论文标题
基于强度的神经网络的复制均值模型的混乱和泊松假设的传播
Propagation of chaos and Poisson Hypothesis for replica mean-field models of intensity-based neural networks
论文作者
论文摘要
由峰值神经元之间无数相互作用引起的神经计算可以建模为具有点状相互作用的网络动力学。但是，大多数相关的动力学不允许进行计算障碍。为了避免这种困难，泊松假说制度取代了泊松过程之间神经元之间的相互作用时间。我们证明，泊松假说在复制品均值模型中的无限副本数量的极限，该模型由随机相互作用的副本组成。该证明是通过将陈 - 斯坦方法的新颖应用在伯努利随机变量和固定点方法的随机总和中获得的，以证明用于可交换随机变量的大量定律。
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.
