# Tighter Sparse Approximation Bounds for ReLU Neural Networks

@article{DomingoEnrich2021TighterSA, title={Tighter Sparse Approximation Bounds for ReLU Neural Networks}, author={Carles Domingo-Enrich and Youssef Mroueh}, journal={ArXiv}, year={2021}, volume={abs/2110.03673} }

A well-known line of work [Barron, 1993, Breiman, 1993, Klusowski and Barron, 2018] provides bounds on the width n of a ReLU two-layer neural network needed to approximate a function f over the ball BR(R) up to error , when the Fourier based quantity Cf = 1 (2π)d/2 ∫ Rd ‖ξ‖ |f̂(ξ)| dξ is finite. More recently Ongie et al. [2019] used the Radon transform as a tool for analysis of infinite-width ReLU two-layer networks. In particular, they introduce the concept of Radon-based R-norms and show…

## One Citation

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