# MINT-CoT: Enabling Interleaved Visual Tokens in Mathematical Chain-of-Thought Reasoning

arXiv: https://arxiv.org/abs/2506.05331 · HTML: https://mlsanity.com/paper/2506.05331/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 46 of its 86 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)

## Builds on (most cited first, 30 of 46)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [MiniGPT-4: Enhancing Vision-Language Understanding with Advanced Large Language Models](https://mlsanity.com/paper/2304.10592/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Video-MME: The First-Ever Comprehensive Evaluation Benchmark of Multi-modal LLMs in Video Analysis](https://mlsanity.com/paper/2405.21075/) (2024)
- [Chameleon: Mixed-Modal Early-Fusion Foundation Models](https://mlsanity.com/paper/2405.09818/) (2024)
- [Are We on the Right Way for Evaluating Large Vision-Language Models?](https://mlsanity.com/paper/2403.20330/) (2024)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [VideoChat: Chat-Centric Video Understanding](https://mlsanity.com/paper/2305.06355/) (2023)
- [Multimodal Chain-of-Thought Reasoning in Language Models](https://mlsanity.com/paper/2302.00923/) (2023)
- [LLaMA-Adapter V2: Parameter-Efficient Visual Instruction Model](https://mlsanity.com/paper/2304.15010/) (2023)
- [Seed1.5-VL Technical Report](https://mlsanity.com/paper/2505.07062/) (2025)
- [R1-Onevision: Advancing Generalized Multimodal Reasoning through Cross-Modal Formalization](https://mlsanity.com/paper/2503.10615/) (2025)
- [PointLLM: Empowering Large Language Models to Understand Point Clouds](https://mlsanity.com/paper/2308.16911/) (2023)
- [MM-Eureka: Exploring the Frontiers of Multimodal Reasoning with Rule-based Reinforcement Learning](https://mlsanity.com/paper/2503.07365/) (2025)
- [R1-VL: Learning to Reason with Multimodal Large Language Models via Step-wise Group Relative Policy Optimization](https://mlsanity.com/paper/2503.12937/) (2025)
- [Visual Sketchpad: Sketching as a Visual Chain of Thought for Multimodal Language Models](https://mlsanity.com/paper/2406.09403/) (2024)
- [Enhancing the Reasoning Ability of Multimodal Large Language Models via Mixed Preference Optimization](https://mlsanity.com/paper/2411.10442/) (2024)
- [G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model](https://mlsanity.com/paper/2312.11370/) (2023)
- [Imagine while Reasoning in Space: Multimodal Visualization-of-Thought](https://mlsanity.com/paper/2501.07542/) (2025)
- [Point-Bind & Point-LLM: Aligning Point Cloud with Multi-modality for 3D Understanding, Generation, and Instruction Following](https://mlsanity.com/paper/2309.00615/) (2023)
- [Mulberry: Empowering MLLM with o1-like Reasoning and Reflection via Collective Monte Carlo Tree Search](https://mlsanity.com/paper/2412.18319/) (2024)
- [T2I-R1: Reinforcing Image Generation with Collaborative Semantic-level and Token-level CoT](https://mlsanity.com/paper/2505.00703/) (2025)
- [WorldSense: Evaluating Real-world Omnimodal Understanding for Multimodal LLMs](https://mlsanity.com/paper/2502.04326/) (2025)
- [Math-LLaVA: Bootstrapping Mathematical Reasoning for Multimodal Large Language Models](https://mlsanity.com/paper/2406.17294/) (2024)
- [Can We Generate Images with CoT? Let's Verify and Reinforce Image Generation Step by Step](https://mlsanity.com/paper/2501.13926/) (2025)
- [VideoLLM: Modeling Video Sequence with Large Language Models](https://mlsanity.com/paper/2305.13292/) (2023)
- [Insight-V: Exploring Long-Chain Visual Reasoning with Multimodal Large Language Models](https://mlsanity.com/paper/2411.14432/) (2024)

