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Toshifumi Minemoto, Teijiro Isokawa, Haruhiko Nishimura and Nobuyuki Matsui

Abstract

Hebbian learning rule is well known as a memory storing scheme for associative memory models. This scheme is simple and fast, however, its performance gets decreased when memory patterns are not orthogonal each other. Pseudo-orthogonalization is a decorrelating method for memory patterns which uses XNOR masking between the memory patterns and randomly generated patterns. By a combination of this method and Hebbian learning rule, storage capacity of associative memory concerning non-orthogonal patterns is improved without high computational cost. The memory patterns can also be retrieved based on a simulated annealing method by using an external stimulus pattern. By utilizing complex numbers and quaternions, we can extend the pseudo-orthogonalization for complex-valued and quaternionic Hopfield neural networks. In this paper, the extended pseudo-orthogonalization methods for associative memories based on complex numbers and quaternions are examined from the viewpoint of correlations in memory patterns. We show that the method has stable recall performance on highly correlated memory patterns compared to the conventional real-valued method.

Open access

Sou Nobukawa, Haruhiko Nishimura, Teruya Yamanishi and Jian-Qin Liu

Abstract

Several hybrid neuron models, which combine continuous spike-generation mechanisms and discontinuous resetting process after spiking, have been proposed as a simple transition scheme for membrane potential between spike and hyperpolarization. As one of the hybrid spiking neuron models, Izhikevich neuron model can reproduce major spike patterns observed in the cerebral cortex only by tuning a few parameters and also exhibit chaotic states in specific conditions. However, there are a few studies concerning the chaotic states over a large range of parameters due to the difficulty of dealing with the state dependent jump on the resetting process in this model. In this study, we examine the dependence of the system behavior on the resetting parameters by using Lyapunov exponent with saltation matrix and Poincaré section methods, and classify the routes to chaos.

Open access

Teijiro Isokawa, Hiroki Yamamoto, Haruhiko Nishimura, Takayuki Yumoto, Naotake Kamiura and Nobuyuki Matsui

Abstract

In this paper, we investigate the stability of patterns embedded as the associative memory distributed on the complex-valued Hopfield neural network, in which the neuron states are encoded by the phase values on a unit circle of complex plane. As learning schemes for embedding patterns onto the network, projection rule and iterative learning rule are formally expanded to the complex-valued case. The retrieval of patterns embedded by iterative learning rule is demonstrated and the stability for embedded patterns is quantitatively investigated.