GeoWorld: Geometric World Models

TL;DR

GeoWorld introduces a hyperbolic geometric approach to improve energy-based predictive world models for multi-step visual planning, addressing limitations of Euclidean latent representations and long-horizon prediction degradation.

Contribution

It proposes a Hyperbolic JEPA for preserving geometric and hierarchical structures in latent space and introduces Geometric Reinforcement Learning for stable multi-step planning.

Findings

Achieved around 3% SR improvement in 3-step planning.

Achieved around 2% SR improvement in 4-step planning.

Demonstrated effectiveness on CrossTask and COIN datasets.

Abstract

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.