# UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression

arXiv: https://arxiv.org/abs/2212.02746 · HTML: https://mlsanity.com/paper/2212.02746/

## Key facts

- Cited by 137 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 41 references that are in the map.
- First posted on arXiv 6 Dec 2022.

## Placed in

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

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Flamingo: a Visual Language Model for Few-Shot Learning](https://mlsanity.com/paper/2204.14198/) (2022)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Unifying Vision-and-Language Tasks via Text Generation](https://mlsanity.com/paper/2102.02779/) (2021)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning](https://mlsanity.com/paper/2209.14610/) (2022)
- [A simple neural network module for relational reasoning](https://mlsanity.com/paper/1706.01427/) (2017)
- [Deep Modular Co-Attention Networks for Visual Question Answering](https://mlsanity.com/paper/1906.10770/) (2019)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [IconQA: A New Benchmark for Abstract Diagram Understanding and Visual Language Reasoning](https://mlsanity.com/paper/2110.13214/) (2021)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [NumGLUE: A Suite of Fundamental yet Challenging Mathematical Reasoning Tasks](https://mlsanity.com/paper/2204.05660/) (2022)
- [NaturalProofs: Mathematical Theorem Proving in Natural Language](https://mlsanity.com/paper/2104.01112/) (2021)
- [Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks](https://mlsanity.com/paper/2107.01431/) (2021)
- [Semantically-Aligned Universal Tree-Structured Solver for Math Word Problems](https://mlsanity.com/paper/2010.06823/) (2020)
- [LogicSolver: Towards Interpretable Math Word Problem Solving with Logical Prompt-enhanced Learning](https://mlsanity.com/paper/2205.08232/) (2022)
- [Plane Geometry Diagram Parsing](https://mlsanity.com/paper/2205.09363/) (2022)
- [Unbiased Math Word Problems Benchmark for Mitigating Solving Bias](https://mlsanity.com/paper/2205.08108/) (2022)

## Built on by (most cited first, 30 of 137)

- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [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)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Models](https://mlsanity.com/paper/2503.06749/) (2025)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?](https://mlsanity.com/paper/2407.01284/) (2024)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [LMM-R1: Empowering 3B LMMs with Strong Reasoning Abilities Through Two-Stage Rule-Based RL](https://mlsanity.com/paper/2503.07536/) (2025)
- [G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model](https://mlsanity.com/paper/2312.11370/) (2023)
- [TheoremQA: A Theorem-driven Question Answering dataset](https://mlsanity.com/paper/2305.12524/) (2023)
- [Mulberry: Empowering MLLM with o1-like Reasoning and Reflection via Collective Monte Carlo Tree Search](https://mlsanity.com/paper/2412.18319/) (2024)
- [Math-LLaVA: Bootstrapping Mathematical Reasoning for Multimodal Large Language Models](https://mlsanity.com/paper/2406.17294/) (2024)
- [MAmmoTH-VL: Eliciting Multimodal Reasoning with Instruction Tuning at Scale](https://mlsanity.com/paper/2412.05237/) (2024)
- [NVLM: Open Frontier-Class Multimodal LLMs](https://mlsanity.com/paper/2409.11402/) (2024)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [MAVIS: Mathematical Visual Instruction Tuning with an Automatic Data Engine](https://mlsanity.com/paper/2407.08739/) (2024)
- [Baichuan-Omni-1.5 Technical Report](https://mlsanity.com/paper/2501.15368/) (2025)
- [GeomVerse: A Systematic Evaluation of Large Models for Geometric Reasoning](https://mlsanity.com/paper/2312.12241/) (2023)
- [A Comprehensive Survey of Scientific Large Language Models and Their Applications in Scientific Discovery](https://mlsanity.com/paper/2406.10833/) (2024)
- [Mini-InternVL: A Flexible-Transfer Pocket Multimodal Model with 5% Parameters and 90% Performance](https://mlsanity.com/paper/2410.16261/) (2024)
- [SPIQA: A Dataset for Multimodal Question Answering on Scientific Papers](https://mlsanity.com/paper/2407.09413/) (2024)
- [Eagle 2: Building Post-Training Data Strategies from Scratch for Frontier Vision-Language Models](https://mlsanity.com/paper/2501.14818/) (2025)
- [Vision-Language Models Can Self-Improve Reasoning via Reflection](https://mlsanity.com/paper/2411.00855/) (2024)
- [Virgo: A Preliminary Exploration on Reproducing o1-like MLLM](https://mlsanity.com/paper/2501.01904/) (2025)
- [Ming-Omni: A Unified Multimodal Model for Perception and Generation](https://mlsanity.com/paper/2506.09344/) (2025)
- [A Survey on Deep Learning for Theorem Proving](https://mlsanity.com/paper/2404.09939/) (2024)
- [A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagram](https://mlsanity.com/paper/2302.11097/) (2023)
- [Advancing Multimodal Reasoning: From Optimized Cold Start to Staged Reinforcement Learning](https://mlsanity.com/paper/2506.04207/) (2025)
- [FineVision: Open Data Is All You Need](https://mlsanity.com/paper/2510.17269/) (2025)

## Abstract (arXiv)

Geometry problem solving is a well-recognized testbed for evaluating the high-level multi-modal reasoning capability of deep models. In most existing works, two main geometry problems: calculation and proving, are usually treated as two specific tasks, hindering a deep model to unify its reasoning capability on multiple math tasks. However, in essence, these two tasks have similar problem representations and overlapped math knowledge which can improve the understanding and reasoning ability of a deep model on both two tasks. Therefore, we construct a large-scale Unified Geometry problem benchmark, UniGeo, which contains 4,998 calculation problems and 9,543 proving problems. Each proving problem is annotated with a multi-step proof with reasons and mathematical expressions. The proof can be easily reformulated as a proving sequence that shares the same formats with the annotated program sequence for calculation problems. Naturally, we also present a unified multi-task Geometric Transformer framework, Geoformer, to tackle calculation and proving problems simultaneously in the form of sequence generation, which finally shows the reasoning ability can be improved on both two tasks by unifying formulation. Furthermore, we propose a Mathematical Expression Pretraining (MEP) method that aims to predict the mathematical expressions in the problem solution, thus improving the Geoformer model. Experiments on the UniGeo demonstrate that our proposed Geoformer obtains state-of-the-art performance by outperforming task-specific model NGS with over 5.6% and 3.2% accuracies on calculation and proving problems, respectively.