Neural Comput - How to compress sequential memory patterns into periodic oscillations: general reduction rules.

Tópicos

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Resumo

A neural network with symmetric reciprocal connections always admits a Lyapunov function, whose minima correspond to the memory states stored in the network. Networks with suitable asymmetric connections can store and retrieve a sequence of memory patterns, but the dynamics of these networks cannot be characterized as readily as that of the symmetric networks due to the lack of established general methods. Here, a reduction method is developed for a class of asymmetric attractor networks that store sequences of activity patterns as associative memories, as in a Hopfield network. The method projects the original activity pattern of the network to a low-dimensional space such that sequential memory retrievals in the original network correspond to periodic oscillations in the reduced system. The reduced system is self-contained and provides quantitative information about the stability and speed of sequential memory retrieval in the original network. The time evolution of the overlaps between the network state and the stored memory patterns can also be determined from extended reduced systems. The reduction procedure can be summarized by a few reduction rules, which are applied to several network models, including coupled networks and networks with time-delayed connections, and the analytical solutions of the reduced systems are confirmed by numerical simulations of the original networks. Finally, a local learning rule that provides an approximation to the connection weights involving the pseudoinverse is also presented.

Resumo Limpo

neural network symmetr reciproc connect alway admit lyapunov function whose minima correspond memori state store network network suitabl asymmetr connect can store retriev sequenc memori pattern dynam network character readili symmetr network due lack establish general method reduct method develop class asymmetr attractor network store sequenc activ pattern associ memori hopfield network method project origin activ pattern network lowdimension space sequenti memori retriev origin network correspond period oscil reduc system reduc system selfcontain provid quantit inform stabil speed sequenti memori retriev origin network time evolut overlap network state store memori pattern can also determin extend reduc system reduct procedur can summar reduct rule appli sever network model includ coupl network network timedelay connect analyt solut reduc system confirm numer simul origin network final local learn rule provid approxim connect weight involv pseudoinvers also present

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