Generalized hetero-associative neural networks
Abstract
Auto-associative neural networks (e.g., the Hopfield model implementing the standard Hebbian prescription) serve as a foundational framework for pattern recognition and associative memory in statistical mechanics. However, their hetero-associative counterparts, though less explored, exhibit even richer computational capabilities. In this work, we examine a straightforward extension of Kosko's Bidirectional Associative Memory (BAM), introducing a Three-directional Associative Memory (TAM), that is a tripartite neural network equipped with generalized Hebbian weights. Through both analytical approaches (using replica-symmetric statistical mechanics) and computational methods (via Monte Carlo simulations), we derive phase diagrams within the space of control parameters, revealing a region where the network can successfully perform pattern recognition as well as other tasks tasks. In particular, it can achieve pattern disentanglement, namely, when presented with a mixture of patterns, the network can recover the original patterns. Furthermore, the system is capable of retrieving Markovian sequences of patterns and performing generalized frequency modulation.
Cite
@article{arxiv.2409.08151,
title = {Generalized hetero-associative neural networks},
author = {Elena Agliari and Andrea Alessandrelli and Adriano Barra and Martino Salomone Centonze and Federico Ricci-Tersenghi},
journal= {arXiv preprint arXiv:2409.08151},
year = {2025}
}