Gradient descent learning rule for complex‐valued associative memories with large constant terms

Kobayashi, Masaki

doi:10.1002/tee.22225

Cited by 23 publications

(13 citation statements)

References 19 publications

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“…We have two plans in future. One is to develop new learning algorithms, such as the gradient descent learning rule and the projection rule [38][39][40][41][42][43]. The other is to extend the activation functions to multistate functions.…”

Section: Resultsmentioning

confidence: 99%

Hyperbolic Hopfield neural networks with four‐state neurons

Kobayashi

2016

IEEJ Transactions Elec Engng

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In recent years, applications of neural networks with Clifford algebra have become widespread. Clifford algebra is also referred to as geometric algebra and is useful in dealing with geometric objects. Hopfield neural networks with Clifford algebra, such as complex numbers and quaternions, have been proposed. However, it has been difficult to construct Hopfield neural networks by Clifford algebra with positive part of the signature, such as hyperbolic numbers. Hyperbolic numbers are useful algebra to deal with hyperbolic geometry. Kuroe proposed hyperbolic Hopfield neural networks and provided their continuous activation functions and stability conditions. However, the learning algorithm has not been provided. In this paper, we provide two quantized activation functions and the primitive learning algorithm satisfying the stability condition. We also perform computer simulations and compare the activation functions.

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Section: Resultsmentioning

confidence: 99%

Hyperbolic Hopfield neural networks with four‐state neurons

Kobayashi

2016

IEEJ Transactions Elec Engng

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“…Rotational invariance reduces noise tolerance. Several ideas have been proposed to avoid rotational invariance .…”

Section: Introductionmentioning

confidence: 99%

Dual‐numbered Hopfield neural networks

Kobayashi

2017

IEEJ Transactions Elec Engng

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In recent years, Hopfield neural networks using Clifford algebra have been studied. Clifford algebra is also referred to as geometric algebra, and is useful to deal with geometric objects. There are three kinds of Clifford algebra with degree 2; complex, hyperbolic, and dual-numbered. Complex-valued Hopfield neural networks have been studied by many researchers. Several models of hyperbolic Hopfield neural networks have also been proposed. It has been difficult to construct dual-numbered Hopfield neural networks. In this work, we propose dual-numbered Hopfield neural networks by modification of hyperbolic Hopfield neural networks with the split activation function. The stability condition and Hebbian learning rule are also provided.

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“…In recent decades, analysis and design of neurodynamic systems have received much attention [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Specifically, neurodynamics of associative memories is a hot research issue [9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, neurodynamics of associative memories is a hot research issue [9][10][11][12][13][14][15][16]. Associative memories refer to brain-inspired computing designed to store a set of prototype patterns such that the stored patterns can be retrieved with the recalling probes containing sufficient information about the contents of patterns.…”

Section: Introductionmentioning

confidence: 99%

“…In associative memories, for any given probe (e.g., noisy or corrupted version of a prototype pattern), the retrieval dynamics can converge to an ideal equilibrium point representing the prototype pattern. At present, system analysts have two main theories for explaining strange dynamical behaviors in recalling processes: autoassociative memories and heteroassociative memories [12,13]. Two types of methods are usually used for solving problems in regard to analysis and synthesis of associative memories.…”

Section: Introductionmentioning

confidence: 99%

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Analysis and Design of Associative Memories for Memristive Neural Networks with Deviating Argument

Zhang

2017

Mathematical Problems in Engineering

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We investigate associative memories for memristive neural networks with deviating argument. Firstly, the existence and uniqueness of the solution for memristive neural networks with deviating argument are discussed. Next, some sufficient conditions for this class of neural networks to possess invariant manifolds are obtained. In addition, a global exponential stability criterion is presented. Then, analysis and design of autoassociative memories and heteroassociative memories for memristive neural networks with deviating argument are formulated, respectively. Finally, several numerical examples are given to demonstrate the effectiveness of the obtained results.

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Gradient descent learning rule for complex‐valued associative memories with large constant terms

Cited by 23 publications

References 19 publications

Hyperbolic Hopfield neural networks with four‐state neurons

Hyperbolic Hopfield neural networks with four‐state neurons

Dual‐numbered Hopfield neural networks

Analysis and Design of Associative Memories for Memristive Neural Networks with Deviating Argument

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