arXiv AI September 24, 2026 By Hao Yu

Path Regularization: A Near-Complete and Optimal Nonasymptotic Generalization Theory for Multilayer Neural Networks and Double Descent Phenomenon

The paper presents a near-complete, nonasymptotic generalization theory for multilayer neural networks using path regularization, applicable to broad Lipschitz loss functions without requiring bounded loss or extreme network hyperparameters. It provides an explicit upper bound that addresses approximation rates in generalized Barron spaces and demonstrates the double descent phenomenon for ReLU networks. The authors claim near-minimax optimality for regression problems and plan to establish matching lower bounds in future work.

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arXiv Machine Learning

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Error Bound Analysis for the Regularized Loss of Deep Linear Neural Networks

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By Junyu Zhou, Puyu Wang, Yunwen Lei, Marius Kloft, Yiming Ying

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arXiv Machine Learning

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By Yuqing Wang, Ioannis G. Kevrekidis, Mikhail Belkin

arXiv Machine Learning

Aug 13

Convergence Guarantees of Gradient Descent for Neural Networks via Generalized Lipschitz Smoothness

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By Siqiao Mu, Diego Klabjan

arXiv Machine Learning

Jul 30

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent

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By Junyu Zhou, Puyu Wang, Dennis Wagner, Yunwen Lei, Marius Kloft, Yiming Ying

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