## Built on by (most cited first, 30 of 49)

- [Monet: Reasoning in Latent Visual Space Beyond Images and Language](https://mlsanity.com/paper/2511.21395/) (2025)
- [Are Video Models Ready as Zero-Shot Reasoners? An Empirical Study with the MME-CoF Benchmark](https://mlsanity.com/paper/2510.26802/) (2025)
- [VisMem: Latent Vision Memory Unlocks Potential of Vision-Language Models](https://mlsanity.com/paper/2511.11007/) (2025)
- [MathCanvas: Intrinsic Visual Chain-of-Thought for Multimodal Mathematical Reasoning](https://mlsanity.com/paper/2510.14958/) (2025)
- [Video-Thinker: Sparking "Thinking with Videos" via Reinforcement Learning](https://mlsanity.com/paper/2510.23473/) (2025)
- [From Perception to Cognition: A Survey of Vision-Language Interactive Reasoning in Multimodal Large Language Models](https://mlsanity.com/paper/2509.25373/) (2025)
- [CodePlot-CoT: Mathematical Visual Reasoning by Thinking with Code-Driven Images](https://mlsanity.com/paper/2510.11718/) (2025)
- [Reasoning via Video: The First Evaluation of Video Models' Reasoning Abilities through Maze-Solving Tasks](https://mlsanity.com/paper/2511.15065/) (2025)
- [When Visualizing is the First Step to Reasoning: MIRA, a Benchmark for Visual Chain-of-Thought](https://mlsanity.com/paper/2511.02779/) (2025)
- [Perceptual-Evidence Anchored Reinforced Learning for Multimodal Reasoning](https://mlsanity.com/paper/2511.18437/) (2025)
- [Thinking-while-Generating: Interleaving Textual Reasoning throughout Visual Generation](https://mlsanity.com/paper/2511.16671/) (2025)
- [Generative Universal Verifier as Multimodal Meta-Reasoner](https://mlsanity.com/paper/2510.13804/) (2025)
- [CodeDance: A Dynamic Tool-integrated MLLM for Executable Visual Reasoning](https://mlsanity.com/paper/2512.17312/) (2025)
- [DraCo: Draft as CoT for Text-to-Image Preview and Rare Concept Generation](https://mlsanity.com/paper/2512.05112/) (2025)
- [Can World Models Benefit VLMs for World Dynamics?](https://mlsanity.com/paper/2510.00855/) (2025)
- [BLINK-Twice: You see, but do you observe? A Reasoning Benchmark on Visual Perception](https://mlsanity.com/paper/2510.09361/) (2025)
- [GSM8K-V: Can Vision Language Models Solve Grade School Math Word Problems in Visual Contexts](https://mlsanity.com/paper/2509.25160/) (2025)
- [Omni-R1: Towards the Unified Generative Paradigm for Multimodal Reasoning](https://mlsanity.com/paper/2601.09536/) (2026)
- [PatchCue: Enhancing Vision-Language Model Reasoning with Patch-Based Visual Cues](https://mlsanity.com/paper/2603.05869/) (2026)
- [TerraScope: Pixel-Grounded Visual Reasoning for Earth Observation](https://mlsanity.com/paper/2603.19039/) (2026)
- [Beyond Textual CoT: Interleaved Text-Image Chains with Deep Confidence Reasoning for Image Editing](https://mlsanity.com/paper/2510.08157/) (2025)
- [CrystaL: Spontaneous Emergence of Visual Latents in MLLMs](https://mlsanity.com/paper/2602.20980/) (2026)
- [TVI-CoT: Text-Visual Interleaved Chain-of-Thought Reasoning for Multimodal Understanding](https://mlsanity.com/paper/2606.08464/) (2026)
- [Aligning Perception, Reasoning, Modeling and Interaction: A Survey on Physical AI](https://mlsanity.com/paper/2510.04978/) (2025)
- [See Less, See Right: Bi-directional Perceptual Shaping For Multimodal Reasoning](https://mlsanity.com/paper/2512.22120/) (2025)
- [ATLAS: Agentic or Latent Visual Reasoning? One Word is Enough for Both](https://mlsanity.com/paper/2605.15198/) (2026)
- [Latent Visual States for Efficient Multimodal Reasoning](https://mlsanity.com/paper/2606.24233/) (2026)
- [OpenCoF: Learning to Reason Through Video Generation](https://mlsanity.com/paper/2607.08763/) (2026)
- [MorphoBench: A Benchmark with Difficulty Adaptive to Model Reasoning](https://mlsanity.com/paper/2510.14265/) (2025)
- [MM-CondChain: A Programmatically Verified Benchmark for Visually Grounded Deep Compositional Reasoning](https://mlsanity.com/paper/2603.12266/) (2026)

## Abstract (arXiv)

Chain-of-Thought (CoT) has widely enhanced mathematical reasoning in Large Language Models (LLMs), but it still remains challenging for extending it to multimodal domains. Existing works either adopt a similar textual reasoning for image input, or seek to interleave visual signals into mathematical CoT. However, they face three key limitations for math problem-solving: reliance on coarse-grained box-shaped image regions, limited perception of vision encoders on math content, and dependence on external capabilities for visual modification. In this paper, we propose MINT-CoT, introducing Mathematical INterleaved Tokens for Chain-of-Thought visual reasoning. MINT-CoT adaptively interleaves relevant visual tokens into textual reasoning steps via an Interleave Token, which dynamically selects visual regions of any shapes within math figures. To empower this capability, we construct the MINT-CoT dataset, containing 54K mathematical problems aligning each reasoning step with visual regions at the token level, accompanied by a rigorous data generation pipeline. We further present a three-stage MINT-CoT training strategy, progressively combining text-only CoT SFT, interleaved CoT SFT, and interleaved CoT RL, which derives our MINT-CoT-7B model. Extensive experiments demonstrate the effectiveness of our method for effective visual interleaved reasoning in mathematical domains, where MINT-CoT-7B outperforms the baseline model by +34.08% on MathVista, +28.78% on GeoQA, and +23.2% on MMStar, respectively. Our code and data are available at https://github.com/xinyan-cxy/MINT-CoT