GeoWorld: Geometric World Models
About
Energy-based predictive world models provide a powerful approach for multi-step visual planning by reasoning over latent energy landscapes rather than generating pixels. However, existing approaches face two major challenges: (i) their latent representations are typically learned in Euclidean space, neglecting the underlying geometric and hierarchical structure among states, and (ii) they struggle with long-horizon prediction, which leads to rapid degradation across extended rollouts. To address these challenges, we introduce GeoWorld, a geometric world model that preserves geometric structure and hierarchical relations through a Hyperbolic JEPA, which maps latent representations from Euclidean space onto hyperbolic manifolds. We further introduce Geometric Reinforcement Learning for energy-based optimization, enabling stable multi-step planning in hyperbolic latent space. Extensive experiments on CrossTask and COIN demonstrate around 3% SR improvement in 3-step planning and 2% SR improvement in 4-step planning compared to the state-of-the-art V-JEPA 2. Project website: https://steve-zeyu-zhang.github.io/GeoWorld.
Related benchmarks
| Task | Dataset | Result | Rank | |
|---|---|---|---|---|
| Goal-conditioned visual planning | CrossTask T=4 88 (test) | SR37.04 | 40 | |
| Goal-conditioned visual planning | CrossTask T=3 88 | Success Rate (SR)47.47 | 27 | |
| Goal-conditioned visual planning | COIN T=3 71 | Success Rate (SR)34.85 | 20 | |
| Goal-conditioned visual planning | COIN T=4 71 | SR27.79 | 20 | |
| Goal-conditioned visual planning | CrossTask T=3 88 (test) | Success Rate (SR)51.71 | 13 | |
| Goal-conditioned visual planning | COIN T=3 71 (test) | SR45.29 | 13 | |
| Goal-conditioned visual planning | COIN T=4 71 (test) | Success Rate (SR)33.29 | 13 |