Quaternionic multistate Hopfield neural network with extended projection rule

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

doi:10.1007/s10015-015-0247-4

Cited by 58 publications

(35 citation statements)

References 12 publications

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“…Analyzing other types of learning schemes, such as the scheme in [11], will be necessary. The analysis of this learning scheme for higher dimensional associative memory is also a challenging problem, such as for quaternionic multistate Hopfield neural networks [19,20,21] …”

Section: Resultsmentioning

confidence: 99%

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Complex-Valued Associative Memories with Projection and Iterative Learning Rules

Isokawa

Yamamoto

Nishimura

et al. 2018

Journal of Artificial Intelligence and Soft Computing Research

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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.

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Section: Resultsmentioning

confidence: 99%

“…One of our future researches directs to de- [19,20,21] ues are avai 10 Table 1: An example of evolutions for the averaged phase differences according to the iterations by iterative learning rule. At the first iteration of learning, all the patterns are involved in learning.…”

Section: T)mentioning

confidence: 99%

Complex-Valued Associative Memories with Projection and Iterative Learning Rules

Isokawa

Yamamoto

Nishimura

et al. 2018

Journal of Artificial Intelligence and Soft Computing Research

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“…In Quaternionic Hopfield Neural Network (QHNN), all neuronal parameters in the network are encoded by quaternions [11,12,13]. Let the m-th element of a µ-th quaternionic learning pattern be ξ…”

Section: Quaternionic Hopfield Neural Networkmentioning

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

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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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“…There exists a vast literature on hypercomplex versions of the Hopfield network which include generalizations using quaternions [9,18], hyperbolic numbers [11,12], Lie algebra [21], and Clifford algebra [24]. Recently, Kuroe and Iima introduced a class of octonionic Hopfield neural networks and provided conditions for the existence of an energy function for the stability analysis of their model [13].…”

Section: Introductionmentioning

confidence: 99%

“…For instance, complex-valued, quaternion-valued, and octonion-valued neural networks are able to process two, four, and eight dimensional data, respectively. Applications of hypercomplexvalued neural networks include control [1,4], color image processing [14,17,18], and prediction [3,16,22].…”

Section: Introductionmentioning

confidence: 99%

Continuous-Valued Octonionic Hopfield Neural Network

Castro¹,

Valle²

2018

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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In this paper, we generalize the famous Hopfield neural network to unit octonions. In the proposed model, referred to as the continuous-valued octonionic Hopfield neural network (CV-OHNN), the next state of a neuron is obtained by setting its octonionic activation potential to length one. We show that, like the traditional Hopfield network, a CV-OHNN operating in an asynchronous update mode always settles down to an equilibrium state under mild conditions on the octonionic synaptic weights.

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Quaternionic multistate Hopfield neural network with extended projection rule

Cited by 58 publications

References 12 publications

Complex-Valued Associative Memories with Projection and Iterative Learning Rules

Complex-Valued Associative Memories with Projection and Iterative Learning Rules

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

Continuous-Valued Octonionic Hopfield Neural Network

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