SIGMA: Skill-Incidence Graphs for Compositional Multi-Agent Design

2026-06-17

AI Summary

Existing graph-based multi-agent systems struggle to generalize to novel tasks requiring unseen capability combinations, as their nodes represent closed, fixed entities. This work proposes SIGMA, a novel framework that introduces a skill-affiliation graph structure, modeling agents as task-conditioned, composable ensembles of reusable skills. By predicting a skill-agent affiliation matrix, aggregating skill embeddings, decoding communication topologies, and enabling skill-specific message routing, SIGMA endows agent nodes with compositional flexibility, overcoming the limitations of static roles. Evaluated across six reasoning and programming benchmarks, SIGMA achieves state-of-the-art average performance, outperforming the strongest baseline, CARD, by 1.75–2.36 points. Moreover, when tested with an unseen skill set, SIGMA exhibits only a marginal average drop of 0.96 points, demonstrating significantly enhanced generalization across both tasks and skills.

Abstract

Existing graph-based multi-agent system (MAS) designers mainly improve collaboration by optimizing communication topologies over predefined agents, roles, or groups. However, because each node remains a closed-set entity, these methods struggle to generalize to tasks that require unseen combinations of capabilities. We propose SIGMA, a skill-incidence graph framework that constructs agents as task-conditioned bundles of reusable skills. Given a task and a skill library, SIGMA predicts a skill-agent incidence matrix, composes agent node embeddings from selected skills, and decodes a communication topology over the constructed agents. During execution, skill-specific mailboxes route messages to the relevant assigned capabilities, making the incidence structure directly operational. Across six reasoning and coding benchmarks with three base LLMs, SIGMA achieves the best average performance and improves over CARD, the strongest non-compositional topology-based baseline, by 2.06, 2.36, and 1.75 points, respectively. It also shows stronger robustness to unseen skill libraries, with an average performance drop of only 0.96 points. These results suggest that compositional node construction is a complementary and important axis for multi-agent design beyond communication topology optimization. Code is available at https://anonymous.4open.science/r/SIGMA-2338/.

Problem

• multi-agent system
• compositional generalization
• skill composition
• communication topology
• agent design

Innovation

• skill-incidence graph
• compositional multi-agent design
• dynamic agent composition
• task-conditioned skills
• communication topology decoding