Hyperbolic-Valued Hopfield Neural Networks in Synchronous Mode.

Neural Computation
Masaki Kobayashi

Abstract

For most multistate Hopfield neural networks, the stability conditions in asynchronous mode are known, whereas those in synchronous mode are not. If they were to converge in synchronous mode, recall would be accelerated by parallel processing. Complex-valued Hopfield neural networks (CHNNs) with a projection rule do not converge in synchronous mode. In this work, we provide stability conditions for hyperbolic Hopfield neural networks (HHNNs) in synchronous mode instead of CHNNs. HHNNs provide better noise tolerance than CHNNs. In addition, the stability conditions are applied to the projection rule, and HHNNs with a projection rule converge in synchronous mode. By computer simulations, we find that the projection rule for HHNNs in synchronous mode maintains a high noise tolerance.

References

Sep 28, 2006·IEEE Transactions on Neural Networks·Donq-Liang Lee
Feb 2, 2008·IEEE Transactions on Neural Networks·M K MuezzinogluJ M Zurada
Jan 1, 1996·IEEE Transactions on Neural Networks·S JankowskiJ M Zurada
May 3, 2008·International Journal of Neural Systems·Teijiro IsokawaNobuyuki Matsui
Aug 1, 2009·IEEE Transactions on Neural Networks·Gouhei Tanaka, Kazuyuki Aihara
Feb 1, 2013·IEEE Transactions on Neural Networks and Learning Systems·M Kobayashi
Jan 6, 2017·IEEE Transactions on Neural Networks and Learning Systems·Masaki Kobayashi
May 11, 2017·IEEE Transactions on Neural Networks and Learning Systems·Marcos Eduardo Valle, Fidelis Zanetti de Castro
Jul 12, 2018·IEEE Transactions on Neural Networks and Learning Systems·Qiankun Song, Xiaofeng Chen
Mar 21, 2019·IEEE Transactions on Neural Networks and Learning Systems·Masaki Kobayashi

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