A Structural Dynamics Graph World Model: Unified Modeling, Constrained Rollout, and Interpretable Calibration

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.

World models let agents plan against predicted physical state, but that state drifts; re-observation is costly and delayed, and repair can fail. We present TRACE-RealWorld (TRW), to our knowledge the first commitment-level consistency contract for world models. TRW treats predicted state as a materialized view and a physical commitment as a read whose authorization can expire. Typed, calibrated claims specify consequence-conditioned freshness and priced verification. Adaptive refresh generalizes dual-Kalman synchronization to consult the world when evidence could change a decision; dependency-scoped SagaLLM compensation repairs reversible commitments invalidated after authorization. Under an event-aligned risk oracle and recovery-liveness assumptions, we prove that synchronization and compensation are insufficient alone, whereas their composition gives a conditional consistency guarantee. Otherwise, the argument yields an auditable decomposition of violations into named debts. We implement TRW in Flood-SAR, a search-and-rescue simulator over real geography, and test six preregistered questions at frozen operating points on held-out seeds. Adaptive refresh reduces stale execution but does not dominate fixed refresh on cost, coverage, or rescue outcomes. Localized repair reduces repair work by 9.56 units per mission and restoration latency by 80.7 seconds relative to global recovery; the observed residual-violation difference is zero without establishing equivalence. Detection coverage is 0.83-0.89, and 10 of 97 invoked restorations are incomplete by mission end. The campaign treats empirical slack as sensitivity inputs rather than discharging the theorem's assumptions or providing a simultaneous population certificate. Exact replay reconstructs a disputed dispatch. TRW thus makes a world model an auditable predictive interface rather than a self-validating source of truth.