# TrustGeoGen: Formal-Verified Data Engine for Trustworthy Multi-modal Geometric Problem Solving

arXiv: https://arxiv.org/abs/2504.15780 · HTML: https://mlsanity.com/paper/2504.15780/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 38 of its 59 references that are in the map.
- First posted on arXiv 22 Apr 2025.

## Placed in

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

## Builds on (most cited first, 30 of 38)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [BLIP-2: Bootstrapping Language-Image Pre-training with Frozen Image Encoders and Large Language Models](https://mlsanity.com/paper/2301.12597/) (2023)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [MME: A Comprehensive Evaluation Benchmark for Multimodal Large Language Models](https://mlsanity.com/paper/2306.13394/) (2023)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [How Far Are We to GPT-4V? Closing the Gap to Commercial Multimodal Models with Open-Source Suites](https://mlsanity.com/paper/2404.16821/) (2024)
- [DeepSeek-VL: Towards Real-World Vision-Language Understanding](https://mlsanity.com/paper/2403.05525/) (2024)
- [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)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Accelerating scientific discovery with Co-Scientist](https://mlsanity.com/paper/2502.18864/) (2025)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [InternLM-XComposer2: Mastering Free-form Text-Image Composition and Comprehension in Vision-Language Large Model](https://mlsanity.com/paper/2401.16420/) (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)
- [InternLM-XComposer2-4KHD: A Pioneering Large Vision-Language Model Handling Resolutions from 336 Pixels to 4K HD](https://mlsanity.com/paper/2404.06512/) (2024)
- [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)
- [MME-CoT: Benchmarking Chain-of-Thought in Large Multimodal Models for Reasoning Quality, Robustness, and Efficiency](https://mlsanity.com/paper/2502.09621/) (2025)
- [Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2](https://mlsanity.com/paper/2502.03544/) (2025)
- [ReasonFlux: Hierarchical LLM Reasoning via Scaling Thought Templates](https://mlsanity.com/paper/2502.06772/) (2025)
- [A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagram](https://mlsanity.com/paper/2302.11097/) (2023)

## Built on by (most cited first, 13 of 13)

- [Thinking with Images for Multimodal Reasoning: Foundations, Methods, and Future Frontiers](https://mlsanity.com/paper/2506.23918/) (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)
- [MathReal: We Keep It Real! A Real Scene Benchmark for Evaluating Math Reasoning in Multimodal Large Language Models](https://mlsanity.com/paper/2508.06009/) (2025)
- [Plane Geometry Problem Solving with Multi-modal Reasoning: A Survey](https://mlsanity.com/paper/2505.14340/) (2025)
- [GenesisGeo: Technical Report](https://mlsanity.com/paper/2509.21896/) (2025)
- [Socratic-Geo: Synthetic Data Generation and Geometric Reasoning via Multi-Agent Interaction](https://mlsanity.com/paper/2602.03414/) (2026)
- [How RL Unlocks the Aha Moment in Geometric Interleaved Reasoning](https://mlsanity.com/paper/2603.01070/) (2026)
- [DynaSolidGeo: A Dynamic Benchmark for Genuine Spatial Mathematical Reasoning of VLMs in Solid Geometry](https://mlsanity.com/paper/2510.22340/) (2025)
- [GeoChallenge: A Multi-Answer Multiple-Choice Benchmark for Geometric Reasoning with Diagrams](https://mlsanity.com/paper/2603.19252/) (2026)
- [GeoSym127K: Scalable Symbolically-verifiable Synthesis for Multimodal Geometric Reasoning](https://mlsanity.com/paper/2605.16371/) (2026)
- [A Survey of Multimodal Mathematical Reasoning: From Perception, Alignment to Reasoning](https://mlsanity.com/paper/2603.08291/) (2026)
- [Draw2Think: Harnessing Geometry Reasoning through Constraint Engine Interaction](https://mlsanity.com/paper/2605.20743/) (2026)

## Abstract (arXiv)

Geometric problem solving (GPS) requires precise multimodal understanding and rigorous, step-by-step logical reasoning. However, developing capable Multimodal Large Language Models (MLLMs) for GPS is heavily bottlenecked by the scarcity of high-quality, verifiable data. Existing data acquisition paradigms either suffer from modality incompleteness and unverified logical gaps ("leaps-of-faith"), or rely on formal engines that generate rigid, structurally homogeneous data, failing to produce high-difficulty problems or foster genuine natural-language reasoning. To overcome these limitations, we introduce TrustGeoGen, an autonomous and formalized geometric data generation engine. TrustGeoGen strictly guarantees reasoning trustworthiness through formal verification while generating multimodally integrated data, including premises, visual diagrams, and solutions. To systematically scale problem difficulty, we incorporates difficulty-aware filtering and iterative bootstrapping mechanism. Furthermore, we propose "connection thinking" to bridge the semantic gap between rigid formal logic and fluent human-like reasoning, ensuring coherent logical transitions. We also introduce the GeoExplore family of sampling algorithms to extract diverse problem-solving trajectories based on various thinking templates. Extensive experiments demonstrate that training models on our synthesized dataset, GeoTrust, substantially enhances deep geometric reasoning capabilities and yields significant performance gains across out-of-distribution (OOD) benchmarks, including GeoQA, Geometry3K, and OlympiadBench.Our code and data can be found at https://github.com/InternScience/TrustGeoGen