title: On unique representations of certain dynamical systems produced by continuous-time recurrent neural networks.
abstract: This article extends previous mathematical studies on elucidating the redundancy for describing functions by feedforward neural networks (FNNs) to the elucidation of redundancy for describing dynamical systems (DSs) by continuous-time recurrent neural networks (RNNs). In order to approximate a DS on R(n) using an RNN with n visible units, an n-dimensional affine neural dynamical system (A-NDS) can be used as the DS actually produced by the above RNN under an affine map from its visible state-space R(n) to its hidden state-space. Therefore, we consider the problem of clarifying the redundancy for describing A-NDSs by RNNs and affine maps. We clarify to what extent a pair of an RNN and an affine map is uniquely determined by its corresponding A-NDS and also give a nonredundant sufficient search set for the DS approximation problem based on A-NDS.
authors.affiliation: NTT Communication Science Laboratories, Seika-cho, Kyoto 619-0237, Japan. kimura@cslab.kecl.ntt.co.jp
authors.forename: Masahiro
authors.initials: M
authors.lastname: Kimura