Identifiable Representation and Model Learning for Latent Dynamic Systems

Learning identifiable representations and models from low-level observations is helpful for an intelligent spacecraft to complete downstream tasks reliably. For temporal observations, to ensure that the data generating process is provably inverted, most existing works either assume that the noise variables in the dynamic mechanisms are (conditionally) independent or require that the interventions can directly affect each latent variable. However, in practice, the relationship between the exogenous inputs/interventions and the latent variables may follow some complex deterministic mechanisms. In this work, we study the problem of identifiable representation and model learning for latent dynamic systems. The key idea is to use an inductive bias inspired by controllable canonical forms, which are sparse and input-dependent by definition. We prove that, for linear and affine nonlinear latent dynamic systems with sparse input matrices, it is possible to identify the latent variables up to scaling and determine the dynamic models up to some simple transformations. The results have the potential to provide some theoretical guarantees for developing more trustworthy decision-making and control methods for intelligent spacecrafts.