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 stabilit...
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| Format: | Article |
| Language: | English |
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Saratov State University
2023-01-01
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| Series: | Известия высших учебных заведений: Прикладная нелинейная динамика |
| Subjects: | |
| Online Access: | https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2023/01/and_2023_soloviev-klinshov.pdf |
| _version_ | 1797938784761806848 |
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| author | Soloviev, Igor Aleksandrovich Klinshov, Vladimir Viktorovich |
| author_facet | Soloviev, Igor Aleksandrovich Klinshov, Vladimir Viktorovich |
| author_sort | Soloviev, Igor Aleksandrovich |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T19:05:09Z |
| format | Article |
| id | doaj.art-fc1522195cf2444990329289fe4bc02c |
| institution | Directory Open Access Journal |
| issn | 0869-6632 2542-1905 |
| language | English |
| last_indexed | 2024-04-10T19:05:09Z |
| publishDate | 2023-01-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия высших учебных заведений: Прикладная нелинейная динамика |
| spelling | doaj.art-fc1522195cf2444990329289fe4bc02c2023-01-31T04:41:45ZengSaratov State UniversityИзвестия высших учебных заведений: Прикладная нелинейная динамика0869-66322542-19052023-01-01311758510.18500/0869-6632-003028Stability thresholds of attractors of the Hopfield networkSoloviev, Igor Aleksandrovich0Klinshov, Vladimir Viktorovich1Institute of Applied Physics of the Russian Academy of Sciences, ul. Ul'yanova, 46, Nizhny Novgorod , 603950, RussiaLobachevsky State University of Nizhny Novgorod, 603950 Nizhny Novgorod, Gagarin Avenue, 23Purpose 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.https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2023/01/and_2023_soloviev-klinshov.pdfdynamical networkscollective dynamicsassociative memory |
| spellingShingle | Soloviev, Igor Aleksandrovich Klinshov, Vladimir Viktorovich Stability thresholds of attractors of the Hopfield network Известия высших учебных заведений: Прикладная нелинейная динамика dynamical networks collective dynamics associative memory |
| title | Stability thresholds of attractors of the Hopfield network |
| title_full | Stability thresholds of attractors of the Hopfield network |
| title_fullStr | Stability thresholds of attractors of the Hopfield network |
| title_full_unstemmed | Stability thresholds of attractors of the Hopfield network |
| title_short | Stability thresholds of attractors of the Hopfield network |
| title_sort | stability thresholds of attractors of the hopfield network |
| topic | dynamical networks collective dynamics associative memory |
| url | https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2023/01/and_2023_soloviev-klinshov.pdf |
| work_keys_str_mv | AT solovievigoraleksandrovich stabilitythresholdsofattractorsofthehopfieldnetwork AT klinshovvladimirviktorovich stabilitythresholdsofattractorsofthehopfieldnetwork |