How dual numbers allow computers to calculate derivatives automatically and efficiently
In short: This lecture explains forward-mode automatic differentiation, a technique for computing derivatives in software. By introducing dual numbers—a special numerical type that tracks both a value and its derivative simultaneously—you can implement a functional differentiation system using only a few lines of Julia code.
Automatic differentiation (AD) is a method for evaluating the derivative of a function defined by a computer program. Unlike symbolic or numerical differentiation, forward-mode AD leverages the properties of dual numbers to propagate derivative information alongside the primary calculation.
Presented by Alan Edelman and Steven G. Johnson as part of the 2023 MIT course 'Matrix Calculus For Machine Learning And Beyond,' this session demonstrates that building an AD system is surprisingly concise. By redefining how numbers behave within a program, one can automate calculus tasks essential to modern machine learning workflows.
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Sources
- Summary by Intellect · source: Lecture 5 Part 2: Forward Automatic Differentiation via Dual Numbers
- Also: Lecture 5 Part 2: Forward Automatic Differentiation via Dual Numbers | Matrix Calculus for Machine Learning and Beyond | Mathematics | MIT OpenCourseWare
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