PROPAGATION OF CHAOS AND POISSON HYPOTHESIS FOR REPLICA MEAN-FIELD MODELS OF INTENSITY-BASED NEURAL NETWORKS

• 成果类型: Article
• 署名作者: Davydova, Michel
• 署名单位: Inria; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP2015
• 发表日期: 2024
• 页码: 2107-2135
• 关键词: connections

摘要

Neural computations arising from myriads of interactions between spiking neurons can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this difficulty, the Poisson hypothesis regime replaces interaction times between neurons by Poisson processes. We prove that the Poisson hypothesis holds at the limit of an infinite number of replicas in the replica-mean-field model, which consists of randomly interacting copies of the network of interest. The proof is obtained through a novel application of the Chen-Stein method to the case of a random sum of Bernoulli random variables and a fixed point approach to prove a law of large numbers for exchangeable random variables.