Identifiable Representation and Model Learning for Latent Dynamic Systems
Congxi Zhang, Yongchun Xie
TL;DR
This work tackles the challenge of recovering identifiable latent representations and their dynamics from low-level observations in latent dynamic systems. It introduces an inductive bias based on controllable canonical forms to enable identifiability under deterministic high-order dynamics with sparse inputs, providing theoretical guarantees that latents are identifiable up to scaling and dynamics up to simple transformations for linear and affine nonlinear cases, respectively (e.g., τ(z) = (ˆb/b) z in the linear single-input setting). The authors validate the approach on synthetic data, demonstrating near-perfect latent recovery and accurate one-step predictions with low noise, while highlighting robustness to moderate noise and the necessity of high-order modeling over first-order integrators. These results offer principled guarantees that can support trustworthy decision-making and control for intelligent spacecraft operating in complex observation environments, where interpretable latent dynamics are essential for downstream control tasks.
Abstract
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 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.