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• W2080254111 abstract "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." @default.
• W2080254111 created "2016-06-24" @default.
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• W2080254111 date "2000-08-10" @default.
• W2080254111 modified "2023-09-25" @default.
• W2080254111 title "(1 + ∞)-dimensional attractor neural networks" @default.
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• W2080254111 doi "https://doi.org/10.1088/0305-4470/33/33/301" @default.
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