WorldGraph: Graph-Native World Modeling

Zezhong Ding; Yipeng Li; Xike Xie

cs.LGSep 28, 2026

WorldGraph: Graph-Native World Modeling

Authors: Zezhong Ding, Yipeng Li, Xike Xie

Organizations: School of Artificial Intelligence and Data Science, University of Science and Technology of China (USTC) · Data Darkness Lab, Suzhou Institute for Advanced Research, USTC · School of Biomedical Engineering, USTC

Abstract

World models infer latent states of an environment to capture its underlying dynamics and predict future evolution. Many real-world environments, however, are inherently relational and observed as evolving graphs, where entities, relations, and their properties change over time. Prior graph-related world models use graph structures to organize internal states or support task-specific reasoning, rather than treating an evolving graph itself as the modeled world. We instead study graph world modeling (GWM), where graph evolution itself constitutes the world dynamics. We formulate graph world modeling over observed graph evolution, latent graph states, and heterogeneous graph-transition predictions. Based on this formulation, we construct GWM-Zero, a benchmark covering node-, edge-, and graph-level transitions over eight temporal graph datasets. We propose WorldGraph, which combines a state-aware graph transformer for multi-granularity structural and transition-conditioned evolution modeling with transition-aware GRPO using dynamic grouping and structure-aware verifiable rewards. Extensive experiments on GWM-Zero show that WorldGraph consistently outperforms representative graph representation, temporal graph learning, graph pretraining, and graph world-model baselines across all three transition granularities.

Figures & tables

Panel of Figure 1 — Figure 1: World Model ( Ha and Schmidhuber, 2018 ) vs. Our Proposed GWM

Figure 2: Overview of WorldGraph . The state-aware graph transformer constructs latent world states by integrating multi-granularity graph structure with transition-conditioned history. The transition-aware RL algorithm learns heterogeneous graph transitions through dynamic grouping and structure-aware verifiable rewards across node-, edge-, and graph-level tasks.

Method	Type	TGBN-Trade				TGBN-Genre				TGBN-Reddit
Method	Type	Add. F1	Rem. F1	Sem. F1	NDCG@10	Add. F1	Rem. F1	Sem. F1	NDCG@10	Add. F1	Rem. F1	Sem. F1	NDCG@10
GCN	MPNN	0.4718	0.1540	0.5741	0.6357	0.7112	0.8488	0.6375	0.2469	0.9706	0.8976	0.6284	0.2161
GAT	MPNN	0.5248	0.1385	0.6275	0.6386	0.7253	0.8598	0.6523	0.2699	0.9720	0.8972	0.6440	0.2237
GraphSAGE	MPNN	0.5864	0.0000	0.6595	0.6246	0.7256	0.8538	0.6496	0.2780	0.9705	0.8902	0.6435	0.2519
SGFormer	Graph Transformer	0.6874	0.0308	0.6732	0.6324	0.7252	0.8564	0.6497	0.2822	0.9731	0.9024	0.6445	0.2413
NodeFormer	Graph Transformer	0.7069	0.0878	0.6669	0.6336	0.7080	0.8394	0.6470	0.2344	0.8011	0.7329	0.5409	0.1275

Table 1: Overall Performance on the 3 Graph-Transition Tasks. Add., Rem., and Sem. denote addition, deletion, and property-change F1, respectively. Higher is better for F1, Macro-F1, and NDCG@10, while lower is better for MAE and RMSE. The best results are shown in bold and the second best results are underlined . We use an existing Controller design ( Dinella et al., 2020 ) to enable the baselines in the first three categories to predict node-, edge-, and graph-level changes.

Figure 3: Ablation Study on Node-Level Tasks/TGBN-Trade and Graph-Level Tasks/Enron. The left panel reports the equal-weight average of the 4 TGBN-Trade metrics, while the right panel reports Macro-F1.

Figure 4: Sensitivity Analysis on Graph-Level Tasks/Flights. Performance remains remarkably stable across varying maximum hop numbers

L_{\max}

, random-walk numbers

M

, and GRPO rollout budgets

\mathcal{B}

Figure 5: Comparison with L 3 P on PointMaze and FetchPickAndPlace. Solid curves show the mean test success rate and shaded regions show the standard deviation.

Env.	Model	1 Step		5 Steps		10 Steps
Env.	Model	H@1	MRR	H@1	MRR	H@1	MRR
Pong	C-SWM	35.00	51.45	11.33	27.24	6.67	19.03
Pong	+ WorldGraph	40.33	57.68	26.33	45.85	16.00	34.62
SI	C-SWM	63.67	75.49	41.33	56.66	29.67	46.16
SI	+ WorldGraph	68.00	79.68	62.67	76.04	61.00	75.71

Table 2: Comparison with C-SWM on Multi-Step Latent-State Ranking Tasks. Higher H@1 and MRR are better.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Description
Graph World
$t,\ \tau,\ T$	Current time, historical time, and sequence length.
$g_{t}=(V_{t},E_{t},X_{t})\in\mathcal{G}$	Observed graph at time $t$ , its node, edge, and property sets, and the graph space.
$\Delta g_{t}$	Graph change associated with the transition from $g_{t}$ to $g_{t+1}$ .
$\mathbf{s}_{t}\in\mathcal{S},\ f_{s}$	Latent world state, world-state space, and state model.
$f_{\Delta}$	Transition model that predicts $\Delta g_{t}$ from the current graph, the preceding graph change, and $\mathbf{s}_{t}$ .

Appendix

Table 4: Core notations used in WorldGraph.

