# GeoCoder: Solving Geometry Problems by Generating Modular Code through Vision-Language Models

arXiv: https://arxiv.org/abs/2410.13510 · HTML: https://mlsanity.com/paper/2410.13510/

## Key facts

- Cited by 5 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 59 references that are in the map.
- First posted on arXiv 17 Oct 2024.

## 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)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [ChartQA: A Benchmark for Question Answering about Charts with Visual and Logical Reasoning](https://mlsanity.com/paper/2203.10244/) (2022)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [PaLI: A Jointly-Scaled Multilingual Language-Image Model](https://mlsanity.com/paper/2209.06794/) (2022)
- [A Survey on Large Language Models for Code Generation](https://mlsanity.com/paper/2406.00515/) (2024)
- [ViperGPT: Visual Inference via Python Execution for Reasoning](https://mlsanity.com/paper/2303.08128/) (2023)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [Visual Programming: Compositional visual reasoning without training](https://mlsanity.com/paper/2211.11559/) (2022)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [PlotQA: Reasoning over Scientific Plots](https://mlsanity.com/paper/1909.00997/) (2019)
- [ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving](https://mlsanity.com/paper/2309.17452/) (2023)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model](https://mlsanity.com/paper/2312.11370/) (2023)
- [MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning](https://mlsanity.com/paper/2310.03731/) (2023)
- [UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression](https://mlsanity.com/paper/2212.02746/) (2022)
- [GeomVerse: A Systematic Evaluation of Large Models for Geometric Reasoning](https://mlsanity.com/paper/2312.12241/) (2023)
- [MARIO: MAth Reasoning with code Interpreter Output -- A Reproducible Pipeline](https://mlsanity.com/paper/2401.08190/) (2024)
- [VISTA: Visualized Text Embedding For Universal Multi-Modal Retrieval](https://mlsanity.com/paper/2406.04292/) (2024)
- [InfiMM-WebMath-40B: Advancing Multimodal Pre-Training for Enhanced Mathematical Reasoning](https://mlsanity.com/paper/2409.12568/) (2024)
- [GeoGPT4V: Towards Geometric Multi-modal Large Language Models with Geometric Image Generation](https://mlsanity.com/paper/2406.11503/) (2024)
- [Multimodal Self-Instruct: Synthetic Abstract Image and Visual Reasoning Instruction Using Language Model](https://mlsanity.com/paper/2407.07053/) (2024)

## Built on by (most cited first, 5 of 5)

- [BlueLM-V-3B: Algorithm and System Co-Design for Multimodal Large Language Models on Mobile Devices](https://mlsanity.com/paper/2411.10640/) (2024)
- [Towards Geometry Problem Solving in the Large Model Era: A Survey](https://mlsanity.com/paper/2506.02690/) (2025)
- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)
- [Thinking with Constructions: A Benchmark and Policy Optimization for Visual-Text Interleaved Geometric Reasoning](https://mlsanity.com/paper/2603.18662/) (2026)
- [NeedleChain: Measuring Intact Context Comprehension Capability of Large Language Models](https://mlsanity.com/paper/2507.22411/) (2025)

## Abstract (arXiv)

Geometry problem-solving demands advanced reasoning abilities to process multimodal inputs and employ mathematical knowledge effectively. Vision-language models (VLMs) have made significant progress in various multimodal tasks. Yet, they still struggle with geometry problems and are significantly limited by their inability to perform mathematical operations not seen during pre-training, such as calculating the cosine of an arbitrary angle, and by difficulties in correctly applying relevant geometry formulas. To overcome these challenges, we present GeoCoder, which leverages modular code-finetuning to generate and execute code using a predefined geometry function library. By executing the code, we achieve accurate and deterministic calculations, contrasting the stochastic nature of autoregressive token prediction, while the function library minimizes errors in formula usage. We also propose a multimodal retrieval-augmented variant of GeoCoder, named RAG-GeoCoder, which incorporates a non-parametric memory module for retrieving functions from the geometry library, thereby reducing reliance on parametric memory. Our modular code-finetuning approach enhances the geometric reasoning capabilities of VLMs, yielding an average improvement of over 16% across various question complexities on the GeomVerse dataset compared to other finetuning methods.