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• W2912004605 abstract "Loss functions with a large number of saddle points are one of the main obstacles to training many modern machine learning models. Gradient descent (GD) is a fundamental algorithm for machine learning and converges to a saddle point for certain initial data. We call the region formed by these initial values the For quadratic functions, GD converges to a saddle point if the initial data is in a subspace of up to n-1 dimensions. In this paper, we prove that a small modification of the recently proposed Laplacian smoothing gradient descent (LSGD) [Osher, et al., arXiv:1806.06317] contributes to avoiding saddle points without sacrificing the convergence rate of GD. In particular, we show that the dimension of the LSGD's attraction region is at most floor((n-1)/2) for a class of quadratic functions which is significantly smaller than GD's (n-1)-dimensional attraction region." @default.
• W2912004605 created "2019-02-21" @default.
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• W2912004605 date "2019-01-21" @default.
• W2912004605 modified "2023-09-27" @default.
• W2912004605 title "A Deterministic Approach to Avoid Saddle Points." @default.
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