# Beyond the Answer Key: Robustness Evaluation of Large Language Models for Step-Level Mathematical Verification

arXiv: https://arxiv.org/abs/2608.28725 · HTML: https://mlsanity.com/paper/2608.28725/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 19 references that are in the map.
- First posted on arXiv 28 Aug 2026.

## Builds on (most cited first, 13 of 13)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers](https://mlsanity.com/paper/2402.19255/) (2024)
- [T-Eval: Evaluating the Tool Utilization Capability of Large Language Models Step by Step](https://mlsanity.com/paper/2312.14033/) (2023)
- [MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations](https://mlsanity.com/paper/2502.06453/) (2025)
- [VerifyBench: A Systematic Benchmark for Evaluating Reasoning Verifiers Across Domains](https://mlsanity.com/paper/2507.09884/) (2025)
- [Exploring LLM Reasoning Through Controlled Prompt Variations](https://mlsanity.com/paper/2504.02111/) (2025)
- [Step-level Verifier-guided Hybrid Test-Time Scaling for Large Language Models](https://mlsanity.com/paper/2507.15512/) (2025)
- [Numerical Sensitivity and Robustness: Exploring the Flaws of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2511.08022/) (2025)

## Abstract (arXiv)

Large language models (LLMs) are increasingly used as graders, verifiers, and process auditors, but most mathematical evaluations still emphasize final-answer accuracy. This can obscure whether a model can verify a non-canonical but valid solution trace. We introduce a controlled linear-equation benchmark for evaluating LLMs in the evaluator role. Each instance asks the model to judge final-answer correctness, step-level trace correctness, and the first incorrect step. Our evaluation of state-of-the-art open LLMs reveals a significant robustness gap: models that accurately evaluate canonical solutions often fail when presented with perturbed but logically equivalent variants. Across GPT-OSS 20B, Qwen3-14B, and Phi-4-Reasoning, base models perform well on canonical traces but degrade substantially on perturbed traces, especially for error localization. On valid perturbed traces, base-model false-rejection rates reach 75.6-85.3%, showing strong sensitivity to canonical solution form. Supervised fine-tuning, distillation, and test-time compute improve robustness in some settings, but gains are model dependent and can trade off against canonical performance. The results show that reliable process-level verification remains challenging, and evaluator robustness should be measured separately from solver accuracy, even in a simple algebraic domain with exact ground truth.