| Автор | N S Skantzos |
| Автор | A C C Coolen |
| Дата выпуска | 2000-08-25 |
| dc.description | We solve a class of attractor neural network models with a mixture of 1D nearest-neighbour interactions and infinite-range interactions, which are both of a Hebbian-type form. Our solution is based on a combination of mean-field methods, transfer matrices, and 1D random-field techniques, and is obtained both for Boltzmann-type equilibrium (following sequential Glauber dynamics) and Peretto-type equilibrium (following parallel dynamics). Competition between the alignment forces mediated via short-range interactions, and those mediated via infinite-range ones, is found to generate novel phenomena, such as multiple locally stable `pure' states, first-order transitions between recall states, 2-cycles and non-recall states, and domain formation leading to extremely long relaxation times. We test our results against numerical simulations and simple benchmark cases, and find excellent agreement. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | (1 + ∞)-dimensional attractor neural networks |
| Тип | paper |
| DOI | 10.1088/0305-4470/33/33/301 |
| Print ISSN | 0305-4470 |
| Журнал | Journal of Physics A: Mathematical and General |
| Том | 33 |
| Первая страница | 5785 |
| Последняя страница | 5807 |
| Аффилиация | N S Skantzos; Department of Mathematics, King's College London, The Strand, London WC2R 2LS, UK |
| Аффилиация | A C C Coolen; Department of Mathematics, King's College London, The Strand, London WC2R 2LS, UK |
| Выпуск | 33 |
