Dense auto-hetero associative memories applied to noisy communication channels

2026-09-26

AI Summary

This study addresses the limitations of existing modular networks, which are constrained by pairwise interactions and consequently exhibit inadequate mixed-pattern processing capabilities and poor robustness in noisy channel decoding. To overcome these challenges, this work proposes a dense auto-hetero-associative memory network based on higher-order Hebbian learning rules, elevating module coupling to higher-order interactions for effective pattern disentanglement. Theoretical analysis and dynamical validation are conducted using Guerra's interpolation method combined with Monte Carlo simulations. By transcending pairwise constraints, the proposed approach enables storage capacity to scale linearly with module size and successfully achieves graceful degradation decoding under strong noise conditions. Both theoretical derivations and simulation results consistently demonstrate that this method significantly outperforms conventional secure transmission schemes.

Abstract

Networks of interacting Hebbian networks have recently been shown to perform a task beyond associative memory, namely \emph{pattern disentanglement}: when fed with a spurious mixture of stored patterns, the different modules spontaneously specialize on, and retrieve, the different constituents of the mixture. So far, this capability has only been established for pairwise interactions, which limits the number of patterns that can be handled. Here we introduce a dense extension of these modular networks, in which both the auto-associative couplings within each module and the hetero-associative couplings among modules are promoted to higher-order Hebbian interactions. We show that, with a suitable choice of the interaction orders, the network disentangles mixtures while storing a number of patterns that scales linearly with the module size, a regime where its pairwise counterpart fails. Through a statistical-mechanical analysis based on Guerra's interpolation, we derive the self-consistency equations for the order parameters and draw the phase diagrams identifying the region where disentanglement is achieved; these predictions are confirmed by Monte Carlo simulations. Finally, we show that disentanglement provides a natural decoding primitive, and we illustrate it with two applications: the explicit reconstruction of all the hidden patterns from the Hebbian tensors and a stream of unlabeled mixtures, and a proof-of-concept communication protocol in which each message token is transmitted as a masked mixture of hidden patterns and decoded by the network dynamics. Owing to its attractor-based decoding, the protocol degrades gracefully under strong channel corruption, where conventional secure-transmission pipelines fail abruptly.

Problem

• pattern disentanglement
• Hebbian networks
• noisy communication channels
• higher-order interactions
• associative memory

Innovation

• dense auto-hetero associative memory
• higher-order Hebbian interactions
• pattern disentanglement
• Guerra interpolation
• noisy communication channels