# Graph-Operator World Models for Morphology-Parameter Generalization in Continuous Control

arXiv: https://arxiv.org/abs/2608.20936 · HTML: https://mlsanity.com/paper/2608.20936/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Embodied and robot world models, one of 11 directions in World models.
- Builds on 3 of its 22 references that are in the map.
- First posted on arXiv 21 Aug 2026.

## Placed in

- World models / [Embodied and robot world models](https://mlsanity.com/wm/embodied-and-robot-world-models/)

## Builds on (most cited first, 3 of 3)

- [Scaling Cross-Embodiment World Models for Dexterous Manipulation](https://mlsanity.com/paper/2511.01177/) (2025)
- [Morphology-Conditioned World Model for Cross-Embodiment Quadrupedal Locomotion](https://mlsanity.com/paper/2604.08780/) (2026)
- [WestWorld: A Knowledge-Encoded Scalable Trajectory World Model for Diverse Robotic Systems](https://mlsanity.com/paper/2603.14392/) (2026)

## Abstract (arXiv)

World models for continuous control are commonly trained for a fixed physical system and can degrade when known morphology parameters such as link lengths, masses, damping, and actuation change. Existing approaches often provide these parameters as conditioning information, but leave unspecified which part of the learned transition should remain reusable and which part should change with morphology. We propose Graph-Operator World Models (GraphOp-WM), a structured world model for generalization across unseen morphology parameters within related articulated robot families. GraphOp-WM represents bodies and their kinematic relations as an attributed graph and factorizes each transition into a morphology-independent local dynamics basis and a morphology-conditioned structured operator. The operator combines node-local modulation, kinematic-tree coupling, and a low-rank global correction, while architectural information separation, basis normalization, and paired-morphology supervision encourage static morphology dependence to be carried by the operator pathway. Graph-level readout and edge-wise action representations provide a compatible interface for reward, value, and TD-MPC-style planning. We further define controlled MuJoCo parameter splits covering interpolation, extrapolation, and held-out compositions of link geometry, mass, damping, and actuation parameters in Hopper, Walker2d, and HalfCheetah.