Generalized hetero-associative neural networks

Fuente: arXiv
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Main Authors: Agliari, Elena, Alessandrelli, Andrea, Barra, Adriano, Centonze, Martino Salomone, Ricci-Tersenghi, Federico
Format: Preprint
Published: 2024
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author Agliari, Elena
Alessandrelli, Andrea
Barra, Adriano
Centonze, Martino Salomone
Ricci-Tersenghi, Federico
author_facet Agliari, Elena
Alessandrelli, Andrea
Barra, Adriano
Centonze, Martino Salomone
Ricci-Tersenghi, Federico
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2409_08151
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Generalized hetero-associative neural networks
Agliari, Elena
Alessandrelli, Andrea
Barra, Adriano
Centonze, Martino Salomone
Ricci-Tersenghi, Federico
Disordered Systems and Neural Networks
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.
title Generalized hetero-associative neural networks
topic Disordered Systems and Neural Networks
url https://arxiv.org/abs/2409.08151