Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach

Abstract

It is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a continuous function on a compact set on an n-dimensional space, then there exists a one-hidden-layer feedforward network which approximates the function. Such result proves the existence, but it does not provide a method for finding it. In this paper, a constructive approach to the proof of this property is given for the case of two-hidden-layer feedforward networks. This approach is based on an approximation of continuous functions by simplicial maps. Once a triangulation of the space is given, a concrete architecture and set of weights can be obtained. The quality of the approximation depends on the refinement of the covering of the space by simplicial complexes.