Approximation bounds for norm constrained neural networks with applications to regression and GANs
This work provides theoretical guarantees for norm-constrained neural networks, benefiting researchers in machine learning theory and applications like regression and generative modeling, though it is incremental as it builds on existing approximation theory.
The paper tackles the problem of approximating smooth functions using ReLU neural networks with weight norm constraints, proving upper and lower bounds on approximation error and applying these to derive convergence rates for regression and GANs, showing GANs can achieve optimal distribution learning rates.
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.