Meta-iLaD: Identifiable Latent Dynamics via Meta-Learning of Dynamics Environments

Learning latent dynamics is central to assessing current states and forecasting future trajectories for high-dimensional time series. For locally-stationary latent dynamics parameterized by past latent states and an environment variable c, with latent dynamics state z t, prior identifiability results largely focus on z t when conditioned on pre-defined label u of the dynamics environment. This leaves two limitations: reliance on pre-defined labels that hinder generalization to unseen environments, and limited understanding of the identifiability of F and c which---while offering important structural properties for the identifiability of z t---are learned jointly with z t. We address these challenges with Meta-iLaD, a novel latent dynamics framework to attain identifiability by meta-learning across dynamics environments. Meta-iLaD replaces the conditioning of c on pre-defined labels with a novel conditional prior, modeled as a feedforward meta-learner that rapidly extracts c from few-shot examples. We further establish simultaneous identifiability for z_t, c and F, for a general formulation of the dynamics function F over past latent states and c, without restricting the dimension of c or how it modulates F. We provide strong empirical evidence that 1) conditioning on few-shot examples enables generalization to out-of-distribution environments, and 2) identifiability for c and F is critical for accurate forecasting beyond reconstructing observed trajectories.