mlsanityData to 7 Oct 2026

UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression

arXiv 2212.02746 ↗First posted 6 Dec 2022cs.AI cs.LGcited by 137

On the map: LLM reasoning → Spatial and embodied reasoning

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.

Key facts. Cited by 137 papers in the map (data through 7 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.

Builds on

22 of 41 references.

References · 22

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10 more
  1. 2020ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Languagecited by 309
  2. 2021IconQA: A New Benchmark for Abstract Diagram Understanding and Visual Language Reasoningcited by 262
  3. 2021GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoningcited by 224
  4. 2022NumGLUE: A Suite of Fundamental yet Challenging Mathematical Reasoning Taskscited by 110
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 9; 2024: 48; 2025: 51; 2026: 28.

137 papers.

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  1. 2024LLaVA-OneVision: Easy Visual Task Transfercited by 2,669
  2. 2023MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contextscited by 1,582
  3. 2024Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scalingcited by 1,573
  4. 2024OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problemscited by 1,099
  5. 2025Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Modelscited by 653
  6. 2024MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?cited by 573
  7. 2024Large Language Models for Mathematical Reasoning: Progresses and Challengescited by 283
  8. 2024We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?cited by 281
  9. 2025LMM-R1: Empowering 3B LMMs with Strong Reasoning Abilities Through Two-Stage Rule-Based RLcited by 244
  10. 2023G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Modelcited by 208
  11. 2023TheoremQA: A Theorem-driven Question Answering datasetcited by 189
  12. 2024Mulberry: Empowering MLLM with o1-like Reasoning and Reflection via Collective Monte Carlo Tree Searchcited by 171
38 more
  1. 2024Math-LLaVA: Bootstrapping Mathematical Reasoning for Multimodal Large Language Modelscited by 133
  2. 2024MAmmoTH-VL: Eliciting Multimodal Reasoning with Instruction Tuning at Scalecited by 125
  3. 2022A Survey of Deep Learning for Mathematical Reasoningcited by 124
  4. 2024NVLM: Open Frontier-Class Multimodal LLMscited by 124
  5. 2024MAVIS: Mathematical Visual Instruction Tuning with an Automatic Data Enginecited by 111
  6. 2023GeomVerse: A Systematic Evaluation of Large Models for Geometric Reasoningcited by 107
  7. 2025Baichuan-Omni-1.5 Technical Reportcited by 107
  8. 2024A Comprehensive Survey of Scientific Large Language Models and Their Applications in Scientific Discoverycited by 96
  9. 2024Mini-InternVL: A Flexible-Transfer Pocket Multimodal Model with 5% Parameters and 90% Performancecited by 94
  10. 2024SPIQA: A Dataset for Multimodal Question Answering on Scientific Paperscited by 75
  11. 2025Eagle 2: Building Post-Training Data Strategies from Scratch for Frontier Vision-Language Modelscited by 69
  12. 2025Virgo: A Preliminary Exploration on Reproducing o1-like MLLMcited by 68
  13. 2024Vision-Language Models Can Self-Improve Reasoning via Reflectioncited by 66
  14. 2025Ming-Omni: A Unified Multimodal Model for Perception and Generationcited by 62
  15. 2023A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagramcited by 55
  16. 2024A Survey on Deep Learning for Theorem Provingcited by 55
  17. 2025Advancing Multimodal Reasoning: From Optimized Cold Start to Staged Reinforcement Learningcited by 51
  18. 2025FineVision: Open Data Is All You Needcited by 51
  19. 2024Is Your Model Really A Good Math Reasoner? Evaluating Mathematical Reasoning with Checklistcited by 48
  20. 2024AV-Odyssey Bench: Can Your Multimodal LLMs Really Understand Audio-Visual Information?cited by 46
  21. 2024Process-Driven Autoformalization in Lean 4cited by 45
  22. 2024GeoEval: Benchmark for Evaluating LLMs and Multi-Modal Models on Geometry Problem-Solvingcited by 44
  23. 2024MMInstruct: A High-Quality Multi-Modal Instruction Tuning Dataset with Extensive Diversitycited by 38
  24. 2024Theorem-Validated Reverse Chain-of-Thought Problem Generation for Geometric Reasoningcited by 32
  25. 2025SeePhys: Does Seeing Help Thinking? -- Benchmarking Vision-Based Physics Reasoningcited by 32
  26. 2024GeoGPT4V: Towards Geometric Multi-modal Large Language Models with Geometric Image Generationcited by 31
  27. 2025SlowFast-LLaVA-1.5: A Family of Token-Efficient Video Large Language Models for Long-Form Video Understandingcited by 30
  28. 2024AutoGeo: Automating Geometric Image Dataset Creation for Enhanced Geometry Understandingcited by 28
  29. 2024Autoformalizing Euclidean Geometrycited by 27
  30. 2025InteractiveOmni: A Unified Omni-modal Model for Audio-Visual Multi-turn Dialoguecited by 27
  31. 2023FormalGeo: An Extensible Formalized Framework for Olympiad Geometric Problem Solvingcited by 26
  32. 2024Distractor Generation in Multiple-Choice Tasks: A Survey of Methods, Datasets, and Evaluationcited by 25
  33. 2024BlueLM-V-3B: Algorithm and System Co-Design for Multimodal Large Language Models on Mobile Devicescited by 25
  34. 2024PVC: Progressive Visual Token Compression for Unified Image and Video Processing in Large Vision-Language Modelscited by 25
  35. 2024U-MATH: A University-Level Benchmark for Evaluating Mathematical Skills in LLMscited by 24
  36. 2025GeoSense: Evaluating Identification and Application of Geometric Principles in Multimodal Reasoningcited by 24
  37. 2023LANS: A Layout-Aware Neural Solver for Plane Geometry Problemcited by 23
  38. 2024GeoX: Geometric Problem Solving Through Unified Formalized Vision-Language Pre-trainingcited by 23

50 most cited of 137 All 137 (JSON)

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  1. 2025GeoUni: A Unified Model for Generating Geometry Diagrams, Problems and Problem Solutions
  2. 2022EuclidNet: Deep Visual Reasoning for Constructible Problems in Geometry
  3. 2026NoReGeo: Non-Reasoning Geometry Benchmark
  4. 2025Geoint-R1: Formalizing Multimodal Geometric Reasoning with Dynamic Auxiliary Constructions
  5. 2025DynaSolidGeo: A Dynamic Benchmark for Genuine Spatial Mathematical Reasoning of VLMs in Solid Geometry
  6. 2026Milestones over Outcome: Unlocking Geometric Reasoning with Sub-Goal Verifiable Reward
  7. 2026VeriGeo: Controllable Geometry Question Generation with Numerical and Analytical Verification
  8. 2026Dense Neuro-Symbolic Reasoning in a Unified Geometry State