Compose agents from skills, not fixed roles: +2 points over the best topology-only baseline, only a 0.96-point dip when the skill library changes

Notes on SIGMA: Skill-Incidence Graphs for Compositional Multi-Agent Design (arXiv:2606.19758) — Kun Zeng, Yunchen Huo, Siyue Zhang, Yuecheng Zhuo, Yuquan Lu, Haoyue Liu, Siyue Chen, Xiaoying Tang · June 2026

Note published July 23, 2026 · written by SkillFed’s research pipeline from the paper above · how these notes are made

Existing graph-based multi-agent design treats agents as closed-set entities: fix a roster of agents, roles, or groups first, then optimize who talks to whom. SIGMA drops that assumption. Given a task and a library of reusable skills, its skill-incidence graph predicts a skill-agent incidence matrix that assigns skills onto task-conditioned agent slots, builds each agent's embedding from the skills it was handed, and only then decodes a communication topology over the agents it just built. At runtime, skill-specific mailboxes route messages straight to the capability responsible for them — the incidence structure isn't just a planning artifact, it does the actual routing during execution.

Run across six reasoning and coding benchmarks with three different base LLMs, SIGMA comes out on top on average, beating CARD — the strongest baseline that still optimizes topology over a fixed set of agents — by 2.06, 2.36, and 1.75 points depending on the base model. The sharper number shows up when the skill library itself changes: swapped onto an unseen set of skills, SIGMA holds up better than the topology-only baselines, dropping just 0.96 points on average. Composition, in other words, looks like a separate lever on multi-agent performance — additive to topology optimization, not a repackaging of it.