Complex-valued Associative Memories Research Articles

Complex-Valued Associative Memories with Projection and Iterative Learning Rules

Abstract 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.

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

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. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

On Energy Function for Complex-Valued Neural Networks

Recently models of neural networks that can deal with complex numbers, complex-valued neural networks, have been proposed and several studies on their abilities of information processing have been done. In this paper we consider a class of fully connected complex-valued neural networks and discuss existence conditions of energy functions for the networks, analogous to those of real-valued Hopfield type neural networks. Based on the conditions we propose an energy function for the complex-valued neural networks. It is also shown that, similar to the real-valued counterparts, this energy function enables us to analyze qualitative behaviors of the complex-valued neural networks. As an application of the energy function, a synthesizing method of complex-valued associative memories is also discussed.

Qualitative analysis of a self-correlation type complex-valued associative memories

Qualitative analysis of a self-correlation type complex-valued associative memories

Observation of positive Lyapunov exponent induced by gain increase of neuron nonlinearity in complex-valued associative memories

A positive Lyapunov exponent is observed in complex-valued associative memories having dynamical attractors, when a small-signal gain of neuron nonlinearity is increased. When the gain is small, the Lyapunov exponent is constantly zero (normal behaviour). However, it is found in the experiment that, unlike conventional (real-valued) associative memories, the Lyapunov exponent becomes distinctly positive (chaotic behaviour) for a larger neuron gain even if the weighting factors are unchanged. This result suggests that the gain of nonlinear devices has a critical significance on information processing stability in future coherent neural networks.