Scaling Generative Verifiers For Natural Language Mathematical Proof Verification And Selection

• URL: http://arxiv.org/abs/2511.13027v1
• Date: Mon, 17 Nov 2025 06:25:35 GMT
• Title: Scaling Generative Verifiers For Natural Language Mathematical Proof Verification And Selection
• Authors: Sadegh Mahdavi, Branislav Kisacanin, Shubham Toshniwal, Wei Du, Ivan Moshkov, George Armstrong, Renjie Liao, Christos Thrampoulidis, Igor Gitman,
• Abstract summary: Large language models have achieved remarkable success on final-answer mathematical problems.<n>However, the reasoning underlying these solutions is often flawed.<n>We evaluate both proof-based and final-answer reasoning to obtain a more reliable measure of model performance.
• Score: 42.21636315733425
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large language models have achieved remarkable success on final-answer mathematical problems, largely due to the ease of applying reinforcement learning with verifiable rewards. However, the reasoning underlying these solutions is often flawed. Advancing to rigorous proof-based mathematics requires reliable proof verification capabilities. We begin by analyzing multiple evaluation setups and show that focusing on a single benchmark can lead to brittle or misleading conclusions. To address this, we evaluate both proof-based and final-answer reasoning to obtain a more reliable measure of model performance. We then scale two major generative verification methods (GenSelect and LLM-as-a-Judge) to millions of tokens and identify their combination as the most effective framework for solution verification and selection. We further show that the choice of prompt for LLM-as-a-Judge significantly affects the model's performance, but reinforcement learning can reduce this sensitivity. However, despite improving proof-level metrics, reinforcement learning does not enhance final-answer precision, indicating that current models often reward stylistic or procedural correctness rather than mathematical validity. Our results establish practical guidelines for designing and evaluating scalable proof-verification and selection systems.

Related papers

• Proof-RM: A Scalable and Generalizable Reward Model for Math Proof [67.53066972145183]
  Large Language Models (LLMs) have demonstrated strong math reasoning abilities through Reinforcement Learning with *Verifiable Rewards* (RLVR)<n>Many advanced mathematical problems are proof-based, with no guaranteed way to determine the authenticity of a proof by simple answer matching.<n>To enable automatic verification, a Reward Model (RM) capable of reliably evaluating full proof processes is required.
  arXiv  Detail & Related papers  (2026-02-02T17:42:53Z)
• When Does Verification Pay Off? A Closer Look at LLMs as Solution Verifiers [11.937771430269201]
  We present a systematic study across 37 large language models (LLMs)<n>We compare self-verification with verification within the same family and across different families.<n>We analyze how metrics like verifier gain and false positive rate scale with model size and post-training, and characterize differences in dataset verifiability.
  arXiv  Detail & Related papers  (2025-12-02T00:51:14Z)
• Calibrated Reasoning: An Explanatory Verifier for Dynamic and Efficient Problem-Solving [2.357104785442987]
  We propose a pairwise Explanatory Verifier that produces calibrated confidence scores and associated natural language reasoning for generated solutions.<n>Our verifier improves the accuracy and efficiency of test-time strategies like best-of-n and self-reflection.
  arXiv  Detail & Related papers  (2025-09-24T01:36:00Z)
• Learning to Refine: Self-Refinement of Parallel Reasoning in LLMs [102.48588475875749]
  We introduce Generative Self-Refinement (GSR), a novel parallel test-time scaling framework.<n>GSR generates a set of candidate responses in parallel and then performs self-refinement to synthesize a new superior solution.<n>We show that our method achieves state-of-the-art performance across five mathematical benchmarks.
  arXiv  Detail & Related papers  (2025-08-27T06:51:48Z)
• Solving Inequality Proofs with Large Language Models [42.667163027148916]
  Inequality proving is crucial across diverse scientific and mathematical fields.<n>This makes it a demanding frontier for large language models (LLMs)<n>We release IneqMath, an expert-curated dataset of Olympiad-level inequalities.
  arXiv  Detail & Related papers  (2025-06-09T16:43:38Z)
• Scalable Best-of-N Selection for Large Language Models via Self-Certainty [75.1351701045874]
  Best-of-N selection is a key technique for improving the reasoning performance of Large Language Models (LLMs)<n>We propose self-certainty, a novel and efficient metric that leverages the inherent probability distribution of LLM outputs to estimate response quality without requiring external reward models.<n>Our findings establish self-certainty as a practical and efficient way for improving LLM reasoning capabilities.
  arXiv  Detail & Related papers  (2025-02-25T19:08:07Z)
• Improving LLM Reasoning through Scaling Inference Computation with Collaborative Verification [52.095460362197336]
  Large language models (LLMs) struggle with consistent and accurate reasoning. LLMs are trained primarily on correct solutions, reducing their ability to detect and learn from errors. We propose a novel collaborative method integrating Chain-of-Thought (CoT) and Program-of-Thought (PoT) solutions for verification.
  arXiv  Detail & Related papers  (2024-10-05T05:21:48Z)
• Generative Verifiers: Reward Modeling as Next-Token Prediction [29.543787728397643]
  We propose training verifiers using the ubiquitous next-token prediction objective, jointly on verification and solution generation.<n>Compared to standard verifiers, such generative verifiers (GenRM) can benefit from several advantages of LLMs.<n>We observe improvements of 28% $rightarrow$ 44.6% on MATH, and 37.9% $rightarrow$ 53.5% on MMLU abstract algebra.
  arXiv  Detail & Related papers  (2024-08-27T17:57:45Z)
• LLM Critics Help Catch Bugs in Mathematics: Towards a Better Mathematical Verifier with Natural Language Feedback [71.95402654982095]
  We propose Math-Minos, a natural language feedback-enhanced verifier. Our experiments reveal that a small set of natural language feedback can significantly boost the performance of the verifier.
  arXiv  Detail & Related papers  (2024-06-20T06:42:27Z)
• Evaluating Mathematical Reasoning Beyond Accuracy [50.09931172314218]
  We introduce ReasonEval, a new methodology for evaluating the quality of reasoning steps.<n>We show that ReasonEval consistently outperforms baseline methods in the meta-evaluation datasets.<n>We observe that ReasonEval can play a significant role in data selection.
  arXiv  Detail & Related papers  (2024-04-08T17:18:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.