title: Synchronous firing and higher-order interactions in neuron pool.
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.
authors.affiliation: Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Wako-shi, Saitama, Japan. amari@brain.riken.go.jp
authors.forename: Shun-Ichi
authors.initials: S
authors.lastname: Amari
authors.forename: Hiroyuki
authors.initials: H
authors.lastname: Nakahara
authors.forename: Si
authors.initials: S
authors.lastname: Wu
authors.forename: Yutaka
authors.initials: Y
authors.lastname: Sakai
mesh_terms: D009474:Neurons / Q000502:physiology*; D013269:Stochastic Processes; D009435:Synaptic Transmission / Q000502:physiology*