At the critical step-size scaling for SGD in high-dimensional single-layer networks, effective dynamics gain a diffusive correction term that changes the phase diagram and reduces to an Ornstein-Uhlenbeck process near fixed points, with the information exponent governing sample complexity.
A mean field view of the landscape of two-layer neural networks.Proceedings of the National Academy of Sciences, 115(33):E7665–E7671, August 2018
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Limit Theorems for Stochastic Gradient Descent in High-Dimensional Single-Layer Networks
At the critical step-size scaling for SGD in high-dimensional single-layer networks, effective dynamics gain a diffusive correction term that changes the phase diagram and reduces to an Ornstein-Uhlenbeck process near fixed points, with the information exponent governing sample complexity.