Generative Modeling of Neural Dynamics via Latent Stochastic Differential Equations

TL;DR

This paper introduces a probabilistic framework using latent stochastic differential equations to model neural dynamics, integrating mathematical models and neural networks for improved interpretability and efficiency.

Contribution

It presents a novel hybrid modeling approach combining coupled oscillators and neural networks within a stochastic differential equation framework for neural data analysis.

Findings

Achieves competitive prediction of neural responses with fewer parameters.

Provides uncertainty estimates for neural dynamics.

Demonstrates versatility across multiple datasets and species.

Abstract

We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic dynamical system which implements computations through its state evolution. To model this dynamical system, we employ a system of coupled stochastic differential equations with differentiable drift and diffusion functions and use variational inference to infer its states and parameters. This formulation enables seamless integration of existing mathematical models in the literature, neural networks, or a hybrid of both to learn and compare different models. We demonstrate this in our framework by developing a generative model that combines coupled oscillators with neural networks to capture latent population dynamics from single-cell recordings. Evaluation across three neuroscience datasets spanning different species, brain regions, and behavioral tasks show that these hybrid models achieve competitive performance in predicting stimulus-evoked neural and behavioral responses compared to sophisticated black-box approaches while requiring an order of magnitude fewer parameters, providing uncertainty estimates, and offering a natural language for interpretation.