← Back to all news
arXiv Machine Learning By Sebastian Kassing

Deep ReLU Networks Can Fail the Best Approximation Property for Continuous Target Functions

Read the original on arXiv Machine Learning →

arXiv:2610. 31264v1 Announce Type: new Abstract: We construct a continuous function on $[-1,1]^2$ for which the infimum of the $L^2$-approximation error over the class of ReLU networks with two hidden layers and architecture $(2,2,1,1)$ is not attained.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

Related stories

arXiv Machine Learning
Jun 2

Multigrade Neural Network Approximation

arXiv:2601. 16884v3 Announce Type: replace Abstract: We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks.

By Shijun Zhang, Zuowei Shen, Yuesheng Xu
More like this →
arXiv AI
Sep 24

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.

By Hao Yu
efficiencysafety
More like this →