Learning Ad Hoc Network Dynamics via Graph-Structured World Models

World models are increasingly used for planning, yet most analyses of rollout error assume vector-valued states and scalar error amplification. Many planning environments, however, are naturally graph-structured: agents, tools, skills, routes, and dependencies interact through evolving relations. In this work, we study how prediction errors accumulate in Graph World Models (GWMs). We formulate fixed-edge and dynamic-edge GWM rollouts under a unified state-action transition framework and derive topology-aware error bounds. For fixed-edge rollouts, we show that long-horizon node error separates into a topology factor, governed by the graph spectral radius, and a model factor, governed by layer spectral norms. For dynamic-edge rollouts, we introduce a joint node-edge error operator that captures feedback between feature prediction and structure prediction, revealing when edge errors amplify future message passing. Motivated by these bounds, we propose Error-Aware GWM, a training objective that combines spectral regularization, rollout consistency, and critical-node weighting. Across synthetic graph topologies and heterogeneous agent-graph testbeds, we find that rollout error and planning regret grow with horizon, that dynamic-edge training is necessary when structure evolves, and that Error-Aware GWM improves long-horizon stability without sacrificing one-step accuracy. Our results characterize when graph world models remain reliable under autoregressive planning and when topology makes them fail.

As one of the mainstream models of artificial intelligence, world models allow agents to learn the representation of the environment for efficient prediction and planning. However, classical world models based on flat tensors face several key problems, including noise sensitivity, error accumulation and weak reasoning. To address these limitations, many recent studies use graph structure to decompose the environment into entity nodes and interactive edges, and model virtual environments in a structured space. This paper systematically formalizes and unifies these emerging graph-based works under the concept of graph world models (GWMs). To the best of our knowledge, GWMs have not yet been explicitly defined and surveyed as a unified research paradigm. Furthermore, we propose a taxonomy based on relational inductive biases (RIB), categorizing GWMs by the specific structural priors they inject: (1) spatial RIB for topological abstraction; (2) physical RIB for dynamic simulation; and (3) logical RIB for causal and semantic reasoning. For each model category, we outline the key design principles, summarize representative models, and conduct comparative analyses. We further discuss open challenges and future directions, including dynamic graph adaptation, probabilistic relational dynamics, multi-granularity inductive biases, and the need for dedicated benchmarks and evaluation metrics for GWMs.

Emerging 6G wireless networks are expected to operate across diverse deployment scenarios, where variations in network topology, user mobility, traffic demand, and radio conditions challenge the scalability of conventional radio resource management (RRM). While offline reinforcement learning (RL) methods have demonstrated strong decision-making capabilities, learning a single policy that performs consistently across heterogeneous wireless environments remains difficult due to conflicting optimization objectives and limited model specialization. These challenges become particularly pronounced in coordinated multipoint (CoMP) transmission, where selecting the optimal serving-cell combination requires sequential decision-making under evolving network conditions. This paper presents the Wireless Sparse Decision Transformer with Mixture of Experts (WiSDoM), a sparse multi-task offline RL framework for adaptive multi-cell selection. WiSDoM combines Decision Transformers (DTs) with a Mixture-of-Experts (MoE) architecture that dynamically activates specialized experts according to task characteristics. This MoE mechanism improves model capacity without proportionally increasing inference cost, mitigates negative transfer, and enables expert specialization across tasks. WiSDoM is trained jointly on diverse network configurations spanning multiple base station and user equipment densities, mobility levels, and scheduler policies. Experimental results show that WiSDoM consistently outperforms heuristic methods, single-task models, and conventional multi-task DTs, improving quality of experience (QoE) by up to 55% while activating approximately one-third of the parameters of its dense counterpart during inference. Furthermore, WiSDoM exhibits strong task generalization and efficiently adapts to unseen wireless scenarios through few-shot prompting without retraining or fine-tuning.