Large-step GD near a flat-minima manifold of overparametrised least squares has a normal form that yields subcritical, critical, and supercritical convergence theorems, including for deep matrix factorisation.
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A center manifold theorem is established for dynamical systems featuring a manifold of fixed points with boundary, and applied to large-step-size gradient descent on two-layer matrix factorization.
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Dynamics of Gradient Descent with Large Step Size Near a Manifold of Flat Minima
Large-step GD near a flat-minima manifold of overparametrised least squares has a normal form that yields subcritical, critical, and supercritical convergence theorems, including for deep matrix factorisation.
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Centre manifold theorem for maps along manifolds of fixed points
A center manifold theorem is established for dynamical systems featuring a manifold of fixed points with boundary, and applied to large-step-size gradient descent on two-layer matrix factorization.