Correction to “Universal Approximation Power of Deep Residual Neural Networks Through the Lens of Control”
Paulo Tabuada, Bahman Gharesifard · IEEE Transactions on Automatic Control · 2024
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$ n+1$to$2n+1$. This is consistent with recent observations made in [1] regarding the use of neural networks to approximate functions by diffeomorphisms.