# AutoGPS: Automated Geometry Problem Solving via Multimodal Formalization and Deductive Reasoning

arXiv: https://arxiv.org/abs/2505.23381 · HTML: https://mlsanity.com/paper/2505.23381/

## Key facts

- Cited by 14 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 66 references that are in the map.
- First posted on arXiv 29 May 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)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (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)
- [Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling](https://mlsanity.com/paper/2412.05271/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Models](https://mlsanity.com/paper/2503.06749/) (2025)
- [Enhancing the Reasoning Ability of Multimodal Large Language Models via Mixed Preference Optimization](https://mlsanity.com/paper/2411.10442/) (2024)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression](https://mlsanity.com/paper/2212.02746/) (2022)
- [Agentic Reasoning and Tool Integration for LLMs via Reinforcement Learning](https://mlsanity.com/paper/2505.01441/) (2025)
- [Corex: Pushing the Boundaries of Complex Reasoning through Multi-Model Collaboration](https://mlsanity.com/paper/2310.00280/) (2023)
- [PhysReason: A Comprehensive Benchmark towards Physics-Based Reasoning](https://mlsanity.com/paper/2502.12054/) (2025)
- [ScienceBoard: Evaluating Multimodal Autonomous Agents in Realistic Scientific Workflows](https://mlsanity.com/paper/2505.19897/) (2025)
- [GeoEval: Benchmark for Evaluating LLMs and Multi-Modal Models on Geometry Problem-Solving](https://mlsanity.com/paper/2402.10104/) (2024)
- [AutoGeo: Automating Geometric Image Dataset Creation for Enhanced Geometry Understanding](https://mlsanity.com/paper/2409.09039/) (2024)
- [Plane Geometry Diagram Parsing](https://mlsanity.com/paper/2205.09363/) (2022)
- [Proving Olympiad Inequalities by Synergizing LLMs and Symbolic Reasoning](https://mlsanity.com/paper/2502.13834/) (2025)
- [DreamPRM: Domain-Reweighted Process Reward Model for Multimodal Reasoning](https://mlsanity.com/paper/2505.20241/) (2025)
- [Interactive Evolution: A Neural-Symbolic Self-Training Framework For Large Language Models](https://mlsanity.com/paper/2406.11736/) (2024)
- [A Survey of Neural Code Intelligence: Paradigms, Advances and Beyond](https://mlsanity.com/paper/2403.14734/) (2024)
- [Learning to Solve Geometry Problems via Simulating Human Dual-Reasoning Process](https://mlsanity.com/paper/2405.06232/) (2024)
- [NeSyGeo: A Neuro-Symbolic Framework for Multimodal Geometric Reasoning Data Generation](https://mlsanity.com/paper/2505.17121/) (2025)
- [FGeo-HyperGNet: Geometric Problem Solving Integrating FormalGeo Symbolic System and Hypergraph Neural Network](https://mlsanity.com/paper/2402.11461/) (2024)

## Built on by (most cited first, 14 of 14)

- [CoFFT: Chain of Foresight-Focus Thought for Visual Language Models](https://mlsanity.com/paper/2509.22010/) (2025)
- [Multi-Modal Dataset Distillation in the Wild](https://mlsanity.com/paper/2506.01586/) (2025)
- [Do Multi-Agents Solve Better Than Single? Evaluating Agentic Frameworks for Diagram-Grounded Geometry Problem Solving and Reasoning](https://mlsanity.com/paper/2512.16698/) (2025)
- [Non-Parametric Structural Priors for Geometry Theorem Prediction](https://mlsanity.com/paper/2603.04852/) (2026)
- [Artificial Intelligence for Mathematical Reasoning: An Integrated Survey of Language Models, Neuro-symbolic Systems, and Verified Discovery](https://mlsanity.com/paper/2606.08728/) (2026)
- [FormalAnalyticGeo: A Neural-Symbolic Based Framework for Multimodal Analytic Geometry Problem Generation](https://mlsanity.com/paper/2607.12982/) (2026)
- [Tri-Bench: Stress-Testing VLM Reliability on Spatial Reasoning under Camera Tilt and Object Interference](https://mlsanity.com/paper/2512.08860/) (2025)
- [Concise Geometric Description as a Bridge: Unleashing the Potential of LLM for Plane Geometry Problem Solving](https://mlsanity.com/paper/2601.21164/) (2026)
- [Draw2Think: Harnessing Geometry Reasoning through Constraint Engine Interaction](https://mlsanity.com/paper/2605.20743/) (2026)
- [VeriGeo: Controllable Geometry Question Generation with Numerical and Analytical Verification](https://mlsanity.com/paper/2606.14176/) (2026)
- [Verifiable Geometry Problem Solving: Solver-Driven Autoformalization and Theorem Proposing](https://mlsanity.com/paper/2606.27926/) (2026)
- [Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry](https://mlsanity.com/paper/2608.14585/) (2026)
- [From Symbolic Perception to Logical Deduction: A Framework for Guiding Language Models in Geometric Reasoning](https://mlsanity.com/paper/2609.10335/) (2026)
- [GeoReform: Reflective Formalization Evolution for Multimodal Geometry Problem Solving](https://mlsanity.com/paper/2610.12391/) (2026)

## Abstract (arXiv)

Geometry problem solving presents distinctive challenges in artificial intelligence, requiring exceptional multimodal comprehension and rigorous mathematical reasoning capabilities. Existing approaches typically fall into two categories: neural-based and symbolic-based methods, both of which exhibit limitations in reliability and interpretability. To address this challenge, we propose AutoGPS, a neuro-symbolic collaborative framework that solves geometry problems with concise, reliable, and human-interpretable reasoning processes. Specifically, AutoGPS employs a Multimodal Problem Formalizer (MPF) and a Deductive Symbolic Reasoner (DSR). The MPF utilizes neural cross-modal comprehension to translate geometry problems into structured formal language representations, with feedback from DSR collaboratively. The DSR takes the formalization as input and formulates geometry problem solving as a hypergraph expansion task, executing mathematically rigorous and reliable derivation to produce minimal and human-readable stepwise solutions. Extensive experimental evaluations demonstrate that AutoGPS achieves state-of-the-art performance on benchmark datasets. Furthermore, human stepwise-reasoning evaluation confirms AutoGPS's impressive reliability and interpretability, with 99% stepwise logical coherence.