Indexed metadata

On the Universal Approximation Property of Deep Fully Convolutional Neural Networks

Qianxiao Li, Ting Lin, Zuowei Shen

Source record

Source: Crossref

Published: Sep 12, 2025

DOI: 10.1137/23m1570119

Open original source ↗

Source abstract

Abstract. We study the approximation of shift-invariant or equivariant functions by deep fully convolutional networks from the dynamical systems perspective. We prove that deep residual fully convolutional networks and their continuous-layer counterparts can achieve universal approximation of these symmetric functions at constant channel width. Moreover, we show that the same can be achieved by nonresidual variants with at least two channels in each layer and convolutional kernel size of at least 2. In addition, we show that these requirements are necessary in the sense that networks with fewer channels or smaller kernels fail to be universal approximators.

Evidence graph

No public relationships recorded yet.

Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.

On the Universal Approximation Property of Deep Fully Convolutional Neural Networks — Mathematical Frontier Network