Hopfield网络上二次泛函的最小化

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

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引用次数: 2

摘要

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。

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Minimizing of the quadratic functional on Hopfield networks

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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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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.