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Synchronous Firing and Higher-Order Interactions in Neuron Pool

amari{at}brain.riken.go.jp, Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Wako-shi, Saitama, Japan

Hiroyuki Nakahara

hiro{at}brain.riken.go.jp, Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Wako-shi, Saitama, Japan

Si Wu

s.wu{at}dcs.shef.ac.uk, Department of Computer Science, Sheffield University, Sheffield S1, 4DP, U.K.

Yutaka Sakai

sakai{at}bios.ics.saitama-u.ac.jp, Department of Information and Computer Science, Saitama University, Saitama-shi, Saitama, Japan

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.

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