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

arXiv – CS AI|Weigutian Ou, Helmut B\"olcskei|March 4, 2026 at 05:00 AM|1 views

🤖AI Summary

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.

Key Takeaways

→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.

#deep-learning #neural-networks #approximation-theory #regression #network-compression #relu #machine-learning #optimization

Read Original →via arXiv – CS AI

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