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arXiv 2409.08151cond-mat.dis-nn
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广义异联想神经网络

Generalized hetero-associative neural networks

Elena Agliari, Andrea Alessandrelli, Adriano Barra, Martino Salomone Centonze, Federico Ricci-Tersenghi

发表信息：
J. Stat. Mech. (2025) 013302
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AI总结：

本文提出三向联想记忆（TAM）三分神经网络，通过解析与模拟推导相图，证明其在模式识别、模式解耦、检索Markov序列及广义频率调制上具备丰富计算能力。

摘要：

自联想神经网络（例如实现标准Hebbian规则的Hopfield模型）是统计力学中模式识别和联想记忆的基础框架。然而，它们的异联想对应物尽管探索较少，却展现出更丰富的计算能力。在这项工作中，我们研究了Kosko双向联想记忆（BAM）的直接扩展，引入了三向联想记忆（TAM），这是一种配备了广义Hebbian权重的三分神经网络。通过解析方法（使用副本对称统计力学）和计算方法（通过Monte Carlo模拟），我们在控制参数空间中推导了相图，揭示了一个区域，在该区域内网络可以成功执行模式识别以及其他任务。特别地，它能够实现模式解耦，即当输入混合模式时，网络可以恢复原始模式。此外，该系统还能检索模式的Markov序列并执行广义频率调制。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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