Analysis of Bidirectional Associative Memory using SCSNA and Statistical Neurodynamics

TL;DR

This paper provides a theoretical analysis of Bidirectional Associative Memory (BAM) using statistical-mechanical methods, deriving equations for equilibrium states and retrieval dynamics, and assessing capacity.

Contribution

It introduces a novel application of SCSNA and statistical neurodynamics to analyze BAM's equilibrium and retrieval processes, advancing theoretical understanding.

Findings

Derived macroscopic parameter equations for BAM

Established capacity limits of BAM

Validated evolution equations with SCSNA results

Abstract

Bidirectional associative memory (BAM) is a kind of an artificial neural network used to memorize and retrieve heterogeneous pattern pairs. Many efforts have been made to improve BAM from the the viewpoint of computer application, and few theoretical studies have been done. We investigated the theoretical characteristics of BAM using a framework of statistical-mechanical analysis. To investigate the equilibrium state of BAM, we applied self-consistent signal to noise analysis (SCSNA) and obtained a macroscopic parameter equations and relative capacity. Moreover, to investigate not only the equilibrium state but also the retrieval process of reaching the equilibrium state, we applied statistical neurodynamics to the update rule of BAM and obtained evolution equations for the macroscopic parameters. These evolution equations are consistent with the results of SCSNA in the equilibrium state.