# Learning to Solve Geometry Problems via Simulating Human Dual-Reasoning Process

arXiv: https://arxiv.org/abs/2405.06232 · HTML: https://mlsanity.com/paper/2405.06232/

## 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 19 of its 38 references that are in the map.
- First posted on arXiv 10 May 2024.

## Placed in

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

## Builds on (most cited first, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [GLM: General Language Model Pretraining with Autoregressive Blank Infilling](https://mlsanity.com/paper/2103.10360/) (2021)
- [CogVLM: Visual Expert for Pretrained Language Models](https://mlsanity.com/paper/2311.03079/) (2023)
- [CogView: Mastering Text-to-Image Generation via Transformers](https://mlsanity.com/paper/2105.13290/) (2021)
- [Scene Graph Generation by Iterative Message Passing](https://mlsanity.com/paper/1701.02426/) (2017)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [Deep Modular Co-Attention Networks for Visual Question Answering](https://mlsanity.com/paper/1906.10770/) (2019)
- [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)
- [A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagram](https://mlsanity.com/paper/2302.11097/) (2023)
- [Plane Geometry Diagram Parsing](https://mlsanity.com/paper/2205.09363/) (2022)
- [A Symbolic Character-Aware Model for Solving Geometry Problems](https://mlsanity.com/paper/2308.02823/) (2023)

## Built on by (most cited first, 11 of 11)

- [Perception-R1: Advancing Multimodal Reasoning Capabilities of MLLMs via Visual Perception Reward](https://mlsanity.com/paper/2506.07218/) (2025)
- [Advancing Tool-Augmented Large Language Models via Meta-Verification and Reflection Learning](https://mlsanity.com/paper/2506.04625/) (2025)
- [Enhancing the Geometric Problem-Solving Ability of Multimodal LLMs via Symbolic-Neural Integration](https://mlsanity.com/paper/2504.12773/) (2025)
- [AutoGPS: Automated Geometry Problem Solving via Multimodal Formalization and Deductive Reasoning](https://mlsanity.com/paper/2505.23381/) (2025)
- [Pi-GPS: Enhancing Geometry Problem Solving by Unleashing the Power of Diagrammatic Information](https://mlsanity.com/paper/2503.05543/) (2025)
- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)
- [Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspective](https://mlsanity.com/paper/2510.21999/) (2025)
- [Beyond Symbolic Solving: Multi Chain-of-Thought Voting for Geometric Reasoning in Large Language Models](https://mlsanity.com/paper/2604.00890/) (2026)
- [Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry](https://mlsanity.com/paper/2608.14585/) (2026)
- [One Prompt Does Not Fit All: Self-Meta-Evolve for Personalized Information Extraction](https://mlsanity.com/paper/2609.21626/) (2026)
- [Dense Neuro-Symbolic Reasoning in a Unified Geometry State](https://mlsanity.com/paper/2610.04280/) (2026)

## Abstract (arXiv)

Geometry Problem Solving (GPS), which is a classic and challenging math problem, has attracted much attention in recent years. It requires a solver to comprehensively understand both text and diagram, master essential geometry knowledge, and appropriately apply it in reasoning. However, existing works follow a paradigm of neural machine translation and only focus on enhancing the capability of encoders, which neglects the essential characteristics of human geometry reasoning. In this paper, inspired by dual-process theory, we propose a Dual-Reasoning Geometry Solver (DualGeoSolver) to simulate the dual-reasoning process of humans for GPS. Specifically, we construct two systems in DualGeoSolver, namely Knowledge System and Inference System. Knowledge System controls an implicit reasoning process, which is responsible for providing diagram information and geometry knowledge according to a step-wise reasoning goal generated by Inference System. Inference System conducts an explicit reasoning process, which specifies the goal in each reasoning step and applies the knowledge to generate program tokens for resolving it. The two systems carry out the above process iteratively, which behaves more in line with human cognition. We conduct extensive experiments on two benchmark datasets, GeoQA and GeoQA+. The results demonstrate the superiority of DualGeoSolver in both solving accuracy and robustness from explicitly modeling human reasoning process and knowledge application.