Shrey Pandit SalesForce.com, Austin Xu Anthropic, Xuan-Phi Nguyen, Yifei Ming Salesforce AI Research, Caiming Xiong Salesforce Research, Shafiq Joty Nanyang Technological University and SalesForce.com
Large language model (LLM)-based reasoning systems have recently achieved gold medal-level performance in the IMO 2025 competition, writing mathematical proofs where, to receive full credit, each step must be not only correct but also sufficiently supported. To train LLM-based reasoners in such challenging, open-ended settings, strong verifiers capable of catching step-level mistakes are necessary prerequisites. We introduce Hard2Verify, a human-annotated, step-level verification benchmark produced with over 500 hours of human labor. Hard2Verify is designed to rigorously assess step-level verifiers at the frontier: Verifiers must provide step-level annotations or identify the first error in responses generated by frontier LLMs for very recent, challenging, and open-ended math questions. We evaluate 29 generative critics and process reward models, demonstrating that, beyond a few standouts, open-source verifiers lag closed source models. We subsequently analyze what drives poor performance in step-level verification, the impacts of scaling verifier compute, as well as fundamental questions such as self-verification and verification-generation dynamics.
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cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表
Austin Xu Anthropic, Yilun Zhou Massachusetts Institute of Technology, Xuan-Phi Nguyen, Caiming Xiong Salesforce Research, Shafiq Joty Nanyang Technological University and SalesForce.com
To keep pace with the increasing velocity of large language models (LLM) development, model output evaluation has transitioned away from time-consuming human evaluation to automatic evaluation, where LLMs themselves are tasked with assessing and critiquing other model outputs. LLM-as-judge models are a class of generative evaluators that excel in evaluating relatively simple domains, like chat quality, but struggle in reasoning intensive domains where model responses contain more substantive and challenging content. To remedy existing judge shortcomings, we explore training judges with reinforcement learning (RL). We make three key contributions: (1) We propose the Equivalent Initial State Group Relative Policy Optimization (EIS-GRPO) algorithm, which allows us to train our judge to be robust to positional biases that arise in more complex evaluation settings. (2) We introduce ReasoningJudgeBench, a benchmark that evaluates judges in diverse reasoning settings not covered by prior work. (3) We train Judge for Reasoning (J4R), a 7B judge trained with EIS-GRPO that outperforms GPT-4o and the next best small judge by 6.7% and 9%, matching or exceeding the performance of larger GRPO-trained judges on both JudgeBench and ReasoningJudgeBench.
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cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表