mlsanityData to 14 Oct 2026

Theorem-Validated Reverse Chain-of-Thought Problem Generation for Geometric Reasoning

arXiv 2410.17885 ↗First posted 23 Oct 2024cs.AI cs.CVcited by 32

On the map: LLM reasoning → Spatial and embodied reasoning

also in 1 more
Abstract (arXiv)

Large Multimodal Models (LMMs) face limitations in geometric reasoning due to insufficient Chain of Thought (CoT) image-text training data. While existing approaches leverage template-based or LLM-assisted methods for geometric CoT data creation, they often face challenges in achieving both diversity and precision. To bridge this gap, we introduce a two-stage Theorem-Validated Reverse Chain-of-Thought Reasoning Synthesis (TR-CoT) framework. The first stage, TR-Engine, synthesizes theorem-grounded geometric diagrams with structured descriptions and properties. The second stage, TR-Reasoner, employs reverse reasoning to iteratively refine question-answer pairs by cross-validating geometric properties and description fragments. Our approach expands theorem-type coverage, corrects long-standing misunderstandings, and enhances geometric reasoning. Fine-grained CoT improves theorem understanding and increases logical consistency by 24.5%. Our best models surpass the baselines in MathVista and GeoQA by 10.1% and 4.7%, outperforming advanced closed-source models like GPT-4o.

Key facts. Cited by 32 papers in the map (data through 14 Oct 2026). Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning. Builds on 24 of its 45 references that are in the map. First posted on arXiv 23 Oct 2024.

Builds on

24 of 45 references.

Closest ancestors · 2

Same direction, newest first

  1. 2023GeomVerse: A Systematic Evaluation of Large Models for Geometric Reasoning19 Dec
  2. 2022UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression6 Dec

Other references · 22

  1. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,399
  2. 2024Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolutioncited by 4,234
  3. 2023Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyondcited by 2,224
  4. 2024How Far Are We to GPT-4V? Closing the Gap to Commercial Multimodal Models with Open-Source Suitescited by 1,050
  5. 2023Gemini: A Family of Highly Capable Multimodal Modelscited by 872
  6. 2021Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoningcited by 383
  7. 2022Large Language Models are Better Reasoners with Self-Verificationcited by 307
  8. 2023InternLM-XComposer: A Vision-Language Large Model for Advanced Text-image Comprehension and Compositioncited by 297
  9. 2024Visual Sketchpad: Sketching as a Visual Chain of Thought for Multimodal Language Modelscited by 268
  10. 2023G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Modelcited by 210
  11. 2023Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verificationcited by 166
  12. 2024Math-LLaVA: Bootstrapping Mathematical Reasoning for Multimodal Large Language Modelscited by 133
10 more
  1. 2024MAVIS: Mathematical Visual Instruction Tuning with an Automatic Data Enginecited by 113
  2. 2024Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solvingcited by 84
  3. 2024MultiMath: Bridging Visual and Mathematical Reasoning for Large Language Modelscited by 70
  4. 2024Math-PUMA: Progressive Upward Multimodal Alignment to Enhance Mathematical Reasoningcited by 52
  5. 2023RCOT: Detecting and Rectifying Factual Inconsistency in Reasoning by Reversing Chain-of-Thoughtcited by 47
  6. 2023Forward-Backward Reasoning in Large Language Models for Mathematical Verificationcited by 40
  7. 2024Reversal of Thought: Enhancing Large Language Models with Preference-Guided Reverse Reasoning Warm-upcited by 10
  8. 2024Stepwise Self-Consistent Mathematical Reasoning with Large Language Modelscited by 8
  9. 2024BBA: Bi-Modal Behavioral Alignment for Reasoning with Large Vision-Language Modelscited by 4
  10. 2024Look Before You Leap: Problem Elaboration Prompting Improves Mathematical Reasoning in Large Language Modelscited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 21; 2026: 10.

32 papers.

