Unique representations of dynamical systems produced by recurrent neural networks

Abstract

This paper considers learning a dynamical system (DS) by a recurrent neural network (RNN). We propose an affine neural dynamical system (A-NDS) as a DS that an RNN actually produces on the output space to approximate a target DS. We present a unique parametric representation of A-NDSs using RNNs and affine sections with the aim of constructing effective learning algorithms.