>量子机器学习、神经形态机器学习、去中心化人工智能、太空数据中心、脑机接口</td>
|
|
<td>待完成</td>
|
|
</tr>
|
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</tbody>
|
|
</table>
|
|
<h2 id="_5">前言<a class="headerlink" href="#_5" title="Permanent link">¶</a></h2>
|
|
<p>新生婴儿的大脑是一个新初始化的神经网络，通过现实世界的数据和经验训练直至成年……直至永远。能够用法语流利交流并拥有完美口音，意味着接触到了优秀的法语和完美口音。同样，优秀的人工智能研究员和工程师具备出色的问题解决能力，意味着他们吸收了高质量的知识并拥有丰富的经验。</p>
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<p>科瓦舍夫实验是一项长期的塞尔维亚研究，表明为期三年的高强度创造性问题解决训练可以显著提高智力，尤其是流体智力，提升10-15个IQ点。当然，天生高IQ是真实存在的，就像优质的权重初始化能带来更好的训练效果一样——先天与后天之争的实验结果也证明了这一点。</p>
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<p>然而，高IQ个体的真正优势仅在于能更快地学习和识别模式。但重复使用一种模式可以使任何概念都变得绝对可学。查尔斯·达尔文被他的老师和父亲认为是一个非常普通、甚至低于平均水平的学生。他自称并不机智，感觉自己像一个"慢处理器"，需要时间来吸收数据。</p>
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<p>在3到10岁之间，我的学习成绩很好，自然而然地理解概念，从不做笔记或复习。11到13岁之间我有点自大，用这种方式在一个80人的班级中跌到了下半部分。14到15岁之间，我开始像普通学生一样读书，在中学最后一个学期取得了第一名。早期学校课程与自然IQ配合得很好，但现实世界的才华源于高质量的知识摄入和执行力度。</p>
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<p>事实上，大多数学习成绩好的学生只是更勤奋，但学术系统是为快速学习者设计的。这本纲要提供了一个全面且相互关联的知识流，以帮助世界上那些"达尔文们"更好地学习。你只需要初等数学基础和基本的Python编程知识，其他一切都会逐步掌握——只需阅读并相信这个过程！</p>
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<h2 id="_6">如何更好地学习<a class="headerlink" href="#_6" title="Permanent link">¶</a></h2>
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<p>大学第一学期，我同时选了17门课，成绩并不理想，于是我采用了一个技巧：</p>
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<p><strong>第一阶段：课后累积阅读</strong>
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只阅读每张幻灯片/笔记的标题/大标题，合上书，然后在脑海中可视化并写出对该概念的解释。只重读你遗漏的部分，类似于机器学习中的掩码语言建模。重读之后，最终将概念用代码实现。这样你就能对每个概念形成肌肉记忆。</p>
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<p><strong>第二阶段：考前影子阅读</strong>
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阅读每张幻灯片/笔记的副标题，合上书，然后在脑海中可视化并写出对该概念的解释。只重读你遗漏的部分，类似于机器学习中的掩码语言建模。重读之后，最终将概念用代码实现。这样你就能对每个概念形成肌肉记忆。</p>
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<p>这个方法对我不太自信的朋友们非常有效。事实上，其中一位朋友在高等工程数学（涵盖海森矩阵和优化）这门课上超过了我。她现在在一家大型石油天然气公司工作。灵魂的意愿比我们与之工作的身体更重要（罗森塔尔实验）。</p>
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<h2 id="_7">关于作者<a class="headerlink" href="#_7" title="Permanent link">¶</a></h2>
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<p>查看GitHub个人资料！</p>
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<h2 id="_8">引用<a class="headerlink" href="#_8" title="Permanent link">¶</a></h2>
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<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nc">@book</span><span class="p">{</span><span class="nl">ndubuaku2025compendium</span><span class="p">,</span>
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<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="na">title</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">{Maths, CS & AI Compendium}</span><span class="p">,</span>
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<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="w"> </span><span class="na">author</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">{Henry Ndubuaku}</span><span class="p">,</span>
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<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w"> </span><span class="na">year</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">{2026}</span><span class="p">,</span>
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<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="w"> </span><span class="na">publisher</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">{GitHub}</span><span class="p">,</span>
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<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="w"> </span><span class="na">url</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">{https://github.com/HenryNdubuaku/maths-cs-ai-compendium}</span>
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<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="p">}</span>
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</code></pre></div>
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