I Act Therefore I Am: When Is JEPA's Action-Conditioning Enough to Learn Causal Mechanisms?

Recent empirical and theoretical advances suggest that joint-embedding predictive architectures (JEPAs) may learn meaningful representations for action-conditioned prediction of future outcomes, thus becoming one of the foundational structures for world models. However, accurate prediction does not, in general, necessarily imply recovery of underlying causal states that give rise to the observed dynamics. This work investigates when and how JEPAs can recover the underlying causal states from observations. We first introduce a latent variable model, in which high-dimensional observations are generated from latent causal states whose dynamics are governed by action-conditioned transition mechanisms. Based on this formulation, we develop a general information-theoretic objective that combines conditional likelihood maximization for learning transition dynamics with entropy maximization for preserving latent state information. We then establish identifiability conditions under which representations learned by this general objective recover the underlying latent causal states up to component-wise invertible transformations and permutation. One key condition for such identifiability is sufficient action-induced variation in the transition mechanisms. Guided by this finding, we instantiate the general objective with an action-modulated Gaussian additive-noise model, yielding action-modulated JEPA (A-JEPA). Experiments on synthetic environments verify the theoretical findings under the identifiability conditions and robustness to moderate violations, while visual benchmarks demonstrate improved state recovery and transfer to unseen transition mechanisms.