# AutoGeo: Automating Geometric Image Dataset Creation for Enhanced Geometry Understanding

arXiv: https://arxiv.org/abs/2409.09039 · HTML: https://mlsanity.com/paper/2409.09039/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 29 of its 56 references that are in the map.
- First posted on arXiv 28 Aug 2024.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [InstructBLIP: Towards General-purpose Vision-Language Models with Instruction Tuning](https://mlsanity.com/paper/2305.06500/) (2023)
- [CIDEr: Consensus-based Image Description Evaluation](https://mlsanity.com/paper/1411.5726/) (2014)
- [Multimodal Chain-of-Thought Reasoning in Language Models](https://mlsanity.com/paper/2302.00923/) (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)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [Effective Data Augmentation With Diffusion Models](https://mlsanity.com/paper/2302.07944/) (2023)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [AnyGPT: Unified Multimodal LLM with Discrete Sequence Modeling](https://mlsanity.com/paper/2402.12226/) (2024)
- [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)
- [How well do Large Language Models perform in Arithmetic tasks?](https://mlsanity.com/paper/2304.02015/) (2023)
- [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)
- [GPT Can Solve Mathematical Problems Without a Calculator](https://mlsanity.com/paper/2309.03241/) (2023)
- [A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagram](https://mlsanity.com/paper/2302.11097/) (2023)
- [Plane Geometry Diagram Parsing](https://mlsanity.com/paper/2205.09363/) (2022)
- [AQuA: A Benchmarking Tool for Label Quality Assessment](https://mlsanity.com/paper/2306.09467/) (2023)
- [Non-confusing Generation of Customized Concepts in Diffusion Models](https://mlsanity.com/paper/2405.06914/) (2024)
- [MPCODER: Multi-user Personalized Code Generator with Explicit and Implicit Style Representation Learning](https://mlsanity.com/paper/2406.17255/) (2024)
- [Semantic Alignment for Multimodal Large Language Models](https://mlsanity.com/paper/2408.12867/) (2024)
- [RUArt: A Novel Text-Centered Solution for Text-Based Visual Question Answering](https://mlsanity.com/paper/2010.12917/) (2020)
- [General and Task-Oriented Video Segmentation](https://mlsanity.com/paper/2407.06540/) (2024)

