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

arXiv: https://arxiv.org/abs/2410.17885 · HTML: https://mlsanity.com/paper/2410.17885/

## 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.

## 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, 24 of 24)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023)
- [How Far Are We to GPT-4V? Closing the Gap to Commercial Multimodal Models with Open-Source Suites](https://mlsanity.com/paper/2404.16821/) (2024)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [InternLM-XComposer: A Vision-Language Large Model for Advanced Text-image Comprehension and Composition](https://mlsanity.com/paper/2309.15112/) (2023)
- [Visual Sketchpad: Sketching as a Visual Chain of Thought for Multimodal Language Models](https://mlsanity.com/paper/2406.09403/) (2024)
- [G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model](https://mlsanity.com/paper/2312.11370/) (2023)
- [Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification](https://mlsanity.com/paper/2308.07921/) (2023)
- [UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression](https://mlsanity.com/paper/2212.02746/) (2022)
- [Math-LLaVA: Bootstrapping Mathematical Reasoning for Multimodal Large Language Models](https://mlsanity.com/paper/2406.17294/) (2024)
- [MAVIS: Mathematical Visual Instruction Tuning with an Automatic Data Engine](https://mlsanity.com/paper/2407.08739/) (2024)
- [GeomVerse: A Systematic Evaluation of Large Models for Geometric Reasoning](https://mlsanity.com/paper/2312.12241/) (2023)
- [Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solving](https://mlsanity.com/paper/2405.12205/) (2024)
- [MultiMath: Bridging Visual and Mathematical Reasoning for Large Language Models](https://mlsanity.com/paper/2409.00147/) (2024)
- [Math-PUMA: Progressive Upward Multimodal Alignment to Enhance Mathematical Reasoning](https://mlsanity.com/paper/2408.08640/) (2024)
- [RCOT: Detecting and Rectifying Factual Inconsistency in Reasoning by Reversing Chain-of-Thought](https://mlsanity.com/paper/2305.11499/) (2023)
- [Forward-Backward Reasoning in Large Language Models for Mathematical Verification](https://mlsanity.com/paper/2308.07758/) (2023)
- [Reversal of Thought: Enhancing Large Language Models with Preference-Guided Reverse Reasoning Warm-up](https://mlsanity.com/paper/2410.12323/) (2024)
- [Stepwise Self-Consistent Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2402.17786/) (2024)
- [BBA: Bi-Modal Behavioral Alignment for Reasoning with Large Vision-Language Models](https://mlsanity.com/paper/2402.13577/) (2024)
- [Look Before You Leap: Problem Elaboration Prompting Improves Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2402.15764/) (2024)

