学习周期给Hopfield网络带来了混乱

C. Molter, U. Salihoglu, H. Bersini
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引用次数: 0

摘要

本文旨在研究Hebbian学习算法对递归神经网络底层动态特性的影响。为了在Hopfield神经网络的吸引子中编码信息,比较了两种不同的学习方式:静态模式的存储和循环模式的存储。我们表明,如果静态模式的存储导致学习阶段后潜在动态的减少,那么循环模式的学习倾向于增加潜在吸引子的维度。事实上,这样的学习可能被用作额外的“混沌之路”:学习的周期越多,网络就越表现为自发的动态,在短暂的振荡周期中呈现出一种混乱的流动形式。这些结果与Freeman对兔子嗅球的观察结果一致:循环用于存储信息,混沌动力学作为由这些循环“记忆袋”组成的背景机制出现。它证实了先前的论文中观察到的关于循环吸引子的巨大编码容量意味着强混沌的存在。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Learning cycles brings chaos in Hopfield networks
This paper aims at studying the impact of an Hebbian learning algorithm on the recurrent neural network's underlying dynamics. Two different kinds of learning are compared in order to encode information in the attractors of the Hopfield neural net: the storing of static patterns and the storing of cyclic patterns. We show that if the storing of static patterns leads to a reduction of the potential dynamics following the learning phase, the learning of cyclic patterns tends to increase the dimension of the potential attractors instead. In fact, such learning may be used as an extra "route to chaos": the more cycles to be learned, the more the network shows as spontaneous dynamics a form of chaotic itinerancy among brief oscillatory periods. These results are in line with the observations made by Freeman in the olfactory bulb of the rabbit: cycles are used to store information and the chaotic dynamics appears as the background regime composed of those cyclic "memory bags". It confirms precedent papers in which it was observed that huge encoding capacity in term of cyclic attractors implies strong presence of chaos.
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