Generalized hetero-associative neural networks

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

While auto-associative neural networks (e.g., the Hopfield model implementing the standard Hebbian prescription for learning) play as the reference setting for pattern recognition and associative memory in statistical mechanics, hetero-associative extensions (despite much less investigated) display richer emergent computational skills. Here we study the simplest generalization of the Kosko's Bidirectional Associative Memory (BAM), namely a Three-directional Associative Memory (TAM), that is a tripartite neural network equipped with generalized Hebbian weights. We study its information processing capabilities analytically (via statistical mechanics and signal-to-noise techniques) and computationally (via Monte Carlo simulations). Confined to the replica symmetric description, we provide phase diagrams for this network in the space of the control parameters, highlighting the existence of a region where the machine can successful perform recognition as well as other tasks. For instance, it can perform pattern disentanglement, namely when inputted with a mixture of patterns, the network is able to return the original patterns, namely to disentangle the signal's components. Further, they can also perform retrieval of (Markovian) sequences of patterns and they can also disentangle mixtures of periodic patterns: should these mixtures be sequences that combine patterns alternating at different frequencies, these hetero-associative networks can perform generalized frequency modulation by using the slowly variable sequence of patterns as the base-band signal and the fast one as the information carrier.
广义异质关联神经网络
在统计力学中,自关联神经网络(例如,执行标准海比学习处方的霍普菲尔德模型)是模式识别和关联记忆的参考设置,而异关联扩展神经网络(尽管研究较少)则显示出丰富的计算技能。在这里,我们研究了科斯科双向联想记忆(BAM)的最简单广义化,即三向联想记忆(TAM),它是一个配备了广义海比权重的三方神经网络。我们对它的信息处理能力进行了分析研究(通过统计力学和信噪比技术)和计算研究(通过蒙特卡罗模拟)。限于复制对称描述,我们提供了该网络在控制参数空间内的相位图,强调了存在一个区域,在该区域内,机器可以成功执行识别和其他任务。例如,它可以执行模式分解,即当输入混合模式时,网络能够返回原始模式,即分解信号的成分。此外,它们还可以对(马尔可夫)模式序列进行检索,也可以对周期性模式混合物进行解离:如果这些混合物是以不同频率交替出现的模式组合序列,这些异质关联网络就可以使用缓慢变化的模式序列作为基带信号,而快速变化的模式序列作为信息载体,从而执行广义频率调制。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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