Covering Numbers for Deep ReLU Networks with Applications to Function Approximation and Nonparametric Regression

Researchers have derived tight bounds on covering numbers for deep ReLU neural networks, providing fundamental insights into network capacity and approximation capabilities. The work removes a log^6(n) factor from the best known sample complexity rate for estimating Lipschitz functions via deep networks, establishing optimality in nonparametric regression.

• →First tight lower and upper bounds established for metric entropy of deep ReLU networks with various weight constraints.
• →Results provide fundamental understanding of how sparsity, quantization, and weight bounds impact network capacity.
• →Sample complexity for estimating Lipschitz functions via deep networks significantly improved by removing log^6(n) factor.
• →Work unifies numerous results in neural network approximation theory and nonparametric regression.
• →Findings enable characterization of fundamental limits for network compression and transformation.