PEAR: Permutation-Equivariant Adaptive Routing Multi-Agent Debate

arXiv:2606.20621 · cs.AI, cs.CL, cs.LG, cs.MA, stat.ML · Submitted 2026-05-26 · Read on arXiv

cs.AI, cs.CL, cs.LG, cs.MA, stat.ML

Submitted: 2026-05-26

Updated: 2026-08-31

Comments: Published in the 2026 Conference on Empirical Methods in Natural Language Processing (EMNLP) as a Main Conference paper

Code: https://github.com/EVIEHub/PEAR

License: http://creativecommons.org/licenses/by/4.0/

The gist: Multi-agent debate improves the reliability of large language models (LLMs) through iterative peer critiques.

Terminology

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 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 https://github.com/EVIEHub/PEAR.

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