## Built on by (most cited first, 30 of 32)

- [MM-Eureka: Exploring the Frontiers of Multimodal Reasoning with Rule-based Reinforcement Learning](https://mlsanity.com/paper/2503.07365/) (2025)
- [Multimodal Chain-of-Thought Reasoning: A Comprehensive Survey](https://mlsanity.com/paper/2503.12605/) (2025)
- [Baichuan-Omni-1.5 Technical Report](https://mlsanity.com/paper/2501.15368/) (2025)
- [MINT-CoT: Enabling Interleaved Visual Tokens in Mathematical Chain-of-Thought Reasoning](https://mlsanity.com/paper/2506.05331/) (2025)
- [MathCoder-VL: Bridging Vision and Code for Enhanced Multimodal Mathematical Reasoning](https://mlsanity.com/paper/2505.10557/) (2025)
- [Dynamic Parallel Tree Search for Efficient LLM Reasoning](https://mlsanity.com/paper/2502.16235/) (2025)
- [MMR1: Enhancing Multimodal Reasoning with Variance-Aware Sampling and Open Resources](https://mlsanity.com/paper/2509.21268/) (2025)
- [MathCanvas: Intrinsic Visual Chain-of-Thought for Multimodal Mathematical Reasoning](https://mlsanity.com/paper/2510.14958/) (2025)
- [MM-PRM: Enhancing Multimodal Mathematical Reasoning with Scalable Step-Level Supervision](https://mlsanity.com/paper/2505.13427/) (2025)
- [KARL: Knowledge-Aware Reasoning and Reinforcement Learning for Knowledge-Intensive Visual Grounding](https://mlsanity.com/paper/2503.12797/) (2025)
- [Math Blind: Failures in Diagram Understanding Undermine Reasoning in MLLMs](https://mlsanity.com/paper/2503.20745/) (2025)
- [SynthRL: Scaling Visual Reasoning with Verifiable Data Synthesis](https://mlsanity.com/paper/2506.02096/) (2025)
- [Corvid: Improving Multimodal Large Language Models Towards Chain-of-Thought Reasoning](https://mlsanity.com/paper/2507.07424/) (2025)
- [NeSyGeo: A Neuro-Symbolic Framework for Multimodal Geometric Reasoning Data Generation](https://mlsanity.com/paper/2505.17121/) (2025)
- [SyncLoop: A Multimodal Dual-Loop Framework for Self-Improving Mathematical Reasoning](https://mlsanity.com/paper/2507.16518/) (2025)
- [VisuRiddles: Fine-grained Perception is a Primary Bottleneck for Multimodal Large Language Models in Abstract Visual Reasoning](https://mlsanity.com/paper/2506.02537/) (2025)
- [ThinkOmni: Lifting Textual Reasoning to Omni-modal Scenarios via Guidance Decoding](https://mlsanity.com/paper/2602.23306/) (2026)
- [Unveiling Chain of Step Reasoning for Vision-Language Models with Fine-grained Rewards](https://mlsanity.com/paper/2509.19003/) (2025)
- [YingSound: Video-Guided Sound Effects Generation with Multi-modal Chain-of-Thought Controls](https://mlsanity.com/paper/2412.09168/) (2024)
- [CogFlow: Bridging Perception and Reasoning through Knowledge Internalization for Visual Mathematical Problem Solving](https://mlsanity.com/paper/2601.01874/) (2026)
- [Can MLLMs Absorb Math Reasoning Abilities from LLMs as Free Lunch?](https://mlsanity.com/paper/2510.14387/) (2025)
- [Socratic-Geo: Synthetic Data Generation and Geometric Reasoning via Multi-Agent Interaction](https://mlsanity.com/paper/2602.03414/) (2026)
- [Oedipus and the Sphinx: Benchmarking and Improving Visual Language Models for Complex Graphic Reasoning](https://mlsanity.com/paper/2508.00323/) (2025)
- [From Perception to Reasoning: Deep Thinking Empowers Multimodal Large Language Models](https://mlsanity.com/paper/2511.12861/) (2025)
- [GeoChallenge: A Multi-Answer Multiple-Choice Benchmark for Geometric Reasoning with Diagrams](https://mlsanity.com/paper/2603.19252/) (2026)
- [GeoSym127K: Scalable Symbolically-verifiable Synthesis for Multimodal Geometric Reasoning](https://mlsanity.com/paper/2605.16371/) (2026)
- [FormalAnalyticGeo: A Neural-Symbolic Based Framework for Multimodal Analytic Geometry Problem Generation](https://mlsanity.com/paper/2607.12982/) (2026)
- [Failure-Informed Image Self-Augmentation for Multimodal Large Language Model Self-Improvement](https://mlsanity.com/paper/2608.03733/) (2026)
- [MAGMA-Edu: Multi-Agent Generative Multimodal Framework for Text-Diagram Educational Question Generation](https://mlsanity.com/paper/2511.18714/) (2025)
- [R1-SyntheticVL: Is Synthetic Data from Generative Models Ready for Multimodal Large Language Model?](https://mlsanity.com/paper/2602.03300/) (2026)

## 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.