Power law decay of stored pattern stability in sparse Hopfield neural networks  

作　　者：Fei Fang Zhou Yang Sheng-Jun Wang 

机构地区：[1]School of Physics and Information Technology,Shaanxi Normal University,Xi'an 710119,China

出　　处：《Communications in Theoretical Physics》2021年第2期108-116,共9页理论物理通讯（英文版）

基　　金：This work was supported by NSFC(Grant No.11675096);FPALAB-SNNU(Grant No.16QNGG007).

摘　　要：Hopfield neural networks on scale-free networks display the power law relation between the stability of patterns and the number of patterns.The stability is measured by the overlap between the output state and the stored pattern which is presented to a neural network.In simulations the overlap declines to a constant by a power law decay.Here we provide the explanation for the power law behavior through the signal-to-noise ratio analysis.We show that on sparse networks storing a plenty of patterns the stability of stored patterns can be approached by a power law function with the exponent-0.5.There is a difference between analytic and simulation results that the analytic results of overlap decay to 0.The difference exists because the signal and noise term of nodes diverge from the mean-field approach in the sparse finite size networks.

关 键 词：Hopfield neural network attractor neural networks associative memory 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]