Counterexample of a Claim Pertaining to the Synthesis of a Recurrent Neural Network

Recurrent neural networks have received much attention due to their nonlinear dynamic behavior. One such type of dynamic behavior is that of setting a fixed stable state. This paper shows a counterexample to the claim of A.N. Michel et al. (IEEE Control Systems Magazine, vol. 15, pp. 52-65, Jun. 1995), that sparse constraints on the interconnecting structure for a given neural network are usually expressed as constraints which require that pre-determined elements of T [a real n×n matrix acting on a real n-vector valued function] be zero , for the synthesis of sparsely interconnected recurrent neural networks