Learning neural population dynamics across modes

Discovering distinct population dynamics

Fitting all trajectories with one model can obscure differences among conditions. Fitting each labeled condition separately, meanwhile, makes it harder to discover groups that differ from the experimental categories.

I study mixtures of linear dynamical systems (MoLDS), in which each trajectory is associated with an unobserved dynamical component. The goal is to estimate these components and infer which trajectories they explain. This groups recordings by their temporal dynamics and lets us examine how the resulting groups relate to behavior. In this model, component identity is fixed within a trajectory; it can differ across trajectories.

Combining identification and learning

With Shreya Saxena, I introduced Tensor-EM, which combines moment-based identification with likelihood-based refinement. The first stage constructs tensors from input-output statistics and uses simultaneous matrix diagonalization to estimate mixture weights and system parameters. Under the model’s assumptions, this stage supports identifiable recovery. A subsequent Kalman EM stage refines the latent-state estimates and model parameters using the observed trajectories.

We evaluate recovery in synthetic systems and apply the method to two primate neural datasets collected during reaching tasks. These applications show how a mixture model can reveal condition-related differences in population dynamics.

This project connects a mathematical question—when distinct dynamical systems can be identified from data—to a neuroscience question: how population dynamics vary across behavioral conditions. The complementary MTS-SLDS project examines multiple decay timescales and regime changes within a recording.