Affiliation:
1. Department of Mathematics, Uppsala University, S-751 06 Uppsala, Sweden
Abstract
In this paper, we prove that, in the deep limit, the stochastic gradient descent on a ResNet type deep neural network, where each layer shares the same weight matrix, converges to the stochastic gradient descent for a Neural ODE and that the corresponding value/loss functions converge. Our result gives, in the context of minimization by stochastic gradient descent, a theoretical foundation for considering Neural ODEs as the deep limit of ResNets. Our proof is based on certain decay estimates for associated Fokker–Planck equations.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Analysis
Cited by
12 articles.
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