Hard2Verify: A Step-Level Verification Benchmark for Open-Ended Frontier Math

TL;DR

Hard2Verify presents a step-level verification benchmark tailored to frontier open-ended math, aggregating 1,860 annotated steps across 200 frontier-model solutions to challenging Olympiad-level problems. It systematically evaluates 29 verifiers, spanning open-weight and proprietary models, on three tasks: Step-Level, Response-Level, and ErrorID, revealing a persistent gap between large closed models and open-source verifiers. The study shows that increasing inference-time compute via sequential prompting yields notable gains for several models, while parallel best-of-N methods offer limited benefits, and that prompting strategies influence error identification in nuanced ways. The findings highlight the essential role of robust step-level verification in scalable RLHF and frontier math systems, and they chart directions for improving open-source verifiers and prompting protocols.

Abstract

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.

Figures (8)

• Figure 1: Comparison of models evaluated on both ProcessBench zheng2024processbench and our Hard2Verify benchmark. Past benchmarks do not sufficiently evaluate in the frontier-level math settings that Hard2Verify does; On the same error identification task, Qwen2.5-Math-PRM-72B performance drops from ProcessBench state-of-the-art at 78.3 to 37.3 on Hard2Verify.
• Figure 2: Breakdown of correct vs. incorrect steps (left) and responses (right) by model. We consider a response incorrect if any step in the response is labeled incorrect.
• Figure 3: Count of correct (left) and incorrect (right) labels by model solution step. Models tend to begin solutions correctly, but typically start to get derailed after a few steps.
• Figure 4: Weaker models are unable to find mistakes, eventually considering all steps correct: TNR tends toward 0 while TPR tends towards 1.
• Figure 5: Top: Scaling inference-time compute sequentially leads to higher performance in GPT-5 and gpt-oss models, with large gains for gpt-oss-20B (59.69$\rightarrow$70.93) and 120B (61.46 $\rightarrow$ 74.64) in terms of step-level Balanced F1. Bottom: Parallel decoding has little effect on step-level F1 performance for gpt-oss-20B, failing to bridge the gap vs. gpt-oss-20B at high-reasoning effort.