# GeoWorld: Geometric World Models

arXiv: https://arxiv.org/abs/2602.23058 · HTML: https://mlsanity.com/paper/2602.23058/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 64 of its 89 references that are in the map.
- First posted on arXiv 26 Feb 2026.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)

## Builds on (most cited first, 30 of 64)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [The Kinetics Human Action Video Dataset](https://mlsanity.com/paper/1705.06950/) (2017)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [InternVL3.5: Advancing Open-Source Multimodal Models in Versatility, Reasoning, and Efficiency](https://mlsanity.com/paper/2508.18265/) (2025)
- [The "something something" video database for learning and evaluating visual common sense](https://mlsanity.com/paper/1706.04261/) (2017)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [HowTo100M: Learning a Text-Video Embedding by Watching Hundred Million Narrated Video Clips](https://mlsanity.com/paper/1906.03327/) (2019)
- [DROID: A Large-Scale In-The-Wild Robot Manipulation Dataset](https://mlsanity.com/paper/2403.12945/) (2024)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Self Forcing: Bridging the Train-Test Gap in Autoregressive Video Diffusion](https://mlsanity.com/paper/2506.08009/) (2025)
- [Revisiting Feature Prediction for Learning Visual Representations from Video](https://mlsanity.com/paper/2404.08471/) (2024)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [COIN: A Large-scale Dataset for Comprehensive Instructional Video Analysis](https://mlsanity.com/paper/1903.02874/) (2019)
- [MAGI-1: Autoregressive Video Generation at Scale](https://mlsanity.com/paper/2505.13211/) (2025)
- [LongLive: Real-time Interactive Long Video Generation](https://mlsanity.com/paper/2509.22622/) (2025)
- [SkyReels-V2: Infinite-length Film Generative Model](https://mlsanity.com/paper/2504.13074/) (2025)
- [Cross-task weakly supervised learning from instructional videos](https://mlsanity.com/paper/1903.08225/) (2019)
- [Self-Forcing++: Towards Minute-Scale High-Quality Video Generation](https://mlsanity.com/paper/2510.02283/) (2025)
- [Autoregressive Video Generation without Vector Quantization](https://mlsanity.com/paper/2412.14169/) (2024)
- [Predictive Inverse Dynamics Models are Scalable Learners for Robotic Manipulation](https://mlsanity.com/paper/2412.15109/) (2024)
- [Structured World Models from Human Videos](https://mlsanity.com/paper/2308.10901/) (2023)
- [The Debate Over Understanding in AI's Large Language Models](https://mlsanity.com/paper/2210.13966/) (2022)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)

## Built on by (most cited first, 6 of 6)

- [LiveWorld: Simulating Out-of-Sight Dynamics in Generative Video World Models](https://mlsanity.com/paper/2603.07145/) (2026)
- [MWM: Mobile World Models for Action-Conditioned Consistent Prediction](https://mlsanity.com/paper/2603.07799/) (2026)
- [Orca: The World is in Your Mind](https://mlsanity.com/paper/2606.30534/) (2026)
- [Recovering Physical Dynamics from Discrete Observations via Intrinsic Differential Consistency](https://mlsanity.com/paper/2605.08454/) (2026)
- [How You Move Tells What You'll Do: Trajectory-Conditioned Egocentric Prediction](https://mlsanity.com/paper/2605.20388/) (2026)
- [HSG: Hyperbolic Scene Graph](https://mlsanity.com/paper/2604.17454/) (2026)

## Abstract (arXiv)

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.