# GeoSym127K: Scalable Symbolically-verifiable Synthesis for Multimodal Geometric Reasoning

arXiv: https://arxiv.org/abs/2605.16371 · HTML: https://mlsanity.com/paper/2605.16371/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 21 of its 37 references that are in the map.
- First posted on arXiv 10 May 2026.

## 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, 21 of 21)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Models](https://mlsanity.com/paper/2503.06749/) (2025)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [VLMEvalKit: An Open-Source Toolkit for Evaluating Large Multi-Modality Models](https://mlsanity.com/paper/2407.11691/) (2024)
- [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)
- [Seed1.8 Model Card: Towards Generalized Real-World Agency](https://mlsanity.com/paper/2603.20633/) (2026)
- [GeoGPT4V: Towards Geometric Multi-modal Large Language Models with Geometric Image Generation](https://mlsanity.com/paper/2406.11503/) (2024)
- [Theorem-Validated Reverse Chain-of-Thought Problem Generation for Geometric Reasoning](https://mlsanity.com/paper/2410.17885/) (2024)
- [AutoGeo: Automating Geometric Image Dataset Creation for Enhanced Geometry Understanding](https://mlsanity.com/paper/2409.09039/) (2024)
- [NVIDIA Nemotron Nano V2 VL](https://mlsanity.com/paper/2511.03929/) (2025)
- [Math Blind: Failures in Diagram Understanding Undermine Reasoning in MLLMs](https://mlsanity.com/paper/2503.20745/) (2025)
- [TrustGeoGen: Formal-Verified Data Engine for Trustworthy Multi-modal Geometric Problem Solving](https://mlsanity.com/paper/2504.15780/) (2025)
- [NeSyGeo: A Neuro-Symbolic Framework for Multimodal Geometric Reasoning Data Generation](https://mlsanity.com/paper/2505.17121/) (2025)
- [Do Large Language Models Truly Understand Geometric Structures?](https://mlsanity.com/paper/2501.13773/) (2025)
- [GeoSDF: Plane Geometry Diagram Synthesis via Signed Distance Field](https://mlsanity.com/paper/2506.13492/) (2025)
- [GeoBench: Rethinking Multimodal Geometric Problem-Solving via Hierarchical Evaluation](https://mlsanity.com/paper/2512.24119/) (2025)
- [GeoFM: Enhancing Geometric Reasoning of MLLMs via Synthetic Data Generation through Formal Language](https://mlsanity.com/paper/2510.27448/) (2025)

## Built on by (most cited first, 1 of 1)

- [Learning Where Outcomes Change:Credit-Addressable Reasoning for Multimodal Geometry](https://mlsanity.com/paper/2608.30457/) (2026)

## Abstract (arXiv)

Large Multimodal Models (LMMs) often struggle with geometric reasoning due to visual hallucinations and a lack of mathematically precise Chain-of-Thought (CoT) data. To address this, we propose the GeoSym Engine, an automated and scalable neuro-symbolic framework. By leveraging a type-conditional grammar and an analytic SymGT Solver, it derives exact symbolic ground truths and seamlessly integrates with a robust rendering pipeline to produce high-precision geometric diagrams. Using this engine, we construct GeoSym127K, a difficulty-stratified dataset featuring 51K high-resolution images, 127K questions with symbolic ground truths, and 55K answer-verified CoT QA pairs. We also introduce GeoSym-Bench, an expert-curated suite of 511 complex samples for rigorous evaluation. Through extensive supervised fine-tuning (SFT), we demonstrate that GeoSym drives concentrated improvements specifically on diagram-dependent and multi-step geometry tasks. Our Qwen3-VL-8B model gains an absolute +22.21% on the MathVerse Vision-Only subset and reaches 61.52% (+6.19% improvement) on WeMath, mitigating long-horizon logic fragmentation and outperforming advanced closed-source models like Doubao-1.8. Furthermore, applying Reinforcement Learning with Verifiable Rewards (RLVR) via GRPO reveals that initializing from structural SFT checkpoints substantially elevates the performance ceiling over zero-shot RL. Driven by deterministic exact-match signals, this showcases the robust scaling potential of our verifiable reasoning synthesis. Datasets and code are available at https://huggingface.co/datasets/Tomie0506/GeoSym127K and https://github.com/Tomie56/GeoSym127K.