Population Level Activity in Large Random Neural Networks
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911774647779328 |
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| author | MacLaurin, James Silverstein, Moshe Vilanova, Pedro |
| author_facet | MacLaurin, James Silverstein, Moshe Vilanova, Pedro |
| contents | We determine limiting equations for large asymmetric `spin glass' networks. The initial conditions are not assumed to be independent of the disordered connectivity: one of the main motivations for this is that allows one to understand how the structure of the limiting equations depends on the energy landscape of the random connectivity. The method is to determine the convergence of the double empirical measure (this yields population density equations for the joint distribution of the spins and fields). The limiting dynamics is expressed in terms of a fixed point operator. It is proved that repeated applications of this operator must converge to the limiting dynamics (thus yielding a relatively efficient means of numerically simulating the limiting equations, |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15272 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Population Level Activity in Large Random Neural Networks MacLaurin, James Silverstein, Moshe Vilanova, Pedro Disordered Systems and Neural Networks Probability We determine limiting equations for large asymmetric `spin glass' networks. The initial conditions are not assumed to be independent of the disordered connectivity: one of the main motivations for this is that allows one to understand how the structure of the limiting equations depends on the energy landscape of the random connectivity. The method is to determine the convergence of the double empirical measure (this yields population density equations for the joint distribution of the spins and fields). The limiting dynamics is expressed in terms of a fixed point operator. It is proved that repeated applications of this operator must converge to the limiting dynamics (thus yielding a relatively efficient means of numerically simulating the limiting equations, |
| title | Population Level Activity in Large Random Neural Networks |
| topic | Disordered Systems and Neural Networks Probability |
| url | https://arxiv.org/abs/2401.15272 |