Monthly
288 pp. per issue
6 x 9, illustrated
ISSN
0899-7667
E-ISSN
1530-888X
2014 Impact factor:
2.21

Neural Computation

January 1, 2003, Vol. 15, No. 1, Pages 127-142
(doi: 10.1162/089976603321043720)
© 2002 Massachusetts Institute of Technology
Synchronous Firing and Higher-Order Interactions in Neuron Pool
Article PDF (123.15 KB)
Abstract

The stochastic mechanism of synchronous firing in a population of neurons is studied from the point of view of information geometry. Higher-order interactions of neurons, which cannot be reduced to pairwise correlations, are proved to exist in synchronous firing. In a neuron pool where each neuron fires stochastically, the probability distribution q(r) of the activity r, which is the fraction of firing neurons in the pool, is studied. When q(r) has a widespread distribution, in particular, when q(r) has two peaks, the neurons fire synchronously at one time and are quiescent at other times. The mechanism of generating such a probability distribution is interesting because the activity r is concentrated on its mean value when each neuron fires independently, because of the law of large numbers. Even when pairwise interactions, or third-order interactions, exist, the concentration is not resolved. This shows that higher-order interactions are necessary to generate widespread activity distributions. We analyze a simple model in which neurons receive common overlapping inputs and prove that such a model can have a widespread distribution of activity, generating higher-order stochastic interactions.