## Neural Computation

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.