# GeoFocus: Blending Efficient Global-to-Local Perception for Multimodal Geometry Problem-Solving

arXiv: https://arxiv.org/abs/2602.08524 · HTML: https://mlsanity.com/paper/2602.08524/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Embodied and 3D vision-language models, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 46 of its 62 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Placed in

- Multimodal LLMs / vision-language models / [Embodied and 3D vision-language models](https://mlsanity.com/mllm/embodied-and-3d-vision-language-models/)

## Builds on (most cited first, 30 of 46)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling](https://mlsanity.com/paper/2412.05271/) (2024)
- [ChartQA: A Benchmark for Question Answering about Charts with Visual and Logical Reasoning](https://mlsanity.com/paper/2203.10244/) (2022)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Chameleon: Mixed-Modal Early-Fusion Foundation Models](https://mlsanity.com/paper/2405.09818/) (2024)
- [DeepSeek-VL: Towards Real-World Vision-Language Understanding](https://mlsanity.com/paper/2403.05525/) (2024)
- [Automatic Chain of Thought Prompting in Large Language Models](https://mlsanity.com/paper/2210.03493/) (2022)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [HallusionBench: An Advanced Diagnostic Suite for Entangled Language Hallucination and Visual Illusion in Large Vision-Language Models](https://mlsanity.com/paper/2310.14566/) (2023)
- [mPLUG-Owl2: Revolutionizing Multi-modal Large Language Model with Modality Collaboration](https://mlsanity.com/paper/2311.04257/) (2023)
- [Measuring Multimodal Mathematical Reasoning with MATH-Vision Dataset](https://mlsanity.com/paper/2402.14804/) (2024)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [Monkey: Image Resolution and Text Label Are Important Things for Large Multi-modal Models](https://mlsanity.com/paper/2311.06607/) (2023)
- [How Much Can CLIP Benefit Vision-and-Language Tasks?](https://mlsanity.com/paper/2107.06383/) (2021)
- [We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?](https://mlsanity.com/paper/2407.01284/) (2024)
- [Visual Sketchpad: Sketching as a Visual Chain of Thought for Multimodal Language Models](https://mlsanity.com/paper/2406.09403/) (2024)
- [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)
- [UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression](https://mlsanity.com/paper/2212.02746/) (2022)
- [Math-LLaVA: Bootstrapping Mathematical Reasoning for Multimodal Large Language Models](https://mlsanity.com/paper/2406.17294/) (2024)
- [MAVIS: Mathematical Visual Instruction Tuning with an Automatic Data Engine](https://mlsanity.com/paper/2407.08739/) (2024)
- [GeomVerse: A Systematic Evaluation of Large Models for Geometric Reasoning](https://mlsanity.com/paper/2312.12241/) (2023)
- [NoisyRollout: Reinforcing Visual Reasoning with Data Augmentation](https://mlsanity.com/paper/2504.13055/) (2025)
- [MultiMath: Bridging Visual and Mathematical Reasoning for Large Language Models](https://mlsanity.com/paper/2409.00147/) (2024)

## Built on by (most cited first, 1 of 1)

- [DeltaV: Thinking with Visual State Updates in Unified Large Multimodal Models](https://mlsanity.com/paper/2607.08434/) (2026)

## Abstract (arXiv)

Geometry problem-solving remains a significant challenge for Large Multimodal Models (LMMs), requiring not only global shape recognition but also attention to intricate local relationships related to geometric theory. To address this, we propose GeoFocus, a novel framework comprising two core modules. 1) Critical Local Perceptor, which automatically identifies and emphasizes critical local structure (e.g., angles, parallel lines, comparative distances) through thirteen theory-based perception templates, boosting critical local feature coverage by 61% compared to previous methods. 2) VertexLang, a compact topology formal language, encodes global figures through vertex coordinates and connectivity relations. By replacing bulky code-based encodings, VertexLang reduces global perception training time by 20% while improving topology recognition accuracy. When evaluated in Geo3K, GeoQA, and FormalGeo7K, GeoFocus achieves a 4.7% accuracy improvement over leading specialized models and demonstrates superior robustness in MATHVERSE under diverse visual conditions. Project Page -- https://github.com/dle666/GeoFocus