随机神经元大型网络中协方差的决定性作用

IF 2.7 4区 计算机科学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Vincent Painchaud;Patrick Desrosiers;Nicolas Doyon
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引用次数: 0

摘要

生物神经网络因其随机行为和高维度而难以建模。我们通过构建一个动态模型来解决这一问题,该模型既包含对网络种群中活跃神经元和折射神经元的期望值,也包含它们的协方差。为此,我们用连续时间马尔可夫链描述单个神经元状态的演变,并从中正式推导出一个低维动态系统。这是通过解决矩闭合问题来实现的,该问题与激活函数的非线性和有界性相兼容。即使在均值场近似无法捕捉到高维随机模型行为的情况下,我们的动力系统也能捕捉到。考虑到二阶矩会改变用均值场近似得到的解,并可能导致定点和极限循环的出现或消失。此外,我们还进行了数值实验,发现均场近似会导致周期性振荡解,而二阶模型的解可以解释为随机模型多次实现后的平均值。总之,我们的研究结果强调了在研究随机网络时加入高阶矩的重要性,并加深了我们对相关神经元活动的理解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Determining Role of Covariances in Large Networks of Stochastic Neurons
Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active and refractory neurons in the network’s populations. We do so by describing the evolution of the states of individual neurons with a continuous-time Markov chain, from which we formally derive a low-dimensional dynamical system. This is done by solving a moment closure problem in a way that is compatible with the nonlinearity and boundedness of the activation function. Our dynamical system captures the behavior of the high-dimensional stochastic model even in cases where the mean-field approximation fails to do so. Taking into account the second-order moments modifies the solutions that would be obtained with the mean-field approximation and can lead to the appearance or disappearance of fixed points and limit cycles. We moreover perform numerical experiments where the mean-field approximation leads to periodically oscillating solutions, while the solutions of the second-order model can be interpreted as an average taken over many realizations of the stochastic model. Altogether, our results highlight the importance of including higher moments when studying stochastic networks and deepen our understanding of correlated neuronal activity.
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来源期刊
Neural Computation
Neural Computation 工程技术-计算机:人工智能
CiteScore
6.30
自引率
3.40%
发文量
83
审稿时长
3.0 months
期刊介绍: Neural Computation is uniquely positioned at the crossroads between neuroscience and TMCS and welcomes the submission of original papers from all areas of TMCS, including: Advanced experimental design; Analysis of chemical sensor data; Connectomic reconstructions; Analysis of multielectrode and optical recordings; Genetic data for cell identity; Analysis of behavioral data; Multiscale models; Analysis of molecular mechanisms; Neuroinformatics; Analysis of brain imaging data; Neuromorphic engineering; Principles of neural coding, computation, circuit dynamics, and plasticity; Theories of brain function.
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