Swarm-Inspired Generation of Collective Behaviors in Graph Dynamical Systems

How can we design local interaction rules for graph-structured systems that produce desired global collective behaviors while remaining generalizable across different network scales, dynamical regimes, and tasks? The authors seek to bridge the gap between first-principles coupled dynamical systems (CDSs) and data-driven graph neural networks (GNNs).

The authors introduce the Swarm-Inspired Emergent Synchronizer (SIES), a framework that treats each node in a graph as an agent-like unit. SIES combines an explicit dynamical engine with learnable local interaction rules. By using signed, source-target-conditioned attention, the model learns how nodes should influence one another to achieve a target global state. This approach allows the system to incorporate both attractive and repulsive interactions, which are essential for complex collective patterns but often difficult for standard GNNs to capture.

SIES demonstrates significant advantages in both synchronization control and graph representation learning. In synchronization tasks, the model generalizes to unseen network scales, target phase relations, and intrinsic node dynamics without needing retraining. It converges faster than traditional oscillator baselines (such as fully connected or diffusive models) and maintains robust performance even in sparse, irregular network topologies. Furthermore, SIES successfully controls locomotion in simulated multi-legged robots and a physical hexapod, even after simulated leg damage. In graph representation learning, SIES outperforms existing methods on heterophilous node-classification benchmarks, effectively utilizing its ability to model repulsive interactions.