Generative Modeling of Neural Dynamics via Latent Stochastic Differential Equations
This work addresses the challenge of developing interpretable and efficient computational models for neuroscience, offering a framework that integrates existing mathematical models with neural networks, though it is incremental in its hybrid approach.
The authors tackled the problem of modeling biological neural systems by proposing a probabilistic framework that treats physiological recordings as observations of an underlying continuous-time stochastic dynamical system, using latent stochastic differential equations with variational inference. They demonstrated that hybrid models combining coupled oscillators and neural networks achieve competitive performance in predicting neural and behavioral responses across three neuroscience datasets, requiring an order of magnitude fewer parameters than black-box approaches while providing uncertainty estimates and interpretability.
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.