TiDHy: timescale demixing via hypernetworks to learn simultaneous dynamics from mixed observations.

Neural activity and behaviour arise from multiple concurrent time-varying systems, including neuromodulation, neural state and history; however, most current approaches model these data as one set of dynamics with a single timescale. Here, we develop timescale demixing via hypernetworks (TiDHy) as a new computational method to model spatiotemporal data, decomposing them into multiple simultaneous latent dynamical systems that may span orders of magnitude different timescales. Specifically, we train a hypernetwork to dynamically reweigh linear combinations of latent dynamics. This approach enables accurate data reconstruction, converges to true latent dynamics and captures multiple timescales of variation. We first demonstrate that TiDHy can demix dynamics and timescales from synthetic data comprising multiple independent switching linear dynamical systems, even when the observations are mixed. Next, with a simulated locomotion behaviour dataset, we show that TiDHy accurately captures both the fast dynamics of movement kinematics and the slow dynamics of changing terrains. Finally, in an open-source multi-animal social behaviour dataset, we show that the keypoint trajectory dynamics extracted with TiDHy can be used to accurately identify social behaviours of multiple mice. Taken together, TiDHy is a powerful new algorithm for demixing simultaneous latent dynamical systems with applications to diverse computational domains.