GeoSym127K: Scalable Symbolically-verifiable Synthesis for Multimodal Geometric Reasoning

TL;DR

This paper introduces GeoSym127K, a scalable neuro-symbolic framework for precise geometric reasoning, along with a large dataset and evaluation benchmarks, significantly improving multimodal models' reasoning capabilities.

Contribution

It presents the GeoSym Engine for exact symbolic ground truths, constructs the GeoSym127K dataset, and demonstrates enhanced reasoning performance with new training and reinforcement learning methods.

Findings

GeoSym127K contains 127K questions with symbolic ground truths.

Fine-tuning with GeoSym improves model accuracy on geometry tasks.

RLVR with structural SFT checkpoints boosts performance over zero-shot methods.

Abstract

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.