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Gradient Descent Converges to Minimizers
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Gradient Descent Converges to Minimizers
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We show that gradient descent converges to a local minimizer, almost surely with random initialization. This is proved by applying the Stable Manifold Theorem from dynamical systems theory.
Forward citations
Cited by 3 Pith papers
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Accelerated Gradient Methods for Nonconvex Optimization: Escape Trajectories From Strict Saddle Points and Convergence to Local Minima
Theoretical analysis of accelerated gradient methods showing almost-sure escape from strict saddles and linear exit times, plus a subclass achieving near-optimal convergence to local minima in convex neighborhoods of ...
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Weight-space symmetry in deep networks gives rise to permutation saddles, connected by equal-loss valleys across the loss landscape
Permutation symmetries generate permutation saddles and equal-loss valleys linking equivalent global minima, yielding a lower bound on symmetry-induced critical points.
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Combining Stochastic Adaptive Cubic Regularization with Negative Curvature for Nonconvex Optimization
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