Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1162/neco.2009.02-09-960 | Neural Computation |
Keywords | Field | DocType |
rate equation,algorithms,neural network,artificial intelligence,mean field,action potentials | Applied mathematics,Population,Mathematical optimization,Models of neural computation,Mean field theory,Connectivity,Statistics,Order statistic,Artificial neural network,Independent equation,Traffic equations,Mathematics | Journal |
Volume | Issue | ISSN |
22 | 2 | 0899-7667 |
Citations | PageRank | References |
33 | 1.56 | 20 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael A. Buice | 1 | 42 | 2.41 |
| Jack D. Cowan | 2 | 527 | 529.18 |
| Carson C. Chow | 3 | 453 | 60.03 |