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Dynamical systems produced by recurrent neural networks

✍ Scribed by Masahiro Kimura; Ryohei Nakano

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
237 KB
Volume
31
Category
Article
ISSN
0882-1666

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✦ Synopsis

Concerning the learning problems of recurrent neural networks (RNNs), this paper deals with the problem of approximating a dynamical system (DS) by an RNN as one extension of the problem of approximating trajectories by an RNN. In particular, we systematically investigate how an RNN can produce a DS on the visible state space to approximate a target DS. First, it is proved that RNNs without hidden units uniquely produce a certain class of DSs. Next, a neural dynamical system (NDS) is proposed as such a DS that an RNN with hidden units can produce on the visible state space, and affine neural dynamical systems (A-NDSs) are constructed as concrete examples of NDSs. Moreover, we prove that any DS on a Euclidean space can be finitely approximated by some A-NDS with any precision, and propose adopting an A-NDS as such a DS that an RNN with hidden units produces to approximate a target DS.

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