PEAR: Permutation-Equivariant Adaptive Routing Multi-Agent Debate
For practitioners using multi-agent LLM systems, PEAR reduces sensitivity to role assignments and improves reliability without requiring model retraining.
PEAR introduces an inference-time protocol that dynamically reconfigures communication roles and sparse topologies in multi-agent debate, preventing positional biases and improving average accuracy over existing debate baselines across four reasoning benchmarks and six LLM backbones.
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 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 at https://github.com/EVIEHub/PEAR.