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2 Journal of Artificial Intelligence and Soft Computing Research

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Complex-valued associative memories with projection and iterative learning rules

Isokawa T., Yamamoto H., Nishimura H., Yumoto T., Kamiura N., Matsui N.

Journal of Artificial Intelligence and Soft Computing Research

2018

Vol. 8, No. 3

237--249

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.

Pseudo-orthogonalization of memory patterns for complex-valued and quaternionic associative memories

Minemoto T., Isokawa T., Nishimura H., Matsui N.

Journal of Artificial Intelligence and Soft Computing Research

2017

Vol. 7, No. 4

257--264

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.