Correction to “Universal Approximation Power of Deep Residual Neural Networks Through the Lens of Control”

This brief note corrects the statements of Theorem 5.1, and Corollary 5.2, of [3]. The main consequence of these corrections is that the width of residual neural networks that suffices for universal approximation changes from <tex-math notation="LaTeX">$ n+1$</tex-math> to <tex-math notation="LaTeX">$2n+1$</tex-math> . This is consistent with recent observations made in [1] regarding the use of neural networks to approximate functions by diffeomorphisms.