mlsanityData to 14 Oct 2026

Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning

arXiv 2105.04165 ↗First posted 10 May 2021cs.CL cs.AI cs.CVcited by 383

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Cited by 200 in LLM reasoning, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either small in scale or not publicly available. Thus, we construct a new large-scale benchmark, Geometry3K, consisting of 3,002 geometry problems with dense annotation in formal language. We further propose a novel geometry solving approach with formal language and symbolic reasoning, called Interpretable Geometry Problem Solver (Inter-GPS). Inter-GPS first parses the problem text and diagram into formal language automatically via rule-based text parsing and neural object detecting, respectively. Unlike implicit learning in existing methods, Inter-GPS incorporates theorem knowledge as conditional rules and performs symbolic reasoning step by step. Also, a theorem predictor is designed to infer the theorem application sequence fed to the symbolic solver for the more efficient and reasonable searching path. Extensive experiments on the Geometry3K and GEOS datasets demonstrate that Inter-GPS achieves significant improvements over existing methods. The project with code and data is available at https://lupantech.github.io/inter-gps.

Key facts. Cited by 383 papers in the map (data through 14 Oct 2026). Builds on 17 of its 52 references that are in the map. First posted on arXiv 10 May 2021.

Builds on

17 of 52 references.

References · 17

  1. 2017Attention Is All You Needcited by 60,361
  2. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  3. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,399
  4. 2019BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehensioncited by 5,893
  5. 2014Sequence to Sequence Learning with Neural Networkscited by 2,986
  6. 2017FiLM: Visual Reasoning with a General Conditioning Layercited by 2,333
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  8. 2019MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalismscited by 662
  9. 2018Translating a Math Word Problem to an Expression Treecited by 57
  10. 2019Graph Representations for Higher-Order Logic and Theorem Provingcited by 55
  11. 2017Deep Network Guided Proof Searchcited by 47
  12. 2017Mapping to Declarative Knowledge for Word Problem Solvingcited by 36
5 more
  1. 2020Semantically-Aligned Universal Tree-Structured Solver for Math Word Problemscited by 35
  2. 2016Unit Dependency Graph and its Application to Arithmetic Word Problem Solvingcited by 25
  3. 2020Learning by Fixing: Solving Math Word Problems with Weak Supervisioncited by 25
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 3; 2022: 11; 2023: 15; 2024: 90; 2025: 139; 2026: 125.

383 papers.

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  1. 2024LLaVA-OneVision: Easy Visual Task Transfercited by 2,719
  2. 2022Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answeringcited by 1,919
  3. 2024Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phonecited by 1,917
  4. 2025InternVL3: Exploring Advanced Training and Test-Time Recipes for Open-Source Multimodal Modelscited by 1,834
  5. 2023MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contextscited by 1,614
  6. 2024Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scalingcited by 1,599
  7. 2024OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problemscited by 1,136
  8. 2024How Far Are We to GPT-4V? Closing the Gap to Commercial Multimodal Models with Open-Source Suitescited by 1,050
  9. 2025Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?cited by 982
  10. 2024Cambrian-1: A Fully Open, Vision-Centric Exploration of Multimodal LLMscited by 838
  11. 2025Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Modelscited by 665
  12. 2024MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?cited by 586
38 more
  1. 2023Chameleon: Plug-and-Play Compositional Reasoning with Large Language Modelscited by 356
  2. 2022Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoningcited by 350
  3. 2024InternLM-XComposer2: Mastering Free-form Text-Image Composition and Comprehension in Vision-Language Large Modelcited by 326
  4. 2024What matters when building vision-language models?cited by 326
  5. 2025MM-Eureka: Exploring the Frontiers of Multimodal Reasoning with Rule-based Reinforcement Learningcited by 303
  6. 2024We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?cited by 286
  7. 2024Large Language Models for Mathematical Reasoning: Progresses and Challengescited by 284
  8. 2024Visual Sketchpad: Sketching as a Visual Chain of Thought for Multimodal Language Modelscited by 268
  9. 2021IconQA: A New Benchmark for Abstract Diagram Understanding and Visual Language Reasoningcited by 267
  10. 2023SciBench: Evaluating College-Level Scientific Problem-Solving Abilities of Large Language Modelscited by 256
  11. 2025LMM-R1: Empowering 3B LMMs with Strong Reasoning Abilities Through Two-Stage Rule-Based RLcited by 248
  12. 2024Enhancing the Reasoning Ability of Multimodal Large Language Models via Mixed Preference Optimizationcited by 239
  13. 2024CogVLM2: Visual Language Models for Image and Video Understandingcited by 217
  14. 2023G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Modelcited by 210
  15. 2024InternLM-XComposer-2.5: A Versatile Large Vision Language Model Supporting Long-Contextual Input and Outputcited by 195
  16. 2023TheoremQA: A Theorem-driven Question Answering datasetcited by 192
  17. 2024Large Language Models for Education: A Survey and Outlookcited by 188
  18. 2024MuirBench: A Comprehensive Benchmark for Robust Multi-image Understandingcited by 188
  19. 2024Mulberry: Empowering MLLM with o1-like Reasoning and Reflection via Collective Monte Carlo Tree Searchcited by 175
  20. 2024Building and better understanding vision-language models: insights and future directionscited by 173
  21. 2024InternLM-XComposer2-4KHD: A Pioneering Large Vision-Language Model Handling Resolutions from 336 Pixels to 4K HDcited by 159
  22. 2024DynaMath: A Dynamic Visual Benchmark for Evaluating Mathematical Reasoning Robustness of Vision Language Modelscited by 146
  23. 2025SoTA with Less: MCTS-Guided Sample Selection for Data-Efficient Visual Reasoning Self-Improvementcited by 145
  24. 2025VisualPRM: An Effective Process Reward Model for Multimodal Reasoningcited by 139
  25. 2022UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expressioncited by 137
  26. 2024Math-LLaVA: Bootstrapping Mathematical Reasoning for Multimodal Large Language Modelscited by 133
  27. 2024SPHINX-X: Scaling Data and Parameters for a Family of Multi-modal Large Language Modelscited by 131
  28. 2024MAmmoTH-VL: Eliciting Multimodal Reasoning with Instruction Tuning at Scalecited by 127
  29. 2024NVLM: Open Frontier-Class Multimodal LLMscited by 125
  30. 2022A Survey of Deep Learning for Mathematical Reasoningcited by 124
  31. 2024M3CoT: A Novel Benchmark for Multi-Domain Multi-step Multi-modal Chain-of-Thoughtcited by 121
  32. 2024MAVIS: Mathematical Visual Instruction Tuning with an Automatic Data Enginecited by 113
  33. 2025Geometric-Mean Policy Optimizationcited by 111
  34. 2023GeomVerse: A Systematic Evaluation of Large Models for Geometric Reasoningcited by 108
  35. 2025Reason-RFT: Reinforcement Fine-Tuning for Visual Reasoning of Vision Language Modelscited by 99
  36. 2025Perception-Aware Policy Optimization for Multimodal Reasoningcited by 99
  37. 2025Towards Scientific Intelligence: A Survey of LLM-based Scientific Agentscited by 98
  38. 2024A Comprehensive Survey of Scientific Large Language Models and Their Applications in Scientific Discoverycited by 96

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