Exponential Bidirectional Associative Memory Based on Small-world Architecture

Abstract

Most of neural associative memory models have fully- connected structure. However, from both the neurobiological viewpoint and the hardware implementation perspective, it seems more reasonable to consider such networks with both predominantly local connectivity and sparsely global connectivity. Small- world architecture (SWA) provides an interesting approach to implementing this design. Recently, Bohland et al. have introduced SWA into Hopfield network and verified the effectiveness of such structure. However, such an attention has not yet been paid to another important type of associative memories, i.e. bidirectional associative memory (BAM). At the first glance, the introduction of SWA to BAM seems straightforward and easy. However, in fact, the randomly-rewiring procedure done for Hopfield network, cannot be directly applied to BAM or its variants because of their multi-layer structure and bidirectional associative mode. In this paper, we use an artful transformation to overcome the difficulty and propose a new exponential BAM model based on SWA, called SWeBAM. It is a brand-new extension to Hopfield network based on SWA in both associative mode and storage capacity. The experimental results demonstrate that with comparatively much fewer inter-neural connections, SWeBAM can obtain almost equivalent performances to the original exponential BAM (eBAM) in both storage capacity and error-correction capability. Moreover, owing to the introduction of SWA, SWeBAM can be realized more easily in hardware than eBAM.