Utilizing High-Dimensional Neural Networks for Pseudo-orthogonalization of Memory Patterns

Minemoto, Toshifumi; Isokawa, Teijiro; Nishimura, Haruhiko; Matsui, Nobuyuki

doi:10.1007/978-3-319-12637-1_66

Cited by 1 publication

(2 citation statements)

References 7 publications

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“…We present a pseudo-orthogonalization method based on complex numbers and quaternions in this Section [7].…”

Section: Pseudo-orthogonalization Based On Complex Numbers and Quatermentioning

confidence: 99%

“…The complexvalued or quaternionic extensions would be suitable for the pseudo-orthogonalization scheme; the pair of a pattern can be naturally embedded by utilizing imaginary part(s). The pseudo-orthogonalization method has been extended based on complex numbers and quaternions [7]. In previous study, the numerical simulation results show that the proposed method can store the patterns better than the conventional (real-valued) method from the viewpoint of the loading rate, which is defined as the ratio of the number of embedded memory patterns to the number of neurons in the network.…”

Section: Introductionmentioning

confidence: 99%

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Pseudo-Orthogonalization of Memory Patterns for Complex-Valued and Quaternionic Associative Memories

Minemoto

Isokawa

Nishimura

et al. 2017

Journal of Artificial Intelligence and Soft Computing Research

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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.

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“…We present a pseudo-orthogonalization method based on complex numbers and quaternions in this Section [7].…”

Section: Pseudo-orthogonalization Based On Complex Numbers and Quatermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pseudo-Orthogonalization of Memory Patterns for Complex-Valued and Quaternionic Associative Memories

Minemoto

Isokawa

Nishimura

et al. 2017

Journal of Artificial Intelligence and Soft Computing Research

Self Cite

View full text Add to dashboard Cite

show abstract

Utilizing High-Dimensional Neural Networks for Pseudo-orthogonalization of Memory Patterns

Cited by 1 publication

References 7 publications

Pseudo-Orthogonalization of Memory Patterns for Complex-Valued and Quaternionic Associative Memories

Pseudo-Orthogonalization of Memory Patterns for Complex-Valued and Quaternionic Associative Memories

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