Encoder setting	$\\|\mathbf{z}_{v,t}-\mathbf{z}_{v,t}^{(\mathrm{IDEAL})}\\|_{2}$	$\\|\mathbf{s}_{v,t}-\mathbf{s}_{v,t}^{(\mathrm{IDEAL})}\\|_{2}$
SGFormer (Single-view)	$11.2743\pm 0.3400$	$6.2460\pm 0.9255$
WorldGraph (Multi-view SGT)	3.8210 $\pm$ 0.5362	1.5568 $\pm$ 0.3691

Appendix

Table 5: Experimental validation of Theorem 1 on Graph-level tasks/Flights. Values are mean

\pm

standard deviation over five checkpoints; lower is better.

Method	Mean EVR
Standard GRPO	$1.5550$
Transition-aware RL	1.3526

Appendix

Table 6: Experimental validation of Theorem 2 on Node-level tasks/TGBN-Trade. Mean EVR is the arithmetic mean over the three transition groups; lower is better.

Dataset	Domain	Nodes	Temporal Events	Snapshots	Edge Input	Snapshot Interval	Task(s)
TGBN-Trade	Economic interaction	255	468,245	31	Weighted	Annual	Node-Level Tasks, Edge-Level Tasks
TGBN-Genre	User preference	1,505	17,858,395	1,580	Weighted	Daily	Node-Level Tasks
TGBN-Reddit	Social interaction	11,766	27,174,118	1,090	Binary	Daily	Node-Level Tasks
UN Vote	Political interaction	201	1,035,742	72	Weighted	Annual	Edge-Level Tasks
Contact	Physical proximity	692	2,426,279	112	Binary	Six hours	Edge-Level Tasks, Graph-Level Tasks
SocialEvo	Social proximity	74	2,098,119	243	Binary	Daily	Edge-Level Tasks

Appendix

Table 7: Statistics of the eight real-world datasets used in GWM-Zero. The numbers of temporal events and snapshots are computed from the processed artifacts used by all methods.

Hyperparameter	Node-level tasks	Edge-level tasks	Graph-level tasks
Latent-state dimension	64	32	64
Hidden-state dimension	64	32	64
Transition-representation dimension	32	16	32
Maximum historical time span	8	8	8
Dropout rate	0.1	0.1	0.1
Learning rate	$10^{-3}$	$10^{-3}$	$10^{-3}$

Appendix

Table 8: Principal hyperparameters used by WorldGraph.

Model	Time (s/epoch)
GCN	47.26
GAT	51.47
GraphSAGE	43.49
SGFormer	53.45
NodeFormer	72.11
GraphGPS	64.04

Appendix

Table 9: Mean training time per epoch (seconds) on TGBN-Genre, computed over the first five training epochs.

Dataset	Model	Step 2			Step 3			Step 5
Dataset	Model	MAE	RMSE	Macro-F1	MAE	RMSE	Macro-F1	MAE	RMSE	Macro-F1
Flights	GCN	0.9208	1.5297	0.4486	1.3097	2.0548	0.3970	2.2527	3.2212	0.3584
	GAT	0.9080	1.4992	0.4314	1.1381	1.7816	0.3950	1.7601	2.5047	0.3372
	GraphSAGE	0.8764	1.4712	0.4667	1.1325	1.8040	0.4418	1.6862	2.4935	0.3982
	SGFormer	0.8789	1.4686	0.4735	1.1885	1.8848	0.4207	1.8938	2.7597	0.3861
	NodeFormer	0.9694	1.5545	0.4004	1.3759	1.9958	0.3755	2.2803	2.9962	0.3449

Appendix

Table 10: Multi-step prediction results on the Graph-level tasks. Models recursively use their predicted graph states for steps

2

3

, and

5

. MAE and RMSE are lower-is-better, whereas Macro-F1 is higher-is-better. The best results are shown in bold and the second best results are underlined .

Figure 6: Sensitivity analysis on Graph-Level Tasks/Flights (Macro-F1) across the rarity weight exponent

\gamma

, degree importance exponent

\theta

, volatility importance exponent

\eta

, and historical time span

t_{\mathrm{max}}

Figure 7: Transition-conditioned image-to-graph-to-image rollout. The first row shows the ground-truth sequence, and the second row shows the images decoded from the graph states predicted by WorldGraph.

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Beyond Static Graph World Models: Learning Stochastic Latent Dynamics over Evolving Topologies

Alex Schutz, Nick Hawes, Victor-Alexandru Darvariu

Oxford Robotics Institute University of Oxford

Latent Dynamics Topology Stochastic

Open paper AskPDF arXiv

Graph-based world models have recently emerged as a means of learning transitions over relational state representations. However, existing approaches are largely limited to fixed-topology graphs or deterministic, fully observable environments. We propose the Graph Dynamics Model (GDM), a world model for graph-structured observations that is designed to handle the more general setting of evolving topologies in stochastic and partially observable environments. The GDM uses a sparse recurrent adjacency matrix to model topology updates and perform message passing, together with a recurrent state-space architecture for modelling stochastic transitions. Furthermore, we identify a gap in the evaluation of graph-based world models, as existing methods do not provide a means of comparing predicted and true distributions over the joint graph state comprising the interdependent topology, node features, and graph features. We therefore introduce the Graph Distribution Distance (GDD) metric, which uses maximum mean discrepancy with a graph kernel to comprehensively compare joint next-state distributions. We evaluate the GDM across several environments, including stochastic and partially observable settings. We demonstrate that GDM outperforms baseline models and displays zero-shot generalisation on large graphs.

Abstract

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