Cell-Class Neural Ordinary Differential Equation Models for Parsing Biologically-Constrained Contributions to Neural Dynamics

Understanding how populations of individual neurons interact to shape the overall dynamics of neural activity is a central question in computational and systems neuroscience. Recent work has shown that neural ordinary differential equation (NODE) models are able to model neural activity dynamics with high accuracy and interpretability of the underlying dynamics. However, existing NODE models treat all neurons as part of a homogeneous group, preventing understanding of how underlying neural populations (e.g., excitatory and inhibitory cell classes) contribute to the overall dynamics. Here, we introduce Excitatory-Inhibitory NODE (EI-NODE) models. These models A) decompose the overall dynamics into components specific to each population, allowing understanding of each population's interactions with one another; and B) provide biological constraints on the contributions of excitatory and inhibitory populations towards the dynamics, using a variant of monotonic neural networks. Using both synthetic data and recorded neural activity data during a naturalistic climbing task with optogenetic perturbations, we show that EI-NODE models can provide equivalent or greater accuracy in dynamics modeling compared to alternative models, while enabling a newfound biologically constrained understanding of neural populations' interactions and roles in the underlying dynamics.