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The Computational Power of Continuous Time

Neural Networks (Preliminary Version)

Pekka Orponen
Department of Computer Science
University of Helsinki, Finland?

August 28, 1995


We investigate the computational power of continuous-time neural networks with Hopfield-type units. We prove that polynomial-size networks with saturated-linear response functions are at least as powerful as polynomially space-bounded Turing machines.

1 Introduction

In a paper published in 1984 [11], John Hopfield introduced a continuoustime version of the neural network model whose discrete-time variant he had discussed in his seminal 1982 paper [10]. The 1984 paper also contains an electronic implementation scheme for the continuous-time networks, and an argument showing that for sufficiently large-gain nonlinearities, these behave similarly to the discrete-time ones, at least when used as associative memories.

The power of Hopfield's discrete-time networks as general-purpose computational devices was analyzed in [17, 18]. In this paper we conduct a similar analysis for networks consisting of Hopfield's continuous-time units; however we are at this stage able to analyze only the general asymmetric networks, and the very interesting subclass of continuous-time networks

?Address: P. O. Box 26, FIN{00014 University of Helsinki, Finland. E-mail: [email protected]. This work was done during the author's visit to the Institute for Theoretical Computer Science, Technical University of Graz, Austria.