Realization problem of multi-layer cellular neural networks

Abstract

This paper investigates whether the output space of a multi-layer cellular neural network can be realized via a single layer cellular neural network in the sense of the existence of finite-to-one map from one output space to the other. Whenever such realization exists, the phenomena exhibited in the output space of the revealed single layer cellular neural network is at most a constant multiple of the phenomena exhibited in the output space of the original multi-layer cellular neural network. Meanwhile, the computation complexity of a single layer system is much less than the complexity of a multi-layer system. Namely, one can trade the precision of the results for the execution time. We remark that a routine extension of the proposed methodology in this paper can be applied to the substitution of hidden spaces although the detailed illustration is omitted.

Keywords: Covering space; Learning problem; Multi-layer cellular neural networks; Separation property; Sofic shifts; Topological entropy.