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

2026-09-23

AI Summary

This study addresses the limitations of existing graph world models, which are confined to fixed topologies and deterministic environments, rendering them inadequate for handling evolving topologies, stochasticity, and partial observability. To this end, this work proposes GDM, a model that integrates sparse recurrent adjacency matrices, message-passing mechanisms, and recurrent state-space architectures to enable stochastic latent dynamics learning under evolving topologies. Furthermore, it introduces the novel GDD metric, combined with maximum mean discrepancy graph kernels, to fill the evaluation gap in joint graph state distributions. Experimental results demonstrate that the proposed model significantly outperforms baseline methods in stochastic and partially observable environments, while exhibiting strong zero-shot generalization capabilities on large-scale graphs.

Abstract

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.

Problem

• world models
• evolving topologies
• stochastic environments
• partially observable environments
• graph distribution evaluation

Innovation

• Graph World Models
• Evolving Topologies
• Recurrent State-Space Model
• Graph Distribution Distance
• Stochastic Latent Dynamics