An Associative Memory ModelI Derived from Cross-Coupled Hopfield Nets and The Roll of Noise-Space Dynamics
In this paper, the association characteristics of Cross-Coupled Hopfield Nets (CCHN) proposed as a mod ular neural network model are discussed in an analytical way. In the CCHN, an arbitrary number of modules (Hopfield networks) can be mutually connected via feedforward networks called "internetworks", whose out puts generate the interactions among module networks. To evaluate the CCHN as a modular neural network, it has been applied to associative memories so far. Although its excellent association performance is sup ported by many simulation results, it is still difficult to compute the memory capacity exactly and examine the dynamical properties rigorously, because the information processing of the CCHN includes strong non linearity. Hence, as the first step to the analytical approach, this paper focuses on a 1-module CCHN whose interaction is realized by a two-layered feedforward internetwork. In this case, the connection matrix of the CCHN degenerates into a single square-matrix like a conventional au to association type of associative memory. Through the eigenvalue analysis for the connection matrix, we reveal that the essential differences between the association characteristics of the CCHN and a conventional auto-correlation associative memory originate from the dynamics in the noise-space which is the orthogonal complement of the subspace generated from memory patterns.