Modeling Higher-Order Interactions in Sparse and Heavy-Tailed Neural Population Activity.

IF 2.1 4区 计算机科学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Ulises Rodríguez-Domínguez, Hideaki Shimazaki
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引用次数: 0

Abstract

Neurons process sensory stimuli efficiently, showing sparse yet highly variable ensemble spiking activity involving structured higher-order interactions. Notably, while neural populations are mostly silent, they occasionally exhibit highly synchronous activity, resulting in sparse and heavy-tailed spike-count distributions. However, its mechanistic origin-specifically, what types of nonlinear properties in individual neurons induce such population-level patterns-remains unclear. In this study, we derive sufficient conditions under which the joint activity of homogeneous binary neurons generates sparse and widespread population firing rate distributions in infinitely large networks. We then propose a subclass of exponential family distributions that satisfy this condition. This class incorporates structured higher-order interactions with alternating signs and shrinking magnitudes, along with a base-measure function that offsets distributional concentration, giving rise to parameter-dependent sparsity and heavy-tailed population firing rate distributions. Analysis of recurrent neural networks that recapitulate these distributions reveals that individual neurons possess threshold-like nonlinearity, followed by supralinear activation that jointly facilitates sparse and synchronous population activity. These nonlinear features resemble those in modern Hopfield networks, suggesting a connection between widespread population activity and the network's memory capacity. The theory establishes sparse and heavy-tailed distributions for binary patterns, forming a foundation for developing energy-efficient spike-based learning machines.

稀疏和重尾神经群体活动的高阶交互建模。
神经元有效地处理感觉刺激,表现出稀疏但高度可变的集成尖峰活动,涉及结构化的高阶相互作用。值得注意的是,虽然神经种群大多是沉默的,但它们偶尔会表现出高度同步的活动,导致稀疏和重尾的尖峰数分布。然而,它的机制起源,特别是,个体神经元中哪种类型的非线性特性诱导了这种群体水平的模式,仍然不清楚。在本研究中,我们得到了在无限大网络中,同质二值神经元的联合活动产生稀疏而广泛的总体放电率分布的充分条件。然后我们提出了满足这个条件的指数族分布的一个子类。这类包含结构化的高阶相互作用,具有交替的符号和缩小的幅度,以及抵消分布集中的基本测量函数,从而产生依赖参数的稀疏性和重尾种群发射率分布。对概括这些分布的递归神经网络的分析表明,单个神经元具有类似阈值的非线性,随后是超线性激活,共同促进稀疏和同步的种群活动。这些非线性特征与现代Hopfield网络相似,表明广泛的人口活动与网络的记忆容量之间存在联系。该理论建立了二元模式的稀疏和重尾分布,为开发节能的基于峰值的学习机器奠定了基础。
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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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