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

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/.

• The paper's main contribution is the SIGMA framework that constructs agent nodes as dynamic bundles of reusable skill cards.
• It combines skill incidence generation with topology decoding to optimize communication and execute task-dependent operations efficiently.
• Empirical results show SIGMA outperforms fixed-role baselines with higher accuracy, robustness, and reduced token consumption.

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

Motivation and Limitations of Prior MAS Designs

Existing graph-based multi-agent system (MAS) designers predominantly optimize communication topologies over predefined role nodes. The agent nodes themselves are atomic entities—fixed profiles, operations, or groups—restricting compositional generalization. Consequently, these designs struggle to solve tasks requiring unseen combinations of capabilities, cross-role tool use, or API-grounded execution. This node-level rigidity prevents the system from constructing new agent identities as contextually bundled, reusable skills, limiting transferability to unseen domains or skill libraries.

The practical need for procedurally compositional capabilities, tooling flexibility, and operational grounding in agent design has not been directly addressed by prior topology-centric frameworks. While recent approaches allow dynamic communication graphs, they leave agent semantics largely fixed, causing failure on tasks that require the fusion of multiple procedural or retrieval-based capabilities.

SI-MAP Protocol and SIGMA Framework

Protocol Definition

The Skill-Incidence Multi-Agent Protocol (SI-MAP) formalizes four key operational properties for advanced MAS design:

1. Compositionality: Agents are constructed as task-conditioned bundles of explicitly reusable skill cards, not as fixed role tokens.
2. Executability: Assigned skills must affect prompts, tool affordances, memory, and message routing during execution.
3. Topology Compatibility: Constructed node embeddings are exposed to graph decoders, maintaining compatibility with topology optimization.
4. Expandability: New skill cards (tools/API endpoints) can be appended at test time, without retraining the topology decoder.

SIGMA Instantiation

SIGMA operationalizes SI-MAP by representing reusable capabilities as serialized skill cards, predicting a task-specific skill-agent incidence matrix ($B_q$), embedding agent nodes from selected skill cards, and decoding a communication graph over these composite nodes. Skill-specific mailboxes enable executable routing of messages, making skill incidence an operational structure rather than a latent annotation. The design cleanly separates capability composition (via skill incidence) from topology generation, enabling fixed agent slots to express heterogeneous, task-conditioned identities.

During execution, mailbox summaries for each skill-agent pair aggregate routed evidence, allowing prompts, memory, and message passing to be skill-grounded, not flattened into generic contexts.

Methodological Details

Incidence Generation

A frozen text encoder serializes skill cards into vector embeddings. Given a task & skill library, the incidence generator computes soft assignment probabilities for skill-agent pairings, yielding a sparse binary incidence matrix ($B_q$). Hard projection ensures deterministic assignment, avoiding agent bundle duplication within fixed crew sizes. Each node embedding incorporates slot identity, contextual query vector, and pooled selected skill embeddings.

Skill-Aware Topology Decoding

Edges between agent nodes are decoded based on both node-level affinity and skill-bundle compatibility, the latter aggregating pairwise complementarity between selected skills. This enables communication edges to reflect not just structural roles but also task-dependent procedural connections (e.g., retrieval feeding grounding, planning feeding implementation).

Execution Regime

Mailboxes for each skill-agent incident pair summarize routed messages by embedding similarity, exposing only task-relevant evidence in agent prompts. This mechanism ensures that the skill incidence matrix operationalizes, influencing reasoning and tool use at each node, not merely representation learning.

Training Procedure

The incidence generator and topology decoder are jointly optimized with a binary cross-entropy objective on pseudo-labeled skill incidence matrices and edge reconstruction loss. Training relies exclusively on deterministic pseudo-labels from role/tool descriptions, never accessing held-out answers or test skills, enabling robust compositional generalization.

Empirical Evaluation

Benchmark Tasks

SIGMA is evaluated across six benchmarks—code generation (HumanEval), general knowledge reasoning (MMLU), mathematical reasoning (GSM8K, MultiArith, SVAMP), and symbolic problem solving (AQuA)—with three LLM backbones (Qwen3-8B, GPT-OSS-120B, GPT-4o-mini). Controlled variants and baselines include role-based, topology-optimized, and skill-assignment methods.

Main Results

SIGMA achieves highest average scores across all model scales and benchmarks (87.04, 93.97, 88.80 on Qwen3-8B, GPT-OSS-120B, GPT-4o-mini). It outperforms CARD, the strongest non-compositional topology baseline, by consistent margins (2.06, 2.36, and 1.75 points) and ranks first on 16 of 18 benchmark-model combinations. Gains are especially clear on HumanEval and AQuA, where compositional procedural reasoning and executable construction are vital.

Efficiency analysis reveals that SIGMA attains best accuracy with minimal token consumption—reducing usage by over 90% compared to GPTSwarm and LLM-Debate.

Robustness and Generalization

Under source-to-unseen skill library transfer, SIGMA shows smallest performance degradation among all multi-agent methods (average drop: 0.96 points), indicating robust compositional generalization. The model recomposes newly introduced skill cards into agent slots without retraining, outperforming fixed-role and topology-centric methods which depend heavily on training-time skill inventories.

Ablation studies reveal that compositional node construction, skill-aware topology decoding, and mailbox-based execution contribute jointly to strongly improved generalization and accuracy.

Failure Modes and Diagnostics

Analysis of representative failures indicates that aggregation of skill-composed evidence can suppress correct minority signals, and universal misconception among skill bundles leads to irrecoverable errors. Overly sparse topology decoding may turn communication graphs empty, losing collaborative benefit. These findings motivate refinement of aggregation mechanisms, evidence-weight weighting, and better skill diversity.

Practical and Theoretical Implications

SIGMA demonstrates that the axis of agent capability composition is complementary and orthogonal to communication topology optimization. Constructing agent nodes as explicit skill bundles enables unprecedented modularity, transferability, and adaptability for MAS design. The mailbox mechanism operationalizes skill assignments, leading to efficient message routing and reduced token budgets.

Immediate practical implications include improved generalization in tool-augmented, retrieval-intensive, and code-generation tasks, along with efficient handling of frequent skill-library shifts. Theoretical implications lie in the separation of capability and communication: MAS designers should treat skill incidence and topology design as distinct optimization axes. This enables combinatorial skill composition, dynamic agent identities, and scalable expansion to heterogeneous tool ecosystems.

Future developments will likely examine dynamic crew-size prediction, adaptive mailbox routing and conflict resolution, and benchmarking on real-world tool-use environments with noisy APIs and procedural side effects. The framework sets a foundation for modular, expandable MAS workflows beyond fixed-role abstractions.

Conclusion

SIGMA introduces a formal skill-incidence protocol for compositional multi-agent LLM system design, separating capability composition and communication topology and operationalizing skill assignments through mailbox routing. Consistent empirical superiority, efficiency, and robustness to unfamiliar skill libraries establish compositional node construction as a crucial axis in MAS research. Further work is warranted to refine aggregation, adaptivity, and deployment in noisy real-world environments.