PEAR: Permutation-Equivariant Adaptive Routing Multi-Agent Debate
06:00 · June 23, 2026 · arXiv cs.AI RSS
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.
Summary
Multi-agent debate improves the reliability of large language models by letting agents iteratively critique and revise one another’s answers. Fixed communication topologies, however, often create persistent positional advantages, allow unreliable agents to exert disproportionate influence, and make outcomes sensitive to arbitrary role assignments. These issues can reinforce errors through repeated local exchanges or permit early or high-influence agents to anchor the group on incorrect conclusions.
PEAR addresses these limitations with an inference-time protocol that replaces static graphs with state-aware adaptive routing. At each round the router selects a sparse topology by scoring candidate assignments according to three criteria: targeted diversity routes high-confidence dissenting views toward low-confidence agents, influence balancing penalizes agents that have already shaped many prior revisions, and low-confidence filtering suppresses propagation from agents reporting low certainty. The resulting directed edges determine which critiques each agent receives before producing an updated answer.
The method is formally characterized as a permutation-equivariant sparse router. Because routing decisions depend only on label-invariant features such as disagreement and accumulated influence, any relabeling of the agents produces a correspondingly relabeled graph while leaving the distribution of final answers unchanged. This symmetry property yields a uniform generalization guarantee without increasing covering complexity.
Evaluations across MMLU-Pro, TruthfulQA, GSM8K and MATH-500, using six instruction-tuned models that range from open 8 B to 30 B parameter backbones as well as two closed-source systems, show consistent gains over the strongest fixed-topology baselines. Ablation results confirm that each of the three routing components contributes measurably to the observed accuracy improvements.
Why it matters
This research is highly relevant for Dutch AI researchers and advanced practitioners focusing on LLM reliability and multi-agent systems. The introduction of a dynamic, bias-reducing routing protocol aligns with the Netherlands' strategic emphasis on transparent, ethical, and robust AI development, offering actionable methodologies with open-source code.
