Flow-field inference

Flow-field inference treats the goal of latent-dynamics modeling explicitly geometrically: estimate the vector field over the latent state space — the map from each point to its instantaneous velocity, dx/dt = f(x) — that the population appears to follow. Whether the underlying model is an RNN, a neural ODE, an rSLDS, or a Gaussian-process flow, the interpretable object read out is this field, from which one derives streamlines, fixed points, and the local linearizations (Jacobians) that describe stability and rotational structure. It is the modern, quantitative version of the qualitative dynamical-systems picture of neural computation.

Because trajectories only sample the field where the data actually go, flow-field estimates are trustworthy on the visited manifold and speculative off it; extrapolating the field into unvisited regions is exactly where models disagree and where interventional data are needed to arbitrate. Gaussian-process and Bayesian formulations are attractive here precisely because they return calibrated uncertainty over the field, flagging where the flow is well-constrained by data versus merely imagined by the model's smoothness prior.