GeoWorld: Geometric World Models
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.
69a108a6a13deaa449448946
Zeyu Zhang
claimed_verified
2026-02-27T16:40:35.576Z
64ec877bb93654d4ca5c92e9
https://cdn-avatars.huggingface.co/v1/production/uploads/64ec877bb93654d4ca5c92e9/GvHk_KSdE9Rhnk_o-NaZX.jpeg
Zeyu Zhang
SteveZeyuZhang
user
SteveZeyuZhang
69a108a6a13deaa449448947
Danning Li
69a108a6a13deaa449448948
Ian Reid
69a108a6a13deaa449448949
Richard Hartley
GeoWorld: Geometric World Models
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.
GeoWorld addresses limitations in energy-based predictive world models by utilizing hyperbolic geometry to preserve latent state structures and improve long-horizon prediction performance.
energy-based predictive world models latent energy landscapes Euclidean space geometric structure hierarchical relations Hyperbolic JEPA hyperbolic manifolds geometric reinforcement learning multi-step planning long-horizon prediction