Multi-agent debate (MAD) improves the reasoning capabilities of large language models by having multiple agents iteratively refine their responses through discussion. However, MAD suffers from a critical vulnerability known as shared misconception: when a majority of agents initially converge on an incorrect answer, the debate process tends to amplify rather than correct the error. Existing methods primarily address peer skew but leave the agents’ inherently biased concept priors unaddressed. To mitigate this systematic weakness, we propose **R²-MAD** (Remember and Reweight for Multi-Agent Debate), a framework that equips agents with an experience memory accumulated from past debates. R²-MAD intervenes on both failure modes through two complementary mechanisms: A debate-state-aware retrieval policy dynamically calibrates the concept prior by retrieving relevant historical evidence based on the current consensus level. Then these retrieved experiences provide a basis for estimating per-agent reliability, yielding confidence weights to modulate peer influence. Experiments on various benchmarks show that R²-MAD achieves consistent improvements over existing single-agent and MAD baselines.

Contemporary progress in Large Language Models (LLMs) has revealed notable inferential capacities via reinforcement learning (RL) employing verifiable rewards. However, “zero-RL” approaches relying on fixed prompt templates introduce substantial sampling inefficiencies for weak LLMs, as most problems generate invalid outputs during accuracy-driven filtration. To solve this, we propose Cog-Rethinker, a novel hierarchical metacognitive RL framework. Cog-Rethinker enhances the rollout procedure by improving sample utilization through a two-stage framework leveraging human cognition. First, it prompts the policy to decompose zero-accuracy problems into subproblems. Second, it prompts the policy to refine answers by referencing previous wrong solutions. Moreover, to enable cold-starts and maintain train-test consistency, Cog-Rethinker applies supervised fine-tuning using correct samples from these stages. Experimental results demonstrate Cog-Rethinker’s superior performance on mathematical reasoning benchmarks and its improved sample efficiency that accelerates convergence compared to baselines.