基于 Kolmogorov-Arnold 迭加定理的深度 ReLU 网络的误差界。
Error bounds for deep ReLU networks using the Kolmogorov-Arnold superposition theorem.
机构信息
Department of Applied Physics and Applied Mathematics, Columbia University, NY, United States.
Department of Mathematics, National University of Singapore, Singapore.
出版信息
Neural Netw. 2020 Sep;129:1-6. doi: 10.1016/j.neunet.2019.12.013. Epub 2020 May 26.
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.
我们证明了一个关于深度 ReLU 网络逼近多元函数的定理，该定理减轻了维度诅咒。我们的定理基于对 Kolmogorov-Arnold 叠加定理的构造性证明，以及一类多元连续函数的子集，其外部叠加函数可以通过深度 ReLU 网络有效地逼近。
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