288 pp. per issue
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Neural Computation

December 1, 2002, Vol. 14, No. 12, Pages 2981-2996
(doi: 10.1162/089976602760805377)
© 2002 Massachusetts Institute of Technology
On Unique Representations of Certain Dynamical Systems Produced by Continuous-Time Recurrent Neural Networks
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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 Rn 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 Rn 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.