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Tabuada, Paulo; Gharesifard, Bahman
IEEE transactions on automatic control, 2024-July, Letnik: 69, Številka: 7Journal Article
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 <inline-formula><tex-math notation="LaTeX"> n+1</tex-math></inline-formula> to <inline-formula><tex-math notation="LaTeX">2n+1</tex-math></inline-formula>. This is consistent with recent observations made in (Hwang, 2023) regarding the use of neural networks to approximate functions by diffeomorphisms.
