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arXiv · 2309.00508

Geometry and Local Recovery of Global Minima of Two-layer Neural Networks at Overparameterization

Leyang Zhang·Yaoyu Zhang·Tao Luo
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Abstract

Under mild assumptions, we investigate the geometry of the loss landscape for two-layer neural networks in the vicinity of global minima. Utilizing novel techniques, we demonstrate: (i) how global minima with zero generalization error become geometrically separated from other global minima as the sample size grows; and (ii) the local convergence properties and rate of gradient flow dynamics. Our results indicate that two-layer neural networks can be locally recovered in the regime of overparameterization.

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Leyang Zhang, Yaoyu Zhang, Tao Luo. 2023-09-01. Geometry and Local Recovery of Global Minima of Two-layer Neural Networks at Overparameterization. https://arxiv.org/abs/2309.00508

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