Swarm-Inspired Generation of Collective Behaviors in Graph Dynamical Systems

2026-06-23

AI Summary

This work addresses the challenge of designing generalizable local interaction rules to achieve task-oriented controllable collective behavior in graph dynamical systems. It proposes the Swarm Intelligence–Inspired Emergent Synchronizer (SIES) framework, which uniquely integrates swarm-like local decision-making mechanisms with an explicit graph dynamical model. By employing signed source–target conditional attention as an adaptive coupling term, SIES enables synchronization control and graph representation learning without retraining across diverse graph structures, node dynamics, and tasks. The method rapidly generates target phase patterns for synchronization tasks and generalizes effectively to robotic systems of varying scales. It achieves state-of-the-art performance on heterophilic graph node classification benchmarks and demonstrates practical efficacy in adaptive coordination of a hexapod robot following leg failure.

Abstract

Collective behavior arises when locally interacting units produce coordinated global organization, from synchronization in dynamical systems to task-relevant information flow on graphs. The central challenge is not only to explain how collective behavior emerges, but to design local interaction rules that can produce desired global organization and generalize across graphs, dynamics and tasks.To address this challenge, we introduce the Swarm-Inspired Emergent Synchronizer (SIES), a graph-dynamical framework that learns generalizable local-interaction laws for controllable collective organization. Each node is an agent-like dynamical unit with a state and task cue, and signed source-target-conditioned attention acts as an adaptive coupling term inside an explicit evolution model. Therefore, SIES combines an explicit dynamical engine with local agent intelligence, similar to biological swarms. For synchronization control, SIES learns a generalizable coupling operator that produces prescribed synchronization patterns for CDSs across untrained network scales, target phase relations, and intrinsic node dynamics without retraining. The learned operator also reaches gait-related modes faster than three oscillator baselines and generalizes synchronization-driven locomotion to simulated multi-legged robots of different scales and a physical hexapod after leg disablement. For graph representation learning, SIES applies the same signed interaction principle to message passing and achieves the highest performance among the compared methods on heterophilous node-classification benchmarks. Together, these results position SIES as a generalizable and learnable graph-dynamical interaction framework with promise for synchronization control, adaptive robot coordination, and heterophilous graph representation learning.

Problem

• collective behavior
• graph dynamical systems
• local interaction rules
• generalization
• synchronization

Innovation

• Swarm-inspired
• Graph dynamical systems
• Emergent synchronization
• Signed attention
• Heterophilous graph learning