Stochastic Self-Organization in Multi-Agent Systems

🕒 Published (v1): 2026-01-01 · Source: ICLR · Venue: ICLR 2026 · link

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ICLR 2026; LLM-based MAS with dynamic topology beyond fixed orchestration

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TL;DR

SELFORG is a lightweight multi-agent LLM framework that dynamically constructs a directed acyclic communication graph (DAG) each round by approximating Shapley values from agent response embeddings — no pretraining, no external judge, no edge-level RL. Agents self-organize into a hierarchy where high-contributing agents propagate information to lower-contributing ones, amplifying correct signals while suppressing noise. It achieves consistent SOTA across 8 reasoning benchmarks, with the largest gains in the weak-backend regime.

Problem

Existing multi-agent LLM orchestration schemes rely on fixed topologies, pretrained graph generators, edge-level reinforcement learning (e.g., GPTSwarm, AgentPrune), or external LLM judges (e.g., G-Designer, MAS-GPT), all of which add overhead and optimize at the task- or query-level rather than conditioning on the stochastic, per-instance response pool. Because agents are inherently stochastic, a topology optimal for one run may be suboptimal for another run of the same query; prior methods overfit to task labels or incidental response patterns.

Method

SELFORG operates as a \(T\)-round iterative protocol over \(N\) agents:

1. Initialization (round 0): Each agent independently answers the query \(Q\). Responses \(R_n^{(0)}\) are embedded with a lightweight sentence encoder (all-MiniLM-L6) to produce \(r_n^{(0)}\).

2. Contribution estimation: The Shapley value of each agent is approximated in \(O(N)\) as cosine similarity to the mean embedding: $\(\psi_n^{(t)} = \cos\!\left(r_n^{(t)},\, r_{\text{avg}}^{(t)}\right), \quad r_{\text{avg}}^{(t)} = \frac{1}{N}\sum_{n=1}^N r_n^{(t)}.\)$ Theorem 1 gives a bounded error \(|\phi_n - L_n \psi_n| \leq I\Gamma^2\); Corollary 1 proves ranking stability when pairwise score gaps exceed \(2I\Gamma^2/L\).

3. DAG construction: A directed edge \(e_{m\to n}\) is added if \(\cos(r_n^{(t)}, r_m^{(t)}) \geq \tau\) and \(\psi_m^{(t+1)} > \psi_n^{(t+1)}\) (higher-contributor influences lower). Optionally limited to top-\(k\) neighbors. Cycles are removed by severing edges from the weaker node; topological ordering follows.

4. Propagation: Agents are processed in topological order; each reads upstream peer responses, regenerates its answer, and embeddings/contributions are re-estimated for the next round.

5. Aggregation: Final response selected as \(R_{n^*}\) where \(n^* = \arg\max_n \cos(r_n^{(T)}, r_{\text{centroid}}^{(T)})\) and \(r_{\text{centroid}}\) is contribution-weighted (Eq. 6–7). Typically \(T=2\) rounds suffice.

Lemma 2 proves contribution dominance: when correct answers form a tight embedding cluster (\(\cos \geq \alpha\)) and wrong answers scatter (\(\cos \leq \beta < \alpha\)), correct agents provably attain higher \(\psi_n\). Corollary 2 then guarantees correctness amplification in the DAG.

Key Contributions

• Per-instance DAG built entirely from agent responses via semantic alignment — no fixed topology, pretrained generator, or edge-level RL.
• Linear-time Shapley approximation (\(\psi_n = \cos(r_n, r_{\text{avg}})\)) with formal ranking-stability guarantees (Theorem 1, Corollary 1).
• Theoretical proof that correct responses dominate contribution scores under plausible embedding cluster assumptions (Lemmas 1–2, Corollary 2).
• Empirical demonstration of robust weak-backend gains: +4 pp average over the best non-collaborative baseline on Qwen-1.5B, ranking first across all 7 benchmarks (AVG-R = 1.00).
• Heterogeneous-backbone evaluation showing SELFORG extracts signal from mixed-model pools (e.g., 53.94→66.14 on AQUA-RAT for Qwen/Falcon/LLaMA/Mistral mix).

Results

• Qwen-1.5B (weak backend): SELFORG 45.05% avg vs. best baseline 41.24% (Single); AVG-R = 1.00 vs. 2.57 for next best. All other multi-agent baselines collapse to 33–37% avg.
• LLaMA-3.3-70B: SELFORG 70.19% avg, AVG-R = 1.25, beating CoT (68.46%, AVG-R 2.50) and all others.
• Qwen-2.5-72B: SELFORG AVG-R = 1.38; outperforms Single (AVG-R 2.88) and all baselines.
• Scaling (AQUA-RAT): 3B: 65.35→73.62; 14B: 75.79→81.50; gains shrink at 72B (81.10→80.71, slight regression).
• Heterogeneous agents (AQUA-RAT / MMLU-Pro): 53.94→66.14 / 41.60→50.40 over random-single-agent baseline.
• Intervention study: Receiving input from the top-contributor raises a weak agent's solve rate from 49% to 69% on GSM-Hard.
• Benchmarks: MATH, GSM8K, AQUA-RAT, GSM-Hard, MMLU, MMLU-Pro, GPQA, AIME-2024.

Limitations

• Similarity threshold \(\tau\) and neighbor budget \(k\) are hyperparameters requiring tuning; sensitivity analysis not fully detailed in the main text.
• Shapley approximation assumes normalized embeddings and bounded inner products; degenerate embedding spaces could violate Theorem 1's conditions.
• Diminishing returns at very large model scales (72B), where base accuracy is already near-ceiling.
• Performance is bounded by the best backbone in heterogeneous settings; weak models with near-random responses may contribute noise even with Shapley filtering.
• Evaluation limited to classification/short-answer reasoning tasks; long-form generation or tool-use agentic tasks are not tested.
• Embedding clustering assumption (Assumption 1) is empirically motivated but not universally guaranteed across domains or model families.

Relevance to Agentic AI / LLM Agents

SELFORG directly addresses one of the core open problems in LLM multi-agent systems: how to structure inter-agent communication without human-engineered topologies or expensive meta-agents. The Shapley-value-based credit assignment approach provides a principled, theoretically grounded alternative to ad-hoc voting or judge-LLM aggregation, and the self-organizing DAG is a concrete instantiation of emergent coordination. The work is particularly relevant to the question of how MAS can remain robust under weak or heterogeneous backends — a practical concern when deploying agents at scale with smaller, cheaper models. It connects to broader lines of work on multi-agent debate, graph-based agent networks, and cooperative game theory applied to AI ensembles.