教如何对矩阵函数求导，让机器学习优化更高效。
Matrix Calculus (for Machine Learning and Beyond)
- 扩展微积分到矩阵输入输出，支持复杂函数求导。
- 提出反向传播思想，提升大规模计算效率。
- 适合想理解深度学习底层原理的本科生。
本课程面向已掌握初等微积分和线性代数的本科生，介绍微积分在更一般向量空间上的扩展，例如对矩阵输入、输出矩阵逆或分解的函数求导，以及常微分方程解和随机函数的随机导数。强调实际计算应用，如大规模优化与机器学习中，需重新设计导数传播方式以应对复杂计算流程。课程还讨论效率问题，引出伴随（adjoint）或反向模式微分（即反向传播），并为现代自动微分（AD）技术提供温和入门。
原文摘要 · Abstract (English)
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and return a matrix inverse or factorization, derivatives of ODE solutions, and even stochastic derivatives of random functions. It emphasizes practical computational applications, such as large-scale optimization and machine learning, where derivatives must be re-imagined in order to be propagated through complicated calculations. The class also discusses efficiency concerns leading to "adjoint" or "reverse-mode" differentiation (a.k.a. "backpropagation"), and gives a gentle introduction to modern automatic differentiation (AD) techniques.
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