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  1. 2025MM-Eureka: Exploring the Frontiers of Multimodal Reasoning with Rule-based Reinforcement Learningcited by 303
  2. 2025Multimodal Chain-of-Thought Reasoning: A Comprehensive Surveycited by 182
  3. 2025Baichuan-Omni-1.5 Technical Reportcited by 111
  4. 2025MINT-CoT: Enabling Interleaved Visual Tokens in Mathematical Chain-of-Thought Reasoningcited by 49
  5. 2025MathCoder-VL: Bridging Vision and Code for Enhanced Multimodal Mathematical Reasoningcited by 45
  6. 2025Dynamic Parallel Tree Search for Efficient LLM Reasoningcited by 42
  7. 2025MMR1: Enhancing Multimodal Reasoning with Variance-Aware Sampling and Open Resourcescited by 39
  8. 2025MathCanvas: Intrinsic Visual Chain-of-Thought for Multimodal Mathematical Reasoningcited by 35
  9. 2025MM-PRM: Enhancing Multimodal Mathematical Reasoning with Scalable Step-Level Supervisioncited by 31
  10. 2025KARL: Knowledge-Aware Reasoning and Reinforcement Learning for Knowledge-Intensive Visual Groundingcited by 21
  11. 2025Math Blind: Failures in Diagram Understanding Undermine Reasoning in MLLMscited by 16
  12. 2025SynthRL: Scaling Visual Reasoning with Verifiable Data Synthesiscited by 12
20 more
  1. 2025Corvid: Improving Multimodal Large Language Models Towards Chain-of-Thought Reasoningcited by 11
  2. 2025NeSyGeo: A Neuro-Symbolic Framework for Multimodal Geometric Reasoning Data Generationcited by 10
  3. 2025SyncLoop: A Multimodal Dual-Loop Framework for Self-Improving Mathematical Reasoningcited by 8
  4. 2025VisuRiddles: Fine-grained Perception is a Primary Bottleneck for Multimodal Large Language Models in Abstract Visual Reasoningcited by 7
  5. 2026ThinkOmni: Lifting Textual Reasoning to Omni-modal Scenarios via Guidance Decodingcited by 7
  6. 2025Unveiling Chain of Step Reasoning for Vision-Language Models with Fine-grained Rewardscited by 6
  7. 2024YingSound: Video-Guided Sound Effects Generation with Multi-modal Chain-of-Thought Controlscited by 5
  8. 2026CogFlow: Bridging Perception and Reasoning through Knowledge Internalization for Visual Mathematical Problem Solvingcited by 5
  9. 2025Can MLLMs Absorb Math Reasoning Abilities from LLMs as Free Lunch?cited by 2
  10. 2026Socratic-Geo: Synthetic Data Generation and Geometric Reasoning via Multi-Agent Interactioncited by 2
  11. 2025Oedipus and the Sphinx: Benchmarking and Improving Visual Language Models for Complex Graphic Reasoningcited by 1
  12. 2025From Perception to Reasoning: Deep Thinking Empowers Multimodal Large Language Modelscited by 1
  13. 2026GeoChallenge: A Multi-Answer Multiple-Choice Benchmark for Geometric Reasoning with Diagramscited by 1
  14. 2026GeoSym127K: Scalable Symbolically-verifiable Synthesis for Multimodal Geometric Reasoningcited by 1
  15. 2026FormalAnalyticGeo: A Neural-Symbolic Based Framework for Multimodal Analytic Geometry Problem Generationcited by 1
  16. 2026Failure-Informed Image Self-Augmentation for Multimodal Large Language Model Self-Improvementcited by 1
  17. 2025MAGMA-Edu: Multi-Agent Generative Multimodal Framework for Text-Diagram Educational Question Generationcited by 0
  18. 2026R1-SyntheticVL: Is Synthetic Data from Generative Models Ready for Multimodal Large Language Model?cited by 0
  19. 2026VeriGeo: Controllable Geometry Question Generation with Numerical and Analytical Verificationcited by 0
  20. 2026MathVis-Fine: Aligning Visual Supervision with Necessity via Progressive Dependency-Guided Training for Multimodal Mathematical Reasoningcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Geoint-R1: Formalizing Multimodal Geometric Reasoning with Dynamic Auxiliary Constructions
  2. 2025GeoThought: A Dataset for Enhancing Mathematical Geometry Reasoning in Vision-Language Models
  3. 2025GeoBench: Rethinking Multimodal Geometric Problem-Solving via Hierarchical Evaluation
  4. 2026ChitraMiti: Benchmarking Visual Grounding and Modality Reliance in Bengali Geometric Reasoning
  5. 2025DynaSolidGeo: A Dynamic Benchmark for Genuine Spatial Mathematical Reasoning of VLMs in Solid Geometry
  6. 2026Concise Geometric Description as a Bridge: Unleashing the Potential of LLM for Plane Geometry Problem Solving
  7. 2025GeoFM: Enhancing Geometric Reasoning of MLLMs via Synthetic Data Generation through Formal Language
  8. 2026Diagnosing Sampled LLM Reasoning in Formal Geometry: Coverage, Realization, and Validity Evidence