Average number of fixed points and attractors in Hopfield neural networks

Jiandu Liu, Bokui Chen, Dengcheng Yan and Lei Wang
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Jiandu Liu: Department of Physics and Beijing Key Laboratory of Opto-Electronic, Functional Materials and Micro-Nano Devices, Renmin University Beijing, P. R. China
Bokui Chen: #x2020;Division of Logistics and Transportation, Graduate School at Shenzhen, Tsinghua University, Shenzhen, P. R. China‡Department of Computer Science, School of Computing, National University of Singapore, Singapore
Dengcheng Yan: #xA7;Department of Modern Physics, University of Science and Technology of China Hefei, P. R. China
Lei Wang: Department of Physics and Beijing Key Laboratory of Opto-Electronic, Functional Materials and Micro-Nano Devices, Renmin University Beijing, P. R. China

International Journal of Modern Physics C (IJMPC), 2018, vol. 29, issue 08, 1-15

Abstract: Calculating the exact number of fixed points and attractors of an arbitrary Hopfield neural network is a non-deterministic polynomial (NP)-hard problem. In this paper, we first calculate the average number of fixed points in such networks versus their size and threshold of neurons, in terms of a statistical method, which has been applied to the calculation of the average number of metastable states in spin glass systems. Then the same method is expanded to study the average number of attractors in such networks. The results of the calculation qualitatively agree well with the numerical calculation. The discrepancies between them are also well explained.

Keywords: Hopfield neural network; fixed point; attractor; associative memory (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S0129183118500766

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