# PEAR: Permutation-Equivariant Adaptive Routing Multi-Agent Debate

arXiv: https://arxiv.org/abs/2606.20621 · HTML: https://mlsanity.com/paper/2606.20621/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Social simulation and multi-agent debate, one of 16 directions in LLM agents and tool use.
- Builds on 19 of its 28 references that are in the map.
- First posted on arXiv 26 May 2026.

## Placed in

- LLM agents and tool use / [Social simulation and multi-agent debate](https://mlsanity.com/agents/social-simulation-and-multi-agent-debate/)

## Builds on (most cited first, 19 of 19)

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- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [ReConcile: Round-Table Conference Improves Reasoning via Consensus among Diverse LLMs](https://mlsanity.com/paper/2309.13007/) (2023)
- [Confidence Improves Self-Consistency in LLMs](https://mlsanity.com/paper/2502.06233/) (2025)
- [Improving Multi-Agent Debate with Sparse Communication Topology](https://mlsanity.com/paper/2406.11776/) (2024)
- [GroupDebate: Enhancing the Efficiency of Multi-Agent Debate Using Group Discussion](https://mlsanity.com/paper/2409.14051/) (2024)
- [Assemble Your Crew: Automatic Multi-agent Communication Topology Design via Autoregressive Graph Generation](https://mlsanity.com/paper/2507.18224/) (2025)
- [Learning Multi-Agent Communication from Graph Modeling Perspective](https://mlsanity.com/paper/2405.08550/) (2024)
- [Adaptive Graph Pruning for Multi-Agent Communication](https://mlsanity.com/paper/2506.02951/) (2025)
- [Enhancing Multi-Agent Debate System Performance via Confidence Expression](https://mlsanity.com/paper/2509.14034/) (2025)
- [T2MAC: Targeted and Trusted Multi-Agent Communication through Selective Engagement and Evidence-Driven Integration](https://mlsanity.com/paper/2401.10973/) (2024)
- [Multi-Agent Debate with Memory Masking](https://mlsanity.com/paper/2603.20215/) (2026)
- [Hear Both Sides: Efficient Multi-Agent Debate via Diversity-Aware Message Retention](https://mlsanity.com/paper/2603.20640/) (2026)
- [Key Decision-Makers in Multi-Agent Debates: Who Holds the Power?](https://mlsanity.com/paper/2511.11040/) (2025)

## Abstract (arXiv)

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 textitPermutation-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.