Minimizing of the quadratic functional on Hopfield networks

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.14232/ejqtde.2021.1.92

Equations O. Boichuk, D. Bihun, V. Feruk, O. Pokutnyi

引用次数: 2

Abstract

In this paper, we consider the continuous Hopfield model with a weak interaction of network neurons. This model is described by a system of differential equations with linear boundary conditions. Also, we consider the questions of finding necessary and sufficient conditions of solvability and constructive construction of solutions of the given problem, which turn into solutions of the linear generating problem, as the parameter $\varepsilon$ tends to zero. An iterative algorithm for finding solutions has been constructed. The problem of finding the extremum of the target functions on the given problem solution is considered. To minimize a functional, an accelerated method of conjugate gradients is used. Results are illustrated with examples for the case of three neurons.

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Hopfield网络上二次泛函的最小化

本文考虑具有弱相互作用的连续Hopfield模型。该模型用具有线性边界条件的微分方程组来描述。此外，我们还考虑了当参数$\varepsilon$趋于零时，给定问题解的可解性和构造性的充分必要条件的求取问题，这些解转化为线性生成问题的解。构造了一种求解的迭代算法。考虑在给定问题解上求目标函数的极值问题。为了最小化泛函，使用了加速共轭梯度法。用三个神经元的例子说明了结果。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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