H-Lens: Extracting Phase-Space from World Model Representations

World models hold great promise in learning representations for planning, but the dynamical structure hidden in their latent space is opaque. This also bleeds into the problem of evaluating whether the model's predictions have diverged away from reality. We introduce H-Lens, a framework for extracting phase-space dynamics from a world model. Using Hamiltonian Neural Networks (HNN), we extract coordinate and momentum-like variables out of latent states predicted by a world model. We use the learned HNN, to then extract a vector field which can be used to interpret learned dynamics. We further define a phase space error measure that predicts the rollout degradation entirely within the obtained vector field without requiring access to any ground truth states. We evaluate H-Lens on Dreamer, LeWorldModel and DINO-WM on the Pendulum, Mountain Car, and Lunar Lander environments trained on pixel observations. Models are trained and evaluated under default and dynamics-shifted environment parameters. The resulting phase space visualizations and rollout error in the vector field provide a way to inspect the dynamics learned by world models and predict their rollout degradation.