Universal Approximation Power of Deep Residual Neural Networks Through the Lens of Control (vol 68, pg 2715, 2023)

• 成果类型: Correction
• 署名作者: Tabuada, Paulo; Gharesifard, Bahman
• 署名单位: University of California System; University of California Los Angeles
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3390099
• 发表日期: 2024
• 页码: 4891-4892
• 关键词: Neural networks; nonlinear controllability; residual networks; universal approximation

摘要

This brief note corrects the statements of Theorem 5.1 and Corollary 5.2 in (Tabuada and Gharesifard, 2023). The main consequence of these corrections is that the width of residual neural networks that suffices for universal approximation changes from n+1 to 2n+1. This is consistent with recent observations made in (Hwang, 2023) regarding the use of neural networks to approximate functions by diffeomorphisms.