On the universal approximation property of radial basis function neural networks
This work addresses the theoretical foundation of neural network approximation for researchers in machine learning and approximation theory, but it appears incremental as it modifies existing RBF networks rather than introducing a new paradigm.
The authors tackled the problem of approximating continuous multivariate functions using a new class of radial basis function neural networks with shifts instead of smoothing factors, proving that these networks can approximate any such function on compact subsets of Euclidean space under certain conditions, and described conditions for arbitrary precision approximation with fixed centroids.
In this paper we consider a new class of RBF (Radial Basis Function) neural networks, in which smoothing factors are replaced with shifts. We prove under certain conditions on the activation function that these networks are capable of approximating any continuous multivariate function on any compact subset of the $d$-dimensional Euclidean space. For RBF networks with finitely many fixed centroids we describe conditions guaranteeing approximation with arbitrary precision.