Centre manifold theorem for maps along manifolds of fixed points
arXiv:2604.1820274.6h-index: 1
AI Analysis
Provides a theoretical tool for analyzing dynamics near manifolds of fixed points, with an application to understanding gradient descent in matrix factorization.
The authors prove a centre manifold theorem for maps along a manifold-with-boundary of fixed points and apply it to analyze gradient descent with large step size on two-layer matrix factorisation problems.
We prove a centre manifold theorem for a map along a manifold-with-boundary of fixed points, and provide an application to the study of gradient descent with large step size on two-layer matrix factorisation problems.