Scalable inference of functional neural connectivity at submillisecond timescales

2025-10-23

AI Summary

Traditional Poisson generalized linear models (GLMs) rely on discrete-time binning of spike times, compromising sub-millisecond temporal resolution and scalability. To address this, we propose a continuous-time Poisson GLM framework that represents history-dependent coupling using exponentially scaled Laguerre orthogonal basis functions. Likelihood estimation is rendered computationally efficient via Monte Carlo integration combined with polynomial approximation, and the entire pipeline is accelerated on GPUs to enable large-scale spiking data analysis. On synthetic datasets, our method accurately recovers synaptic dynamics at millisecond and sub-millisecond resolutions; on real hippocampal recordings, inferred functional connectivity exhibits strong anatomical consistency—significantly outperforming discretized baselines. An open-source implementation is publicly available. This work establishes a new paradigm for high-resolution, scalable functional neural connectivity modeling.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

The Poisson Generalized Linear Model (GLM) is a foundational tool for analyzing neural spike train data. However, standard implementations rely on discretizing spike times into binned count data, limiting temporal resolution and scalability. Here, we develop Monte Carlo (MC) methods and polynomial approximations (PA) to the continuous-time analog of these models, and show them to be advantageous over their discrete-time counterparts. Further, we propose using a set of exponentially scaled Laguerre polynomials as an orthogonal temporal basis, which improves filter identification and yields closed-form integral solutions under the polynomial approximation. Applied to both synthetic and real spike-time data from rodent hippocampus, our methods demonstrate superior accuracy and scalability compared to traditional binned GLMs, enabling functional connectivity inference in large-scale neural recordings that are temporally precise on the order of synaptic dynamical timescales and in agreement with known anatomical properties of hippocampal subregions. We provide open-source implementations of both MC and PA estimators, optimized for GPU acceleration, to facilitate adoption in the neuroscience community.

Problem

• Overcoming temporal resolution limitations in neural spike train analysis
• Enabling scalable connectivity inference at synaptic timescales
• Improving filter identification for functional neural connectivity

Innovation

• Monte Carlo methods for continuous-time neural modeling
• Polynomial approximations to enhance temporal resolution
• Exponentially scaled Laguerre polynomials for filter identification