Error bounds for deep ReLU networks using the Kolmogorov-Arnold superposition theorem
Error bounds for deep ReLU networks using the Kolmogorov-Arnold superposition theorem
Hadrien Montanelli,Haizhao Yang
2019 · DOI: 10.1016/j.neunet.2019.12.013
Neural Networks · 122 Citations
TLDR
This theorem is based on a constructive proof of the Kolmogorov-Arnold superposition theorem, and on a subset of multivariate continuous functions whose outer superposition functions can be efficiently approximated by deep ReLU networks.
Abstract
We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks, for which the curse of the dimensionality is lessened. Our theorem is based on a constructive proof of the Kolmogorov-Arnold superposition theorem, and on a subset of multivariate continuous functions whose outer superposition functions can be efficiently approximated by deep ReLU networks.