Associative Memory by Recurrent Neural Networks with Delay Elements

TL;DR

This paper analyzes associative memory models with delayed synapses using recurrent neural networks, deriving new steady state equations that reveal storage capacity scales linearly with delay length, supported by simulations.

Contribution

It introduces a computationally efficient method to analyze large delay lengths in associative memory models, extending the Yanai-Kim theory with steady state equations.

Findings

Storage capacity is proportional to delay length L.

Proportionality constant is approximately 0.195.

The new equations are validated by computer simulations.

Abstract

The synapses of real neural systems seem to have delays. Therefore, it is worthwhile to analyze associative memory models with delayed synapses. Thus, a sequential associative memory model with delayed synapses is discussed, where a discrete synchronous updating rule and a correlation learning rule are employed. Its dynamic properties are analyzed by the statistical neurodynamics. In this paper, we first re-derive the Yanai-Kim theory, which involves macrodynamical equations for the dynamics of the network with serial delay elements. Since their theory needs a computational complexity of $O(L^4t)$ to obtain the macroscopic state at time step t where L is the length of delay, it is intractable to discuss the macroscopic properties for a large L limit. Thus, we derive steady state equations using the discrete Fourier transformation, where the computational complexity does not formally depend on L. We show that the storage capacity $\alpha_C$ is in proportion to the delay length L with a large L limit, and the proportion constant is 0.195, i.e., $\alpha_C = 0.195 L$. These results are supported by computer simulations.