# Scalable inference of functional neural connectivity at submillisecond timescales

arXiv: https://arxiv.org/abs/2510.20966 · HTML: https://mlsanity.com/paper/2510.20966/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 36 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Builds on (most cited first, 8 of 8)

- [The Road Less Scheduled](https://mlsanity.com/paper/2405.15682/) (2024)
- [Variance-Reduced Methods for Machine Learning](https://mlsanity.com/paper/2010.00892/) (2020)
- [PASS-GLM: polynomial approximate sufficient statistics for scalable Bayesian GLM inference](https://mlsanity.com/paper/1709.09216/) (2017)
- [Point process models for sequence detection in high-dimensional neural spike trains](https://mlsanity.com/paper/2010.04875/) (2020)
- [Scalable Bayesian Inference for Excitatory Point Process Networks](https://mlsanity.com/paper/1507.03228/) (2015)
- [Efficient non-conjugate Gaussian process factor models for spike count data using polynomial approximations](https://mlsanity.com/paper/1906.03318/) (2019)
- [Circumstantial evidence and explanatory models for synapses in large-scale spike recordings](https://mlsanity.com/paper/2304.09699/) (2023)
- [A causal inference approach of monosynapses from spike trains](https://mlsanity.com/paper/2405.02786/) (2024)

## Abstract (arXiv)

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.