Leveraging the two timescale regime to demonstrate convergence of neural networks

• URL: http://arxiv.org/abs/2304.09576v2
• Date: Wed, 25 Oct 2023 14:13:57 GMT
• Title: Leveraging the two timescale regime to demonstrate convergence of neural networks
• Authors: Pierre Marion and Rapha\"el Berthier
• Abstract summary: We study the training dynamics of neural networks in a two-time regime. We show that the gradient descent behaves according to our description of the optimum flow gradient, but can fail outside this regime.
• Score: 1.2328446298523066
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the training dynamics of shallow neural networks, in a two-timescale regime in which the stepsizes for the inner layer are much smaller than those for the outer layer. In this regime, we prove convergence of the gradient flow to a global optimum of the non-convex optimization problem in a simple univariate setting. The number of neurons need not be asymptotically large for our result to hold, distinguishing our result from popular recent approaches such as the neural tangent kernel or mean-field regimes. Experimental illustration is provided, showing that the stochastic gradient descent behaves according to our description of the gradient flow and thus converges to a global optimum in the two-timescale regime, but can fail outside of this regime.

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