18.S096 Matrix Calculus for Machine Learning and Beyond
18.S096 Matrix Calculus for Machine Learning and Beyond (IAP 2023, MIT OCW). Instructors: Prof. Alan Edelman and Prof. Steven G. Johnson. This class covers a coherent approach to matrix calculus showing techniques that allow you to think of a matrix holistically (not just as an array of scalars), generalize and compute derivatives of important matrix factorizations and many other complicated-looking operations, and understand how differentiation formulas must be reimagined in large-scale computing. We will discuss reverse/adjoint/backpropagation differentiation, custom vector-Jacobian products, and how modern automatic differentiation is more computer science than calculus (it is neither symbolic formulas nor finite differences. (from ocw.mit.edu)
| Lecture 06 - Part2: Calculus of Variations and Gradients of Functionals |
Instructors: Prof. Alan Edelman and Prof. Steven G. Johnson. A "functional" F[u] takes a function u(x) and returns a number (e.g. by integrating), and since functions are perfectly good normed vector spaces we can define derivatives F' with respect to functions u! This is called "calculus of variations."
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