Learning and inference from neural population data across modes and timescales
Inferring neural population dynamics across timescales
Identifying coexisting fast and slow latent dynamics and characterizing their changes across behavioral regimes.
Neural population activity contains fluctuations that evolve over different timescales. Some modes decay quickly, while others persist over longer intervals. These temporal properties can also change during behavior. I am developing methods to identify multiple latent timescales from population recordings and characterize how they vary across dynamical regimes.
From population recordings to latent timescales
The central idea is to infer population dynamics before extracting their timescales. In a multi-timescale switching linear dynamical system (MTS-SLDS), a low-dimensional latent state evolves according to a regime-specific transition matrix. Gaussian or Poisson observation models connect that state to continuous measurements or spike counts. One regime describes a single set of latent dynamics; several regimes allow the dynamics to change within a recording.
For a decaying eigenmode of a fitted transition matrix, its eigenvalue determines the relaxation timescale:
Here, Δt is the sampling interval and λ is a transition eigenvalue. This timescale describes decay with the regime held fixed. Complex eigenvalues additionally encode oscillation. Several modes can coexist within one regime, and their decay timescales differ from the duration for which that regime remains active.
Learning dynamics across regimes
My approach combines multi-lag moment initialization with regime-conditioned Laplace EM. The initialization uses temporal structure in the observations. The refinement stage retains regime dependence in the latent-state statistics used to update the model; Poisson observations use local Laplace approximations. I evaluate the approach through synthetic recovery experiments and neural recordings from visual and somatosensory cortex.
Interpreting the estimates
These are effective dynamical timescales. Without additional assumptions or interventions, they do not separate intrinsic circuit dynamics from unobserved input-driven effects. This distinction guides the interpretation of the estimates and future work on stimulus- and input-dependent dynamics.
For a related published approach to differences across trials and conditions, see the MoLDS project.
Papers and resources
This project is ongoing. Manuscript and code links will be added when publicly available.