{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T18:17:02Z","timestamp":1771525022848,"version":"3.50.1"},"reference-count":8,"publisher":"MIT Press - Journals","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2003,1,1]]},"abstract":"<jats:p> 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. <\/jats:p>","DOI":"10.1162\/089976603321043720","type":"journal-article","created":{"date-parts":[[2003,2,13]],"date-time":"2003-02-13T01:51:52Z","timestamp":1045101112000},"page":"127-142","source":"Crossref","is-referenced-by-count":116,"title":["Synchronous Firing and Higher-Order Interactions in Neuron Pool"],"prefix":"10.1162","volume":"15","author":[{"given":"Shun-ichi","family":"Amari","sequence":"first","affiliation":[{"name":"Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Wako-shi, Saitama, Japan,"}]},{"given":"Hiroyuki","family":"Nakahara","sequence":"additional","affiliation":[{"name":"Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Wako-shi, Saitama, Japan,"}]},{"given":"Si","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Sheffield University, Sheffield S1, 4DP, U.K.,"}]},{"given":"Yutaka","family":"Sakai","sequence":"additional","affiliation":[{"name":"Department of Information and Computer Science, Saitama University, Saitama-shi, Saitama, Japan,"}]}],"member":"281","reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1016\/0959-4388(93)90060-C"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1109\/18.930911"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1162\/089976600300015934"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1109\/10.16444"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1007\/BF00199057"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1162\/08997660260293238"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.ne.18.030195.003011"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1038\/373515a0"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/089976603321043720","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T21:49:53Z","timestamp":1615585793000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/15\/1\/127-142\/6690"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1,1]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,1,1]]}},"alternative-id":["10.1162\/089976603321043720"],"URL":"https:\/\/doi.org\/10.1162\/089976603321043720","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1,1]]}}}