PEAR: Permutation-Equivariant Adaptive Routing Multi-Agent Debate

Abstract:Multi-agent debate improves the reliability of large language models (LLMs) through iterative peer critiques. However, fixed topologies often introduce persistent positional biases, amplify unreliable agents, and cause high sensitivity to role assignments. We introduce \textit{Permutation-Equivariant Adaptive Routing Multi-Agent Debate (PEAR)}, an inference-time train-free protocol that dynamically reconfigures communication roles and sparse topologies across consecutive debate rounds. By strategically switching agent-to-role assignments based on evolving agent states, PEAR prevents any agent from permanently occupying a privileged network position or distributes influence more evenly across the debate. We theoretically characterize PEAR as an equivariant sparse router: it preserves accuracy under agent relabeling while reducing routing complexity and improving generalization. Comprehensive empirical evaluations across four reasoning benchmarks and six diverse LLM backbones demonstrate PEAR significantly improves average accuracy over the strongest debate baselines. The code is available at this https URL.

Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Machine Learning (cs.LG); Multiagent Systems (cs.MA); Machine Learning (stat.ML)

arXiv:2606.20621 [cs.AI]

(or arXiv:2606.20621v2 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2606.20621 Focus to learn more arXiv-issued DOI via DataCite

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