# Open Eyes, Then Reason: Fine-grained Visual Mathematical Understanding in MLLMs

arXiv: https://arxiv.org/abs/2501.06430 · HTML: https://mlsanity.com/paper/2501.06430/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 36 of its 75 references that are in the map.
- First posted on arXiv 11 Jan 2025.

## Placed in

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

## Builds on (most cited first, 30 of 36)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Grounding DINO: Marrying DINO with Grounded Pre-Training for Open-Set Object Detection](https://mlsanity.com/paper/2303.05499/) (2023)
- [MiniGPT-4: Enhancing Vision-Language Understanding with Advanced Large Language Models](https://mlsanity.com/paper/2304.10592/) (2023)
- [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023)
- [MMMU: A Massive Multi-discipline Multimodal Understanding and Reasoning Benchmark for Expert AGI](https://mlsanity.com/paper/2311.16502/) (2023)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Kosmos-2: Grounding Multimodal Large Language Models to the World](https://mlsanity.com/paper/2306.14824/) (2023)
- [Open-vocabulary Object Detection via Vision and Language Knowledge Distillation](https://mlsanity.com/paper/2104.13921/) (2021)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [MiniGPT-v2: large language model as a unified interface for vision-language multi-task learning](https://mlsanity.com/paper/2310.09478/) (2023)
- [LLaMA-Adapter V2: Parameter-Efficient Visual Instruction Model](https://mlsanity.com/paper/2304.15010/) (2023)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [Measuring Multimodal Mathematical Reasoning with MATH-Vision Dataset](https://mlsanity.com/paper/2402.14804/) (2024)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Open-Vocabulary Object Detection Using Captions](https://mlsanity.com/paper/2011.10678/) (2020)
- [InternLM2 Technical Report](https://mlsanity.com/paper/2403.17297/) (2024)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [PandaGPT: One Model To Instruction-Follow Them All](https://mlsanity.com/paper/2305.16355/) (2023)
- [InternLM-XComposer2: Mastering Free-form Text-Image Composition and Comprehension in Vision-Language Large Model](https://mlsanity.com/paper/2401.16420/) (2024)
- [FigureQA: An Annotated Figure Dataset for Visual Reasoning](https://mlsanity.com/paper/1710.07300/) (2017)
- [SPHINX: The Joint Mixing of Weights, Tasks, and Visual Embeddings for Multi-modal Large Language Models](https://mlsanity.com/paper/2311.07575/) (2023)
- [From Sparse to Soft Mixtures of Experts](https://mlsanity.com/paper/2308.00951/) (2023)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model](https://mlsanity.com/paper/2312.11370/) (2023)
- [DetCLIP: Dictionary-Enriched Visual-Concept Paralleled Pre-training for Open-world Detection](https://mlsanity.com/paper/2209.09407/) (2022)
- [MAmmoTH2: Scaling Instructions from the Web](https://mlsanity.com/paper/2405.03548/) (2024)
- [ImageBind-LLM: Multi-modality Instruction Tuning](https://mlsanity.com/paper/2309.03905/) (2023)

## Built on by (most cited first, 16 of 16)

- [Why Reasoning Matters? A Survey of Advancements in Multimodal Reasoning (v1)](https://mlsanity.com/paper/2504.03151/) (2025)
- [OmniCaptioner: One Captioner to Rule Them All](https://mlsanity.com/paper/2504.07089/) (2025)
- [Forgotten Polygons: Multimodal Large Language Models are Shape-Blind](https://mlsanity.com/paper/2502.15969/) (2025)
- [Math Blind: Failures in Diagram Understanding Undermine Reasoning in MLLMs](https://mlsanity.com/paper/2503.20745/) (2025)
- [Constructive Distortion: Improving MLLMs with Attention-Guided Image Warping](https://mlsanity.com/paper/2510.09741/) (2025)
- [MathFlow: Enhancing the Perceptual Flow of MLLMs for Visual Mathematical Problems](https://mlsanity.com/paper/2503.16549/) (2025)
- [GeoDANO: Geometric VLM with Domain Agnostic Vision Encoder](https://mlsanity.com/paper/2502.11360/) (2025)
- [Seeing is Not Reasoning: MVPBench for Graph-based Evaluation of Multi-path Visual Physical CoT](https://mlsanity.com/paper/2505.24182/) (2025)
- [CogFlow: Bridging Perception and Reasoning through Knowledge Internalization for Visual Mathematical Problem Solving](https://mlsanity.com/paper/2601.01874/) (2026)
- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)
- [Plane Geometry Problem Solving with Multi-modal Reasoning: A Survey](https://mlsanity.com/paper/2505.14340/) (2025)
- [Blink: Dynamic Visual Token Resolution for Enhanced Multimodal Understanding](https://mlsanity.com/paper/2512.10548/) (2025)
- [MIRROR: Learning from the Other View for Multi-Modal Reasoning](https://mlsanity.com/paper/2607.21552/) (2026)
- [RoadBench: Benchmarking MLLMs on Fine-Grained Spatial Understanding and Reasoning under Urban Road Scenarios](https://mlsanity.com/paper/2511.18011/) (2025)
- [LatentGeo: Learnable Auxiliary Constructions in Latent Space for Multimodal Geometric Reasoning](https://mlsanity.com/paper/2603.12166/) (2026)
- [CVIF: A Criticality-Driven Visual Intervention Framework for Geometric Diagram Understanding in MLLMs](https://mlsanity.com/paper/2610.06399/) (2026)

## Abstract (arXiv)

Current multimodal large language models (MLLMs) often underperform on mathematical problem-solving tasks that require fine-grained visual understanding. The limitation is largely attributable to inadequate perception of geometric primitives during image-level contrastive pre-training (e.g., CLIP). While recent efforts to improve math MLLMs have focused on scaling up mathematical visual instruction datasets and employing stronger LLM backbones, they often overlook persistent errors in visual recognition. In this paper, we systematically evaluate the visual grounding capabilities of state-of-the-art MLLMs and reveal a significant negative correlation between visual grounding accuracy and problem-solving performance, underscoring the critical role of fine-grained visual understanding. Notably, advanced models like GPT-4o exhibit a 70% error rate when identifying geometric entities, highlighting that this remains a key bottleneck in visual mathematical reasoning. To address this, we propose a novel approach, SVE-Math (Selective Vision-Enhanced Mathematical MLLM), featuring a geometric-grounded vision encoder and a feature router that dynamically adjusts the contribution of hierarchical visual feature maps. Our model recognizes accurate visual primitives and generates precise visual prompts tailored to the language model's reasoning needs. In experiments, SVE-Math-Qwen2.5-7B outperforms other 7B models by 15% on MathVerse and is compatible with GPT-4V on MathVista. Despite being trained on smaller datasets, SVE-Math-7B achieves competitive performance on GeoQA, rivaling models trained on significantly larger datasets. Our findings emphasize the importance of incorporating fine-grained visual understanding into MLLMs and provide a promising direction for future research.