# Improving Multimodal LLMs Ability In Geometry Problem Solving, Reasoning, And Multistep Scoring

arXiv: https://arxiv.org/abs/2412.00846 · HTML: https://mlsanity.com/paper/2412.00846/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 25 of its 45 references that are in the map.
- First posted on arXiv 1 Dec 2024.

## 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, 25 of 25)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Self-RAG: Learning to Retrieve, Generate, and Critique through Self-Reflection](https://mlsanity.com/paper/2310.11511/) (2023)
- [A Multitask, Multilingual, Multimodal Evaluation of ChatGPT on Reasoning, Hallucination, and Interactivity](https://mlsanity.com/paper/2302.04023/) (2023)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [GIT: A Generative Image-to-text Transformer for Vision and Language](https://mlsanity.com/paper/2205.14100/) (2022)
- [Active Retrieval Augmented Generation](https://mlsanity.com/paper/2305.06983/) (2023)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving](https://mlsanity.com/paper/2309.17452/) (2023)
- [RECOMP: Improving Retrieval-Augmented LMs with Compression and Selective Augmentation](https://mlsanity.com/paper/2310.04408/) (2023)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [MuRAG: Multimodal Retrieval-Augmented Generator for Open Question Answering over Images and Text](https://mlsanity.com/paper/2210.02928/) (2022)
- [ZeroGen: Efficient Zero-shot Learning via Dataset Generation](https://mlsanity.com/paper/2202.07922/) (2022)
- [G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model](https://mlsanity.com/paper/2312.11370/) (2023)
- [Corrective Retrieval Augmented Generation](https://mlsanity.com/paper/2401.15884/) (2024)
- [Chain-of-Note: Enhancing Robustness in Retrieval-Augmented Language Models](https://mlsanity.com/paper/2311.09210/) (2023)
- [Retrieval-Augmented Multimodal Language Modeling](https://mlsanity.com/paper/2211.12561/) (2022)
- [A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagram](https://mlsanity.com/paper/2302.11097/) (2023)
- [Self-Guided Noise-Free Data Generation for Efficient Zero-Shot Learning](https://mlsanity.com/paper/2205.12679/) (2022)
- [Retrieval-augmented Multi-modal Chain-of-Thoughts Reasoning for Large Language Models](https://mlsanity.com/paper/2312.01714/) (2023)
- [Enhancing Human-like Multi-Modal Reasoning: A New Challenging Dataset and Comprehensive Framework](https://mlsanity.com/paper/2307.12626/) (2023)

## Built on by (most cited first, 5 of 5)

- [GeoLaux: A Benchmark for Evaluating MLLMs' Geometry Performance on Long-Step Problems Requiring Auxiliary Lines](https://mlsanity.com/paper/2508.06226/) (2025)
- [Multilingual Mathematical Reasoning: Advancing Open-Source LLMs in Hindi and English](https://mlsanity.com/paper/2412.18415/) (2024)
- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)
- [Long-context Non-factoid Question Answering in Indic Languages](https://mlsanity.com/paper/2504.13615/) (2025)
- [From Perception to Reasoning: Deep Thinking Empowers Multimodal Large Language Models](https://mlsanity.com/paper/2511.12861/) (2025)

## Abstract (arXiv)

This paper presents GPSM4K, a comprehensive geometry multimodal dataset tailored to augment the problem-solving capabilities of Large Vision Language Models (LVLMs). GPSM4K encompasses 2157 multimodal question-answer pairs manually extracted from mathematics textbooks spanning grades 7-12 and is further augmented to 5340 problems, consisting of both numerical and theorem-proving questions. In contrast to PGPS9k, Geometry3K, and Geo170K which feature only objective-type questions, GPSM4K offers detailed step-by-step solutions in a consistent format, facilitating a comprehensive evaluation of problem-solving approaches. This dataset serves as an excellent benchmark for assessing the geometric reasoning capabilities of LVLMs. Evaluation of our test set shows that there is scope for improvement needed in open-source language models in geometry problem-solving. Finetuning on our training set increases the geometry problem-solving capabilities of models. Further, We also evaluate the effectiveness of techniques such as image captioning and Retrieval Augmentation generation (RAG) on model performance. We leveraged LLM to automate the task of final answer evaluation by providing ground truth and predicted solutions. This research will help to assess and improve the geometric reasoning capabilities of LVLMs.