Parsing neural dynamics with infinite recurrent switching linear dynamical systems

Unsupervised segmentation of behavior and neural activity into simpler alternating states is providing unprecedented insights onto the neural underpinnings of decision-making. Recurrent Switching Linear Dynamical Systems (rSLDS) models use observations or continuous latent activity to guide the switching in states, providing significant advantages in capturing important temporally and spatially sequential dependencies. In trying to allow for unbounded complexity in the discrete states, most approaches have focused on Dirichlet Process (DP) mixture models. Such non-parametric Bayesian models restrict the distribution over dynamical states to be invariant under permutations (i.e. exchangeable) —a challenging assumption in the modeling of sequential data, and incompatible with recurrent connections. In this work, we leverage nonexchangeable parsing processes to extend the rSLDS model to infinite capacity distributions over dynamical state partitions. Common Pólya-gamma augmentation techniques can be used to provide tractable Bayesian inference, but at a considerable computational cost. We instead leverage partial differential equations (PDE) theory to derive an efficient, semi-parametric formulation for discrete state dynamical sufficient statistics in the infinite rSLDS model class. Finally, we demonstrate the flexibility and synthesizing properties of our model class on synthetic data and mice electrophysiological data during decision-making. For the latter, we present early evidence towards the model’s abilities to uncover slow non-stationary motifs in the discrete state distribution underlying baseline neural activity.