A new design method for the complex-valued multistate hopfield associative memory

Computational Intelligence and Neuroscience

2017

Many models of neural networks have been extended to complex-valued neural networks. A complex-valued Hopfield neural network (CHNN) is a complex-valued version of a Hopfield neural network. Complex-valued neurons can represent multistates, and CHNNs are available for the storage of multilevel data, such as gray-scale images. The CHNNs are often trapped into the local minima, and their noise tolerance is low. Lee improved the noise tolerance of the CHNNs by detecting and exiting the local minima. In the present work, we propose a new recall algorithm that eliminates the local minima. We show that our proposed recall algorithm not only accelerated the recall but also improved the noise tolerance through computer simulations.

Section: Introductionmentioning

confidence: 99%

Fast Recall for Complex-Valued Hopfield Neural Networks with Projection Rules

Computational Intelligence and Neuroscience

2017

“…Hopfield neural networks (HNNs) have also been extended. Complex‐valued HNNs (CHNNs) are multistate HNN models, and have often been applied to the storage of images . Moreover, several quaternionic HNNs (QHNNs), which are extensions using quaternions, have been proposed .…”

Section: Introductionmentioning

confidence: 99%

Dual‐numbered Hopfield neural networks

IEEJ Transactions Elec Engng

2017

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.

“…This rule is not practical because of its extremely low storage capacity . Several advanced learning algorithms, such as the projection learning rule, pseudo‐relaxation learning algorithm, and gradient descent learning rule (GDLR), have been proposed . Projection learning rule has a severe restriction in that the connections must be full .…”

Section: Introductionmentioning

confidence: 99%

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

IEEJ Transactions Elec Engng

2016

Complex-valued associative memories (CAMs) are one of the most promising associative memory models by neural networks. However, the low noise tolerance of CAMs is often a serious problem. A projection learning rule with large constant terms improves the noise tolerance of CAMs. However, the projection learning rule can be applied only to CAMs with full connections. In this paper, we propose a gradient descent learning rule with large constant terms, which is not restricted by network topology. We realize large constant terms by regularization to connection weights. By computer simulations, we prove that the proposed learning algorithm improves noise tolerance.