稠密自-异联想记忆在噪声通信信道中的应用

中文摘要 AI 辅助

最近的研究表明，相互作用的Hebbian网络能够执行超越联想记忆的任务，即模式解缠：当输入为存储模式的混杂混合物时，不同模块自发地专门化并检索混合物中的不同成分。迄今为止，这种能力仅在成对相互作用下得到验证，这限制了可处理的模式数量。本文引入了这些模块化网络的稠密扩展，其中模块内的自联想耦合和模块间的异联想耦合均被提升为高阶Hebbian相互作用。我们证明，在适当选择相互作用阶数的情况下，网络在解缠混合物的同时，能够存储与模块大小线性增长的模式数量，而这一区域中成对对应网络则失效。通过基于Guerra插值的统计力学分析，我们推导了序参量的自洽方程，并绘制了相图以识别实现解缠的区域；这些预测得到了蒙特卡洛模拟的证实。最后，我们表明解缠提供了一种自然的解码原语，并通过两个应用加以说明：从Hebbian张量和无标签混合物流中显式重建所有隐藏模式，以及一个概念验证通信协议，其中每个消息令牌作为隐藏模式的掩蔽混合物传输，并由网络动力学解码。由于其基于吸引子的解码，该协议在强信道损坏下优雅退化，而传统安全传输管道在此情况下会突然失效。

英文摘要

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.

发表机构

• Sapienza Università di Roma（罗马第一大学）
• Istituto Nazionale d’Alta Matematica, Sezione di Roma（罗马高等数学研究所）
• INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Roma（罗马核物理国家研究所）
• CNR, Nanotec, Salento Unit（莱切纳米技术国家研究委员会）
• Università del Salento（萨伦托大学）
• INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Lecce（莱切核物理国家研究所）

机构由 AI 辅助整理，请以论文原文为准。