Error bounds for approximations with deep ReLU networks. (October 2017)

• Record Type: Journal Article
• Authors: Yarotsky, Dmitry
• Is Part Of: Neural networks. Volume 94(2017)
• Page Start: 103
• Page End: 114
• Publication Date: 2017-10
• Subjects: Deep ReLU networks -- Approximation complexity; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2017.07.002
• Languages: English
• ISSNs: 0893-6080

Abstract

Abstract: We study expressive power of shallow and deep neural networks with piece-wise linear activation functions. We establish new rigorous upper and lower bounds for the network complexity in the setting of approximations in Sobolev spaces. In particular, we prove that deep ReLU networks more efficiently approximate smooth functions than shallow networks. In the case of approximations of 1D Lipschitz functions we describe adaptive depth-6 network architectures more efficient than the standard shallow architecture.