# GeoSense: Evaluating Identification and Application of Geometric Principles in Multimodal Reasoning

arXiv: https://arxiv.org/abs/2504.12597 · HTML: https://mlsanity.com/paper/2504.12597/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 46 of its 55 references that are in the map.
- First posted on arXiv 17 Apr 2025.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)
- 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)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [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)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [MiniGPT-4: Enhancing Vision-Language Understanding with Advanced Large Language Models](https://mlsanity.com/paper/2304.10592/) (2023)
- [InternVL: Scaling up Vision Foundation Models and Aligning for Generic Visual-Linguistic Tasks](https://mlsanity.com/paper/2312.14238/) (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)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [mPLUG-Owl: Modularization Empowers Large Language Models with Multimodality](https://mlsanity.com/paper/2304.14178/) (2023)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (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)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [DeepSeek-VL2: Mixture-of-Experts Vision-Language Models for Advanced Multimodal Understanding](https://mlsanity.com/paper/2412.10302/) (2024)
- [mPLUG-Owl2: Revolutionizing Multi-modal Large Language Model with Modality Collaboration](https://mlsanity.com/paper/2311.04257/) (2023)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [InternLM-XComposer2: Mastering Free-form Text-Image Composition and Comprehension in Vision-Language Large Model](https://mlsanity.com/paper/2401.16420/) (2024)

## Built on by (most cited first, 25 of 25)

- [Perception, Reason, Think, and Plan: A Survey on Large Multimodal Reasoning Models](https://mlsanity.com/paper/2505.04921/) (2025)
- [Reinforced MLLM: A Survey on RL-Based Reasoning in Multimodal Large Language Models](https://mlsanity.com/paper/2504.21277/) (2025)
- [Open Vision Reasoner: Transferring Linguistic Cognitive Behavior for Visual Reasoning](https://mlsanity.com/paper/2507.05255/) (2025)
- [We-Math 2.0: A Versatile MathBook System for Incentivizing Visual Mathematical Reasoning](https://mlsanity.com/paper/2508.10433/) (2025)
- [Reinforcement Fine-Tuning Powers Reasoning Capability of Multimodal Large Language Models](https://mlsanity.com/paper/2505.18536/) (2025)
- [GeoGramBench: Benchmarking the Geometric Program Reasoning in Modern LLMs](https://mlsanity.com/paper/2505.17653/) (2025)
- [Euclid's Gift: Enhancing Spatial Perception and Reasoning in Vision-Language Models via Geometric Surrogate Tasks](https://mlsanity.com/paper/2509.24473/) (2025)
- [NeSyGeo: A Neuro-Symbolic Framework for Multimodal Geometric Reasoning Data Generation](https://mlsanity.com/paper/2505.17121/) (2025)
- [Towards Geometry Problem Solving in the Large Model Era: A Survey](https://mlsanity.com/paper/2506.02690/) (2025)
- [Position: Reasoning After Perception Means Reasoning Without Vision](https://mlsanity.com/paper/2507.16863/) (2025)
- [Mixture-of-Visual-Thoughts: Exploring Context-Adaptive Reasoning Mode Selection for General Visual Reasoning](https://mlsanity.com/paper/2509.22746/) (2025)
- [MME-SCI: A Comprehensive and Challenging Science Benchmark for Multimodal Large Language Models](https://mlsanity.com/paper/2508.13938/) (2025)
- [GeoBench: Rethinking Multimodal Geometric Problem-Solving via Hierarchical Evaluation](https://mlsanity.com/paper/2512.24119/) (2025)
- [Milestones over Outcome: Unlocking Geometric Reasoning with Sub-Goal Verifiable Reward](https://mlsanity.com/paper/2601.05073/) (2026)
- [Bridging Formal Language with Chain-of-Thought Reasoning to Geometry Problem Solving](https://mlsanity.com/paper/2508.09099/) (2025)
- [Plane Geometry Problem Solving with Multi-modal Reasoning: A Survey](https://mlsanity.com/paper/2505.14340/) (2025)
- [GeoThought: A Dataset for Enhancing Mathematical Geometry Reasoning in Vision-Language Models](https://mlsanity.com/paper/2510.21881/) (2025)
- [DynaSolidGeo: A Dynamic Benchmark for Genuine Spatial Mathematical Reasoning of VLMs in Solid Geometry](https://mlsanity.com/paper/2510.22340/) (2025)
- [PAGER: Bridging the Semantic-Execution Gap in Point-Precise Geometric GUI Control](https://mlsanity.com/paper/2605.15963/) (2026)
- [Concise Geometric Description as a Bridge: Unleashing the Potential of LLM for Plane Geometry Problem Solving](https://mlsanity.com/paper/2601.21164/) (2026)
- [Draw2Think: Harnessing Geometry Reasoning through Constraint Engine Interaction](https://mlsanity.com/paper/2605.20743/) (2026)
- [Internalizing Geometric Law: Learning from Solver Residuals for Precision-Critical Generation](https://mlsanity.com/paper/2606.09278/) (2026)
- [GeoDial: A Multimodal Conversational Tutoring Dataset for Geometry Problem-Solving with Visual Tutor Turns](https://mlsanity.com/paper/2606.12419/) (2026)
- [Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry](https://mlsanity.com/paper/2608.14585/) (2026)
- [CVIF: A Criticality-Driven Visual Intervention Framework for Geometric Diagram Understanding in MLLMs](https://mlsanity.com/paper/2610.06399/) (2026)

## Abstract (arXiv)

Geometry problem-solving (GPS), a challenging task requiring both visual comprehension and symbolic reasoning, effectively measures the reasoning capabilities of multimodal large language models (MLLMs). Humans exhibit strong reasoning ability in this task through accurate identification and adaptive application of geometric principles within visual contexts. However, existing benchmarks fail to jointly assess both dimensions of the human-like geometric reasoning mechanism in MLLMs, remaining a critical gap in assessing their ability to tackle GPS. To this end, we introduce GeoSense, the first comprehensive bilingual benchmark designed to systematically evaluate the geometric reasoning abilities of MLLMs through the lens of geometric principles. GeoSense features a five-level hierarchical framework of geometric principles spanning plane and solid geometry, an intricately annotated dataset of 1,789 problems, and an innovative evaluation strategy. Through extensive experiments on GeoSense with various open-source and closed-source MLLMs, we observe that Gemini-2.0-pro-flash performs best, achieving an overall score of 65.3. Our in-depth analysis reveals that the identification and application of geometric principles remain a bottleneck for leading MLLMs, jointly hindering their reasoning abilities. These findings underscore GeoSense's potential to guide future advancements in MLLMs' geometric reasoning capabilities, paving the way for more robust and human-like reasoning in artificial intelligence.