Systematic fluctuation expansion for neural network activity equations
Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity. The shortcoming of these equations is that they take into ac...
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| Vydáno v: | Neural computation Ročník 22; číslo 2; s. 377 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
United States
01.02.2010
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| Témata: | |
| ISSN: | 1530-888X, 1530-888X |
| On-line přístup: | Zjistit podrobnosti o přístupu |
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| Shrnutí: | Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity. The shortcoming of these equations is that they take into account only the average firing rate, while leaving out higher-order statistics like correlations between firing. A stochastic theory of neural networks that includes statistics at all orders was recently formulated. We describe how this theory yields a systematic extension to population rate equations by introducing equations for correlations and appropriate coupling terms. Each level of the approximation yields closed equations; they depend only on the mean and specific correlations of interest, without an ad hoc criterion for doing so. We show in an example of an all-to-all connected network how our system of generalized activity equations captures phenomena missed by the mean field rate equations alone. |
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| Bibliografie: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Correspondence-1 content type line 23 |
| ISSN: | 1530-888X 1530-888X |
| DOI: | 10.1162/neco.2009.02-09-960 |