# GeoLaux: A Benchmark for Evaluating MLLMs' Geometry Performance on Long-Step Problems Requiring Auxiliary Lines

arXiv: https://arxiv.org/abs/2508.06226 · HTML: https://mlsanity.com/paper/2508.06226/

## Key facts

- Cited by 6 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 14 of its 30 references that are in the map.
- First posted on arXiv 8 Aug 2025.

## 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, 14 of 14)

- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?](https://mlsanity.com/paper/2407.01284/) (2024)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression](https://mlsanity.com/paper/2212.02746/) (2022)
- [A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagram](https://mlsanity.com/paper/2302.11097/) (2023)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [GeoEval: Benchmark for Evaluating LLMs and Multi-Modal Models on Geometry Problem-Solving](https://mlsanity.com/paper/2402.10104/) (2024)
- [MV-MATH: Evaluating Multimodal Math Reasoning in Multi-Visual Contexts](https://mlsanity.com/paper/2502.20808/) (2025)
- [SOLIDGEO: Measuring Multimodal Spatial Math Reasoning in Solid Geometry](https://mlsanity.com/paper/2505.21177/) (2025)
- [MARS: Multi-Agent Adaptive Reasoning with Socratic Guidance for Automated Prompt Optimization](https://mlsanity.com/paper/2503.16874/) (2025)
- [GeoUni: A Unified Model for Generating Geometry Diagrams, Problems and Problem Solutions](https://mlsanity.com/paper/2504.10146/) (2025)
- [Geoint-R1: Formalizing Multimodal Geometric Reasoning with Dynamic Auxiliary Constructions](https://mlsanity.com/paper/2508.03173/) (2025)
- [Improving Multimodal LLMs Ability In Geometry Problem Solving, Reasoning, And Multistep Scoring](https://mlsanity.com/paper/2412.00846/) (2024)

## Built on by (most cited first, 6 of 6)

- [Can World Simulators Reason? Gen-ViRe: A Generative Visual Reasoning Benchmark](https://mlsanity.com/paper/2511.13853/) (2025)
- [Thinking in Frames: How Visual Context and Test-Time Scaling Empower Video Reasoning](https://mlsanity.com/paper/2601.21037/) (2026)
- [GeoVLMath: Enhancing Geometry Reasoning in Vision-Language Models via Cross-Modal Reward for Auxiliary Line Creation](https://mlsanity.com/paper/2510.11020/) (2025)
- [DynaSolidGeo: A Dynamic Benchmark for Genuine Spatial Mathematical Reasoning of VLMs in Solid Geometry](https://mlsanity.com/paper/2510.22340/) (2025)
- [LogicGraph : Benchmarking Multi-Path Logical Reasoning via Neuro-Symbolic Generation and Verification](https://mlsanity.com/paper/2602.21044/) (2026)
- [GeoChallenge: A Multi-Answer Multiple-Choice Benchmark for Geometric Reasoning with Diagrams](https://mlsanity.com/paper/2603.19252/) (2026)

## Abstract (arXiv)

Geometry problem solving (GPS) poses significant challenges for Multimodal Large Language Models (MLLMs) in diagram comprehension, knowledge application, long-step reasoning, and auxiliary line construction. However, current benchmarks lack fine-grained evaluation for long-step problems necessitating auxiliary construction. To address these limitations, we present GeoLaux, a fine-grained annotated dataset comprising 2186 calculation and proof problems. It features long-step reasoning (with an average solution length of 6.51 steps, maximum of 24 steps) and auxiliary line construction (required in 41.8% of problems). Building on the dataset, we conduct a comprehensive five-dimensional evaluation of 23 leading MLLMs. The evaluation yields three pivotal findings: First, models perform significantly worse on long-step problems compared to short-step ones, with 18 models exhibiting a performance drop of over 50%. Second, it is crucial to enhance models' understanding, awareness, and proficiency in auxiliary line construction, which is vital for overall geometric reasoning. Third, limited answer hints effectively improve process correctness, whereas explicit answers lead models to neglect intermediate reasoning steps. These findings position GeoLaux both to benchmark MLLMs geometry reasoning abilities and to guide their improvement. Data and code are available at https://github.com/Candice-yu/GeoLaux