A three layer neural network can represent any multivariate function
arXiv:2012.03016v224 citations
AI Analysis
This work addresses a foundational theoretical problem in neural network capabilities for all of machine learning.
This paper demonstrates that a three-layer neural network can represent any multivariate function, extending previous work that only proved this for continuous functions to include all discontinuous functions.
In 1987, Hecht-Nielsen showed that any continuous multivariate function can be implemented by a certain type three-layer neural network. This result was very much discussed in neural network literature. In this paper we prove that not only continuous functions but also all discontinuous functions can be implemented by such neural networks.