# VEHME: A Vision-Language Model For Evaluating Handwritten Mathematics Expressions

arXiv: https://arxiv.org/abs/2510.22798 · HTML: https://mlsanity.com/paper/2510.22798/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in VLM benchmarks and visual reasoning, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 25 of its 60 references that are in the map.
- First posted on arXiv 26 Oct 2025.

## Placed in

- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 25 of 25)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Visual-RFT: Visual Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.01785/) (2025)
- [MLLM-as-a-Judge: Assessing Multimodal LLM-as-a-Judge with Vision-Language Benchmark](https://mlsanity.com/paper/2402.04788/) (2024)
- [SWIFT:A Scalable lightWeight Infrastructure for Fine-Tuning](https://mlsanity.com/paper/2408.05517/) (2024)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [ReFT: Reasoning with Reinforced Fine-Tuning](https://mlsanity.com/paper/2401.08967/) (2024)
- [Grammar-Constrained Decoding for Structured NLP Tasks without Finetuning](https://mlsanity.com/paper/2305.13971/) (2023)
- [R1-Zero's "Aha Moment" in Visual Reasoning on a 2B Non-SFT Model](https://mlsanity.com/paper/2503.05132/) (2025)
- [AlphaMath Almost Zero: Process Supervision without Process](https://mlsanity.com/paper/2405.03553/) (2024)
- [Image-to-Markup Generation with Coarse-to-Fine Attention](https://mlsanity.com/paper/1609.04938/) (2016)
- [o1-Coder: an o1 Replication for Coding](https://mlsanity.com/paper/2412.00154/) (2024)
- [JudgeLRM: Large Reasoning Models as a Judge](https://mlsanity.com/paper/2504.00050/) (2025)
- [Training LLM-based Tutors to Improve Student Learning Outcomes in Dialogues](https://mlsanity.com/paper/2503.06424/) (2025)
- [CodeDPO: Aligning Code Models with Self Generated and Verified Source Code](https://mlsanity.com/paper/2410.05605/) (2024)
- [DrawEduMath: Evaluating Vision Language Models with Expert-Annotated Students' Hand-Drawn Math Images](https://mlsanity.com/paper/2501.14877/) (2025)
- [Can Vision-Language Models Evaluate Handwritten Math?](https://mlsanity.com/paper/2501.07244/) (2025)
- [Math Operation Embeddings for Open-ended Solution Analysis and Feedback](https://mlsanity.com/paper/2104.12047/) (2021)
- [BAGS: An automatic homework grading system using the pictures taken by smart phones](https://mlsanity.com/paper/1906.03767/) (2019)
- [MathMistake Checker: A Comprehensive Demonstration for Step-by-Step Math Problem Mistake Finding by Prompt-Guided LLMs](https://mlsanity.com/paper/2503.04291/) (2025)

## Built on by (most cited first, 4 of 4)

- [The Aftermath of DrawEduMath: Vision Language Models Underperform with Struggling Students and Misdiagnose Errors](https://mlsanity.com/paper/2603.00925/) (2026)
- [HyperWalker: Dynamic Hypergraph-Based Deep Diagnosis for Multi-Hop Clinical Modeling across EHR and X-Ray in Medical VLMs](https://mlsanity.com/paper/2601.13919/) (2026)
- [PA-CDM: Position-Aware Character Detection Matching for Evaluating Handwritten Mathematical Expression Recognition](https://mlsanity.com/paper/2609.12917/) (2026)
- [Cross-Domain Few-Shot Writer Adaptation for Real-World Handwritten Mathematical Expression Recognition](https://mlsanity.com/paper/2609.32513/) (2026)

## Abstract (arXiv)

Automatically assessing handwritten mathematical solutions is an important problem in educational technology with practical applications, but it remains a significant challenge due to the diverse formats, unstructured layouts, and symbolic complexity of student work. To address this challenge, we introduce VEHME-a Vision-Language Model for Evaluating Handwritten Mathematics Expressions-designed to assess open-form handwritten math responses with high accuracy and interpretable reasoning traces. VEHME integrates a two-phase training pipeline: (i) supervised fine-tuning using structured reasoning data, and (ii) reinforcement learning that aligns model outputs with multi-dimensional grading objectives, including correctness, reasoning depth, and error localization. To enhance spatial understanding, we propose an Expression-Aware Visual Prompting Module, trained on our synthesized multi-line math expressions dataset to robustly guide attention in visually heterogeneous inputs. Evaluated on AIHub and FERMAT datasets, VEHME achieves state-of-the-art performance among open-source models and approaches the accuracy of proprietary systems, demonstrating its potential as a scalable and accessible tool for automated math assessment. Our training and experiment code is publicly available at our GitHub repository.