Predicting nonlinear locomotion dynamics from neural activity

A central goal of neuroscience is to understand the link between behavior, motion, and neural activity. Recent advances in experimental and machine learning techniques to simultaneously record motion and neural activity provide extraordinary insight into how neural circuits create motion and behavioral states. Linear stochastic models have produced important insights into modeling behavior, motion, and neural activity, but they have yet to be used in manner that jointly captures all these variables and enables the accurate prediction of one given another. Here, we show how linear models can be augmented with structured nonlinearities inferred from the stationary distribution of the data to produce accurate generative models for behavior and motion in combination with low-dimensional mode representations. Equivalent to a Helmholtz decomposition, the dynamics are split between a nonlinear gradient component and a divergence-free component that is approximated to be linear. We combine this approach with a probabilistic model for neural activity suitable for the limitations of experimental data. After validating this approach on synthetic test data, we demonstrate its practical utility through application to C. elegans motion and neural recordings, showing that the resulting model is consistent with the experimentally observed statistics. Our framework is generic, both at the representation level and dynamical modeling level, so we expect our method to be applicable to a range of datasets.