Hopfield网络吸引子的稳定性阈值

IF 0.5 Q4 PHYSICS, MULTIDISCIPLINARY

Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika Pub Date : 2023-01-01 DOI:10.18500/0869-6632-003028

I. Soloviev, V. Klinshov

{"title":"Hopfield网络吸引子的稳定性阈值","authors":"I. Soloviev, V. Klinshov","doi":"10.18500/0869-6632-003028","DOIUrl":null,"url":null,"abstract":"Purpose of the work is the detailed study of the attractors of the Hopfield network and their basins of attraction depending on the parameters of the system, the size of the network and the number of stored images. To characterize the basins of attraction we used the method of the so-called stability threshold, i.e., the minimum distance from an attractor to the boundary of its basin of attraction. For useful attractors, this value corresponds to the minimum distortion of the stored image, after which the system is unable to recognize it. In the result of the study it is shown that the dependence of the average stability threshold of useful attractors on the number of stored images can be nonmonotonic, due to which the stability of the network can improve when new images are memorized. An analysis of the stability thresholds allowed to estimate the maximum number of images that the network can store without fatal errors in their recognition. In this case, the stability threshold of useful attractors turns out to be close to the minimum possible value, that is, to unity. To conclude, calculation of the stability thresholds provides important information about the attraction basins of the network attractors.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"47 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stability thresholds of attractors of the Hopfield network\",\"authors\":\"I. Soloviev, V. Klinshov\",\"doi\":\"10.18500/0869-6632-003028\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Purpose of the work is the detailed study of the attractors of the Hopfield network and their basins of attraction depending on the parameters of the system, the size of the network and the number of stored images. To characterize the basins of attraction we used the method of the so-called stability threshold, i.e., the minimum distance from an attractor to the boundary of its basin of attraction. For useful attractors, this value corresponds to the minimum distortion of the stored image, after which the system is unable to recognize it. In the result of the study it is shown that the dependence of the average stability threshold of useful attractors on the number of stored images can be nonmonotonic, due to which the stability of the network can improve when new images are memorized. An analysis of the stability thresholds allowed to estimate the maximum number of images that the network can store without fatal errors in their recognition. In this case, the stability threshold of useful attractors turns out to be close to the minimum possible value, that is, to unity. To conclude, calculation of the stability thresholds provides important information about the attraction basins of the network attractors.\",\"PeriodicalId\":41611,\"journal\":{\"name\":\"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika\",\"volume\":\"47 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.18500/0869-6632-003028\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18500/0869-6632-003028","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

这项工作的目的是详细研究Hopfield网络的吸引子及其吸引盆地，这取决于系统的参数、网络的大小和存储图像的数量。为了描述吸引盆地，我们使用了所谓的稳定性阈值方法，即从吸引子到其吸引盆地边界的最小距离。对于有用的吸引子，该值对应于存储图像的最小失真，超过该值后系统无法识别它。研究结果表明，有用吸引子的平均稳定性阈值与存储图像数量的依赖关系是非单调的，因此当存储新图像时，网络的稳定性可以得到提高。通过对稳定性阈值的分析，可以估计出网络可以存储的图像的最大数量，而不会在识别中出现致命错误。在这种情况下，有用吸引子的稳定性阈值趋于最小可能值，即趋于一致。综上所述，稳定性阈值的计算提供了网络吸引子吸引盆地的重要信息。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Stability thresholds of attractors of the Hopfield network

Purpose of the work is the detailed study of the attractors of the Hopfield network and their basins of attraction depending on the parameters of the system, the size of the network and the number of stored images. To characterize the basins of attraction we used the method of the so-called stability threshold, i.e., the minimum distance from an attractor to the boundary of its basin of attraction. For useful attractors, this value corresponds to the minimum distortion of the stored image, after which the system is unable to recognize it. In the result of the study it is shown that the dependence of the average stability threshold of useful attractors on the number of stored images can be nonmonotonic, due to which the stability of the network can improve when new images are memorized. An analysis of the stability thresholds allowed to estimate the maximum number of images that the network can store without fatal errors in their recognition. In this case, the stability threshold of useful attractors turns out to be close to the minimum possible value, that is, to unity. To conclude, calculation of the stability thresholds provides important information about the attraction basins of the network attractors.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika PHYSICS, MULTIDISCIPLINARY-

CiteScore

1.20

自引率

25.00%

发文量

期刊介绍： Scientific and technical journal Izvestiya VUZ. Applied Nonlinear Dynamics is an original interdisciplinary publication of wide focus. The journal is included in the List of periodic scientific and technical publications of the Russian Federation, recommended for doctoral thesis publications of State Commission for Academic Degrees and Titles at the Ministry of Education and Science of the Russian Federation, indexed by Scopus, RSCI. The journal is published in Russian (English articles are also acceptable, with the possibility of publishing selected articles in other languages by agreement with the editors), the articles data as well as abstracts, keywords and references are consistently translated into English. First and foremost the journal publishes original research in the following areas: -Nonlinear Waves. Solitons. Autowaves. Self-Organization. -Bifurcation in Dynamical Systems. Deterministic Chaos. Quantum Chaos. -Applied Problems of Nonlinear Oscillation and Wave Theory. -Modeling of Global Processes. Nonlinear Dynamics and Humanities. -Innovations in Applied Physics. -Nonlinear Dynamics and Neuroscience. All articles are consistently sent for independent, anonymous peer review by leading experts in the relevant fields, the decision to publish is made by the Editorial Board and is based on the review. In complicated and disputable cases it is possible to review the manuscript twice or three times. The journal publishes review papers, educational papers, related to the history of science and technology articles in the following sections: -Reviews of Actual Problems of Nonlinear Dynamics. -Science for Education. Methodical Papers. -History of Nonlinear Dynamics. Personalia.