GeoWorld: Geometric World Models
This work provides an incremental improvement for researchers and practitioners working on multi-step visual planning and energy-based predictive world models.
This paper introduces GeoWorld, a geometric world model that addresses challenges in multi-step visual planning by mapping latent representations onto hyperbolic manifolds and using Geometric Reinforcement Learning for optimization. It achieves approximately 3% success rate improvement in 3-step planning and 2% improvement in 4-step planning compared to the state-of-the-art V-JEPA 2 on CrossTask and COIN datasets.
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.