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.
X. Cai and D. C. Wunsch, "Counterexample of a Claim Pertaining to the Synthesis of a Recurrent Neural Network," Proceedings of the 2002 International Joint Conference on Neural Networks, 2002. IJCNN '02, Institute of Electrical and Electronics Engineers (IEEE), Jan 2002.
The definitive version is available at https://doi.org/10.1109/IJCNN.2002.1007451
2002 International Joint Conference on Neural Networks, 2002. IJCNN '02
Electrical and Computer Engineering
Keywords and Phrases
Constraint Theory; Fixed Stable State; Network Synthesis; Neural Net Interconnecting Structure; Nonlinear Dynamic Behavior; Pre-Determined Matrix Elements; Recurrent Neural Nets; Recurrent Neural Network Synthesis; Sparse Constraints; Sparse Matrices; Sparsely Interconnected Networks; Stability
Article - Conference proceedings
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01 Jan 2002