{"title":"Modeling Higher-Order Interactions in Sparse and Heavy-Tailed Neural Population Activity.","authors":"Ulises Rodríguez-Domínguez, Hideaki Shimazaki","doi":"10.1162/neco.a.35","DOIUrl":null,"url":null,"abstract":"<p><p>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.</p>","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":" ","pages":"2011-2078"},"PeriodicalIF":2.1000,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Neural Computation","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1162/neco.a.35","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
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.
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.