## Built on by (most cited first, 29 of 29)

- [Lumina-DiMOO: An Omni Diffusion Large Language Model for Multi-Modal Generation and Understanding](https://mlsanity.com/paper/2510.06308/) (2025)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [MINT-CoT: Enabling Interleaved Visual Tokens in Mathematical Chain-of-Thought Reasoning](https://mlsanity.com/paper/2506.05331/) (2025)
- [OmniCaptioner: One Captioner to Rule Them All](https://mlsanity.com/paper/2504.07089/) (2025)
- [Embracing Imperfection: Simulating Students with Diverse Cognitive Levels Using LLM-based Agents](https://mlsanity.com/paper/2505.19997/) (2025)
- [Reasoning Physical Video Generation with Diffusion Timestep Tokens via Reinforcement Learning](https://mlsanity.com/paper/2504.15932/) (2025)
- [Math Blind: Failures in Diagram Understanding Undermine Reasoning in MLLMs](https://mlsanity.com/paper/2503.20745/) (2025)
- [Towards Transformer-Based Aligned Generation with Self-Coherence Guidance](https://mlsanity.com/paper/2503.17675/) (2025)
- [AutoGPS: Automated Geometry Problem Solving via Multimodal Formalization and Deductive Reasoning](https://mlsanity.com/paper/2505.23381/) (2025)
- [TrustGeoGen: Formal-Verified Data Engine for Trustworthy Multi-modal Geometric Problem Solving](https://mlsanity.com/paper/2504.15780/) (2025)
- [IRBridge: Solving Image Restoration Bridge with Pre-trained Generative Diffusion Models](https://mlsanity.com/paper/2505.24406/) (2025)
- [Knowledge is Power: Harnessing Large Language Models for Enhanced Cognitive Diagnosis](https://mlsanity.com/paper/2502.05556/) (2025)
- [NeSyGeo: A Neuro-Symbolic Framework for Multimodal Geometric Reasoning Data Generation](https://mlsanity.com/paper/2505.17121/) (2025)
- [GeoDANO: Geometric VLM with Domain Agnostic Vision Encoder](https://mlsanity.com/paper/2502.11360/) (2025)
- [From Text to Visuals: Using LLMs to Generate Math Diagrams with Vector Graphics](https://mlsanity.com/paper/2503.07429/) (2025)
- [Generalizable Geometric Image Caption Synthesis](https://mlsanity.com/paper/2509.15217/) (2025)
- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)
- [From Experience to Skill: Multi-Agent Generative Engine Optimization via Reusable Strategy Learning](https://mlsanity.com/paper/2604.19516/) (2026)
- [Tailoring Diagnostic Modeling to Individual Learners: Personalized Distractor Generation via MCTS-Guided Reasoning Reconstruction](https://mlsanity.com/paper/2508.11184/) (2025)
- [WorldEdit: Towards Open-World Image Editing with a Knowledge-Informed Benchmark](https://mlsanity.com/paper/2602.07095/) (2026)
- [Training-free Spatially Grounded Geometric Shape Encoding (Technical Report)](https://mlsanity.com/paper/2604.07522/) (2026)
- [Geoparsing: Diagram Parsing for Plane and Solid Geometry with a Unified Formal Language](https://mlsanity.com/paper/2604.11600/) (2026)
- [GeoSym127K: Scalable Symbolically-verifiable Synthesis for Multimodal Geometric Reasoning](https://mlsanity.com/paper/2605.16371/) (2026)
- [FormalAnalyticGeo: A Neural-Symbolic Based Framework for Multimodal Analytic Geometry Problem Generation](https://mlsanity.com/paper/2607.12982/) (2026)
- [Cognitive-Level Adaptive Generation via Capability-Aware Retrieval and Style Adaptation](https://mlsanity.com/paper/2509.19336/) (2025)
- [Concise Geometric Description as a Bridge: Unleashing the Potential of LLM for Plane Geometry Problem Solving](https://mlsanity.com/paper/2601.21164/) (2026)
- [MathVis-Fine: Aligning Visual Supervision with Necessity via Progressive Dependency-Guided Training for Multimodal Mathematical Reasoning](https://mlsanity.com/paper/2606.17888/) (2026)
- [Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry](https://mlsanity.com/paper/2608.14585/) (2026)
- [MathVis: Can AI Reason through Drawing? A Benchmark for Mathematical Figure Generation](https://mlsanity.com/paper/2610.12954/) (2026)

## Abstract (arXiv)

With the rapid advancement of large language models, there has been a growing interest in their capabilities in mathematical reasoning. However, existing research has primarily focused on text-based algebra problems, neglecting the study of geometry due to the lack of high-quality geometric datasets. To address this gap, this paper introduces AutoGeo, a novel approach for automatically generating mathematical geometric images to fulfill the demand for large-scale and diverse geometric datasets. AutoGeo facilitates the creation of AutoGeo-100k, an extensive repository comprising 100k high-quality geometry image-text pairs. By leveraging precisely defined geometric clauses, AutoGeo-100k contains a wide variety of geometric shapes, including lines, polygons, circles, and complex spatial relationships, etc. Furthermore, this paper demonstrates the efficacy of AutoGeo-100k in enhancing the performance of multimodal large language models through fine-tuning. Experimental results indicate significant improvements in the model's ability in handling geometric images, as evidenced by enhanced accuracy in tasks such as geometric captioning and mathematical reasoning. This research not only fills a critical gap in the availability of geometric datasets but also paves the way for the advancement of sophisticated AI-driven tools in education and research. Project page: https://autogeo-official.github.io/.