Absolute stability of global pattern formation and parallel memory storage by competitive neural networks

Author(s): Cohen, M. | Grossberg, S. |

Year: 1983

Citation: IEEE Transactions on Systems, Man, and Cybernetics, SMC-13, 815-826

Abstract: The process whereby input patterns are transformed and stored by competitive cellular networks is considered. This process arises in such diverse subjects as the short-tenD storage of visual or language patterns by neural networks, pattern formation due to tile firing of morphogenetic gradients in developmental biology, control of choice behavior during macromolecular evolution, and the design of stable context-sensitive parallel processors. In addition to systems capable of approaching one of perhaps infinitely many equilibrium points in response to arbitrary input patterns and initial data, one finds in these subjects a ~ride variety of other behaviors, notably traveling waves, standing waves, resonance, and chaos. The question of what general dynamical constraints cause global approach to equilibria rather than large amplitude waves is therefore of considerable interest. In another tenninology, this is the question of whether global pattern fonnation occurs, A related question is wheter the global pattern fonnation property persists when system parameters slowly change in an unpredictable fashion due to self-organization (devlelopment, learning). This is the question of absolute stability of global pattern fonnation. It is shown that many model systems which exhibit the absolute stability property can be written in the form.

Topics: Mathematical Foundations of Neural Networks, Models: Other,

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