Structured Latent Dynamics in Wireless CSI via Homomorphic World Models

We introduce a self-supervised framework for learning predictive and structured representations of wireless channels by modeling the temporal evolution of channel state information (CSI) in a compact latent space. Our method casts the problem as a world modeling task and leverages the Joint Embedding Predictive Architecture (JEPA) to learn action-conditioned latent dynamics from CSI trajectories. To promote geometric consistency and compositionality, we parameterize transitions using homomorphic updates derived from Lie algebra, yielding a structured latent space that reflects spatial layout and user motion. Evaluations on the DICHASUS dataset show that our approach outperforms strong baselines in preserving topology and forecasting future embeddings across unseen environments. The resulting latent space enables metrically faithful channel charts, offering a scalable foundation for downstream applications such as mobility-aware scheduling, localization, and wireless scene understanding.