# Geoint-R1: Formalizing Multimodal Geometric Reasoning with Dynamic Auxiliary Constructions arXiv: https://arxiv.org/abs/2508.03173 ยท HTML: https://mlsanity.com/paper/2508.03173/ ## Key facts - Cited by 11 papers in the map (data through 14 Oct 2026). - Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning. - Builds on 27 of its 29 references that are in the map. - First posted on arXiv 5 Aug 2025. ## Placed in - LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/) ## Builds on (most cited first, 27 of 27) - [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) - [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024) - [InternVL3: Exploring Advanced Training and Test-Time Recipes for Open-Source Multimodal Models](https://mlsanity.com/paper/2504.10479/) (2025) - [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023) - [Yi: Open Foundation Models by 01.AI](https://mlsanity.com/paper/2403.04652/) (2024) - [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024) - [MM-REACT: Prompting ChatGPT for Multimodal Reasoning and Action](https://mlsanity.com/paper/2303.11381/) (2023) - [We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?](https://mlsanity.com/paper/2407.01284/) (2024) - [Show-o2: Improved Native Unified Multimodal Models](https://mlsanity.com/paper/2506.15564/) (2025) - [Seg-Zero: Reasoning-Chain Guided Segmentation via Cognitive Reinforcement](https://mlsanity.com/paper/2503.06520/) (2025) - [T2I-R1: Reinforcing Image Generation with Collaborative Semantic-level and Token-level CoT](https://mlsanity.com/paper/2505.00703/) (2025) - [GoT: Unleashing Reasoning Capability of Multimodal Large Language Model for Visual Generation and Editing](https://mlsanity.com/paper/2503.10639/) (2025) - [PyVision: Agentic Vision with Dynamic Tooling](https://mlsanity.com/paper/2507.07998/) (2025) - [MathCoder-VL: Bridging Vision and Code for Enhanced Multimodal Mathematical Reasoning](https://mlsanity.com/paper/2505.10557/) (2025) - [VisuoThink: Empowering LVLM Reasoning with Multimodal Tree Search](https://mlsanity.com/paper/2504.09130/) (2025) - [MM-MATH: Advancing Multimodal Math Evaluation with Process Evaluation and Fine-grained Classification](https://mlsanity.com/paper/2404.05091/) (2024) - [From Words to Structured Visuals: A Benchmark and Framework for Text-to-Diagram Generation and Editing](https://mlsanity.com/paper/2411.11916/) (2024) - [CMMCoT: Enhancing Complex Multi-Image Comprehension via Multi-Modal Chain-of-Thought and Memory Augmentation](https://mlsanity.com/paper/2503.05255/) (2025) - [Boosting the Power of Small Multimodal Reasoning Models to Match Larger Models with Self-Consistency Training](https://mlsanity.com/paper/2311.14109/) (2023) - [Polymath: A Challenging Multi-modal Mathematical Reasoning Benchmark](https://mlsanity.com/paper/2410.14702/) (2024) - [ProgRM: Build Better GUI Agents with Progress Rewards](https://mlsanity.com/paper/2505.18121/) (2025) - [SOLIDGEO: Measuring Multimodal Spatial Math Reasoning in Solid Geometry](https://mlsanity.com/paper/2505.21177/) (2025) - [Enhancing Human-like Multi-Modal Reasoning: A New Challenging Dataset and Comprehensive Framework](https://mlsanity.com/paper/2307.12626/) (2023) - [MMSciBench: Benchmarking Language Models on Chinese Multimodal Scientific Problems](https://mlsanity.com/paper/2503.01891/) (2025) - [ControlThinker: Unveiling Latent Semantics for Controllable Image Generation through Visual Reasoning](https://mlsanity.com/paper/2506.03596/) (2025) - [MMFactory: A Universal Solution Search Engine for Vision-Language Tasks](https://mlsanity.com/paper/2412.18072/) (2024) ## Built on by (most cited first, 11 of 11) - [Zooming without Zooming: Region-to-Image Distillation for Fine-Grained Multimodal Perception](https://mlsanity.com/paper/2602.11858/) (2026) - [From Perception to Cognition: A Survey of Vision-Language Interactive Reasoning in Multimodal Large Language Models](https://mlsanity.com/paper/2509.25373/) (2025) - [V-Thinker: Interactive Thinking with Images](https://mlsanity.com/paper/2511.04460/) (2025) - [GeoLaux: A Benchmark for Evaluating MLLMs' Geometry Performance on Long-Step Problems Requiring Auxiliary Lines](https://mlsanity.com/paper/2508.06226/) (2025) - [GGBench: A Geometric Generative Reasoning Benchmark for Unified Multimodal Models](https://mlsanity.com/paper/2511.11134/) (2025) - [Beyond NL2Code: A Structured Survey of Multimodal Code Intelligence](https://mlsanity.com/paper/2606.15932/) (2026) - [How RL Unlocks the Aha Moment in Geometric Interleaved Reasoning](https://mlsanity.com/paper/2603.01070/) (2026) - [PaperFit: Vision-in-the-Loop Typesetting Optimization for Scientific Documents](https://mlsanity.com/paper/2605.10341/) (2026) - [PAGER: Bridging the Semantic-Execution Gap in Point-Precise Geometric GUI Control](https://mlsanity.com/paper/2605.15963/) (2026) - [MIRROR: Learning from the Other View for Multi-Modal Reasoning](https://mlsanity.com/paper/2607.21552/) (2026) - [LatentGeo: Learnable Auxiliary Constructions in Latent Space for Multimodal Geometric Reasoning](https://mlsanity.com/paper/2603.12166/) (2026) ## Abstract (arXiv) Mathematical geometric reasoning is essential for scientific discovery and educational development, requiring precise logic and rigorous formal verification. While recent advances in Multimodal Large Language Models (MLLMs) have improved reasoning tasks, existing models typically struggle with formal geometric reasoning, particularly when dynamically constructing and verifying auxiliary geometric elements. To address these challenges, we introduce Geoint-R1, a multimodal reasoning framework designed to generate formally verifiable geometric solutions from textual descriptions and visual diagrams. Geoint-R1 uniquely integrates auxiliary elements construction, formal reasoning represented via Lean4, and interactive visualization. To systematically evaluate and advance formal geometric reasoning, we propose the Geoint benchmark, comprising 1,885 rigorously annotated geometry problems across diverse topics such as plane, spatial, and solid geometry. Each problem includes structured textual annotations, precise Lean4 code for auxiliary constructions, and detailed solution steps verified by experts. Extensive experiments demonstrate that Geoint-R1 significantly surpasses existing multimodal and math-specific reasoning models, particularly on challenging problems requiring explicit auxiliary element constructions.