# Plane Geometry Problem Solving with Multi-modal Reasoning: A Survey

arXiv: https://arxiv.org/abs/2505.14340 · HTML: https://mlsanity.com/paper/2505.14340/

## Key facts

- Cited by 2 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 111 references that are in the map.
- First posted on arXiv 20 May 2025.

## 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, 27 of 27)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [SAM 2: Segment Anything in Images and Videos](https://mlsanity.com/paper/2408.00714/) (2024)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Are We on the Right Way for Evaluating Large Vision-Language Models?](https://mlsanity.com/paper/2403.20330/) (2024)
- [Set-of-Mark Prompting Unleashes Extraordinary Visual Grounding in GPT-4V](https://mlsanity.com/paper/2310.11441/) (2023)
- [Perception, Reason, Think, and Plan: A Survey on Large Multimodal Reasoning Models](https://mlsanity.com/paper/2505.04921/) (2025)
- [VLSBench: Unveiling Visual Leakage in Multimodal Safety](https://mlsanity.com/paper/2411.19939/) (2024)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [Visual Prompting in Multimodal Large Language Models: A Survey](https://mlsanity.com/paper/2409.15310/) (2024)
- [VisOnlyQA: Large Vision Language Models Still Struggle with Visual Perception of Geometric Information](https://mlsanity.com/paper/2412.00947/) (2024)
- [GeoSense: Evaluating Identification and Application of Geometric Principles in Multimodal Reasoning](https://mlsanity.com/paper/2504.12597/) (2025)
- [Why Vision Language Models Struggle with Visual Arithmetic? Towards Enhanced Chart and Geometry Understanding](https://mlsanity.com/paper/2502.11492/) (2025)
- [Polymath: A Challenging Multi-modal Mathematical Reasoning Benchmark](https://mlsanity.com/paper/2410.14702/) (2024)
- [Open Eyes, Then Reason: Fine-grained Visual Mathematical Understanding in MLLMs](https://mlsanity.com/paper/2501.06430/) (2025)
- [TrustGeoGen: Formal-Verified Data Engine for Trustworthy Multi-modal Geometric Problem Solving](https://mlsanity.com/paper/2504.15780/) (2025)
- [Chimera: Improving Generalist Model with Domain-Specific Experts](https://mlsanity.com/paper/2412.05983/) (2024)
- [Benchmarking Multimodal Mathematical Reasoning with Explicit Visual Dependency](https://mlsanity.com/paper/2504.18589/) (2025)
- [Pi-GPS: Enhancing Geometry Problem Solving by Unleashing the Power of Diagrammatic Information](https://mlsanity.com/paper/2503.05543/) (2025)
- [FGeo-HyperGNet: Geometric Problem Solving Integrating FormalGeo Symbolic System and Hypergraph Neural Network](https://mlsanity.com/paper/2402.11461/) (2024)
- [GeoDANO: Geometric VLM with Domain Agnostic Vision Encoder](https://mlsanity.com/paper/2502.11360/) (2025)
- [Low-hallucination Synthetic Captions for Large-Scale Vision-Language Model Pre-training](https://mlsanity.com/paper/2504.13123/) (2025)
- [Is Your Text-to-Image Model Robust to Caption Noise?](https://mlsanity.com/paper/2412.19531/) (2024)
- [DomainCQA: Crafting Knowledge-Intensive QA from Domain-Specific Charts](https://mlsanity.com/paper/2503.19498/) (2025)

## Built on by (most cited first, 2 of 2)

- [GeoSketch: A Neural-Symbolic Approach to Geometric Multimodal Reasoning with Auxiliary Line Construction and Affine Transformation](https://mlsanity.com/paper/2509.22460/) (2025)
- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)

## Abstract (arXiv)

Plane geometry problem solving (PGPS) has recently gained significant attention as a benchmark to assess the multi-modal reasoning capabilities of large vision-language models. Despite the growing interest in PGPS, the research community still lacks a comprehensive overview that systematically synthesizes recent work in PGPS. To fill this gap, we present a survey of existing PGPS studies. We first categorize PGPS methods into an encoder-decoder framework and summarize the corresponding output formats used by their encoders and decoders. Subsequently, we classify and analyze these encoders and decoders according to their architectural designs. Finally, we outline major challenges and promising directions for future research. In particular, we discuss the hallucination issues arising during the encoding phase within encoder-decoder architectures, as well as the problem of data leakage in current PGPS benchmarks.