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

arXiv: https://arxiv.org/abs/2606.19758 · HTML: https://mlsanity.com/paper/2606.19758/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 17 of its 27 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 17 of 17)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [ToolLLM: Facilitating Large Language Models to Master 16000+ Real-world APIs](https://mlsanity.com/paper/2307.16789/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [Gorilla: Large Language Model Connected with Massive APIs](https://mlsanity.com/paper/2305.15334/) (2023)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [API-Bank: A Comprehensive Benchmark for Tool-Augmented LLMs](https://mlsanity.com/paper/2304.08244/) (2023)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [A Dynamic LLM-Powered Agent Network for Task-Oriented Agent Collaboration](https://mlsanity.com/paper/2310.02170/) (2023)
- [MRKL Systems: A modular, neuro-symbolic architecture that combines large language models, external knowledge sources and discrete reasoning](https://mlsanity.com/paper/2205.00445/) (2022)
- [Assemble Your Crew: Automatic Multi-agent Communication Topology Design via Autoregressive Graph Generation](https://mlsanity.com/paper/2507.18224/) (2025)
- [CARD: Towards Conditional Design of Multi-agent Topological Structures](https://mlsanity.com/paper/2603.01089/) (2026)

## Built on by (most cited first, 2 of 2)

- [Beyond Prompt or Skill? Attribution-Guided Optimization of Modular LLM Programs](https://mlsanity.com/paper/2609.32492/) (2026)
- [Re-derivability Decides What a Staged Agent Pipeline Recovers After an Upstream Fault](https://mlsanity.com/paper/2609.32802/) (2026)

## Abstract (arXiv)

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/.