Critique to Verify: Accurate and Honest Test-Time Scaling with RL-Trained Verifiers

Test-time scaling via solution sampling and aggregation has become a key paradigm for improving the reasoning performance of Large Language Models (LLMs). While reward model selection is commonly employed in this approach, it often fails to identify minority-yet-correct answers, which limits its effectiveness beyond that of simple majority voting. We argue that this limitation stems from a lack of informative critique signals during verifier training. To bridge this gap, we introduce Mirror-Critique, a framework that trains a verifier with informative critiques. Our key insight is to leverage the rich critique signal by contrasting model-generated solutions with ground-truth solutions. We deploy a small instruction-tuned model to synthesize high-quality critique data with rejection sampling that teaches the verifier not only what is wrong, but also why. The synthetic data is used to cold-start the LLMs in the RL VR process to further improve the verification ability. The resulting Mirror-V erifier is deployed to evaluate candidate solutions by generating multiple critiques per solution, aggregating them into a verify score used for weighted voting or selective abstention. The experimental results show that our Mirror-V erifier significantly outperforms majority voting in terms of solution accuracy and also improves the solver's honesty to recognize and abstain from answering beyond its capability boundaries. Reinforcement Learning with V erifiable Reward (RL VR) has emerged as a powerful method for training Large Language Models (LLMs) to perform complex reasoning tasks, enabling significant improvements in domains such as mathematics, code generation, and scientific problem-solving.