Fig. 1: Modeling latent manifolds from neuroimaging data.
A Recorded neural activity y relates to latent neural states on the manifold x via observation model (matrix) D. Neural dynamics (trajectories) on the manifold operate in the tangent space. These linear operators can be summed linearly. The manifold depicted here is an illustration; we do not constrain the model to a particular manifold, nor do we define a particular manifold in the process of learning the dLDS model. B Graphical model depicting the relationships between data y and model parameters from time point to time point (dynamics coefficients c, DO dictionary of matrices f, latent states x, and observation model D). Dynamics coefficients c describe DO use over time. C–E Example of a dLDS decomposition of a nonautonomous dynamical system - the Duffing oscillator, reproduced from Mudrik et al.43. dLDS can recover the activity of a simple nonautonomous system (E) using dynamics coefficients (C) dynamics operators (D) that represent its linear and nonlinear components.
