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 https://github.com/EVIEHub/PEAR.
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BibTeX
@misc{feng2026pear,
title = {{PEAR: Permutation-Equivariant Adaptive Routing Multi-Agent Debate}},
author = {Yang Feng and Ziwei Xu and Xia Hu and Fengxiang He},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2606.20621},
eprint = {2606.20621},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.20621},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - PEAR: Permutation-Equivariant Adaptive Routing Multi-Agent Debate
AU - Yang Feng
AU - Ziwei Xu
AU - Xia Hu
AU - Fengxiang He
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2606.20621
UR - https://arxiv.org/abs/2606.20621
AB - 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 https://github.com/EVIEHub/PEAR.
ER -