Approximation bounds for norm constrained neural networks with applications to regression and GANs

• URL: http://arxiv.org/abs/2201.09418v3
• Date: Thu, 30 Mar 2023 03:26:24 GMT
• Title: Approximation bounds for norm constrained neural networks with applications to regression and GANs
• Authors: Yuling Jiao, Yang Wang, Yunfei Yang
• Abstract summary: We prove upper and lower bounds on the approximation error of ReLU neural networks with norm constraint on the weights. We apply these approximation bounds to analyze the convergences of regression using norm constrained neural networks and distribution estimation by GANs.
• Score: 9.645327615996914
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper studies the approximation capacity of ReLU neural networks with norm constraint on the weights. We prove upper and lower bounds on the approximation error of these networks for smooth function classes. The lower bound is derived through the Rademacher complexity of neural networks, which may be of independent interest. We apply these approximation bounds to analyze the convergences of regression using norm constrained neural networks and distribution estimation by GANs. In particular, we obtain convergence rates for over-parameterized neural networks. It is also shown that GANs can achieve optimal rate of learning probability distributions, when the discriminator is a properly chosen norm constrained neural network.

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