Differential geometry of ML
Machine learning has achieved remarkable advancements largely due to the success of gradient descent algorithms. To gain deeper mathematical insight into these algorithms, it is essential to adopt an accurate geometric perspective. In this article, we introduce the fundamental notion of a manifold as a mathematical abstraction of continuous spaces. By providing a clear geometric interpretation of gradient descent within this manifold framework, we aim to help readers develop a precise understanding of gradient descent algorithms.
Differential geometry of ML Jul 14, 2025 by Kyuhyeon Choi & fal.ai kyuhyeon@fal.ai Machine learning has achieved remarkable advancements largely due to the success of gradient descent algorithms. To gain deeper mathematical insight into these algorithms, it is essential to adopt an accurate geometric perspective. In this article, we introduce the fundamental notion of a manifold as a mathematical abstraction of continuous spaces. By providing a clear geometric interpretation of gradient descent within this manifold framework, we aim to help readers develop a precise understanding of gradient d
Explore this link on the map →related reading
- Modular Manifolds - Thinking Machines Labthinkingmachines.ai
- An Elementary Introduction to Information Geometryfranknielsen.github.io
- The Roadmap of Mathematics for Machine Learningthepalindrome.org
- 2404.17625arxiv.org
- Differentiable Programming from Scratchthenumb.at
- Covariant derivative - Wikipediaen.wikipedia.org
- Just know stuff. (Or, how to achieve success in a machine learning PhD.) · Patrick Kidgerkidger.site
- Lewis Smith - A gentle introduction to information geometryrobots.ox.ac.uk
- Neural Networks, Manifolds, and Topology -- colah's blogcolah.github.io
- Differential form - Wikipediaen.wikipedia.org
- gstom.pdfmath.umd.edu
- Pen and Paper Exercises in Machine Learningarxiv.org