# MathFlow: Enhancing the Perceptual Flow of MLLMs for Visual Mathematical Problems

arXiv: https://arxiv.org/abs/2503.16549 · HTML: https://mlsanity.com/paper/2503.16549/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in VLM benchmarks and visual reasoning, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 72 of its 102 references that are in the map.
- First posted on arXiv 19 Mar 2025.

## Placed in

- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 30 of 72)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Flamingo: a Visual Language Model for Few-Shot Learning](https://mlsanity.com/paper/2204.14198/) (2022)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling](https://mlsanity.com/paper/2412.05271/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [LLaMA-Adapter: Efficient Fine-tuning of Language Models with Zero-init Attention](https://mlsanity.com/paper/2303.16199/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [A Comprehensive Overview of Large Language Models](https://mlsanity.com/paper/2307.06435/) (2023)
- [MiniGPT-v2: large language model as a unified interface for vision-language multi-task learning](https://mlsanity.com/paper/2310.09478/) (2023)
- [LLaMA-Adapter V2: Parameter-Efficient Visual Instruction Model](https://mlsanity.com/paper/2304.15010/) (2023)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [LLaVA-NeXT-Interleave: Tackling Multi-image, Video, and 3D in Large Multimodal Models](https://mlsanity.com/paper/2407.07895/) (2024)
- [OpenFlamingo: An Open-Source Framework for Training Large Autoregressive Vision-Language Models](https://mlsanity.com/paper/2308.01390/) (2023)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [LLaVA-CoT: Let Vision Language Models Reason Step-by-Step](https://mlsanity.com/paper/2411.10440/) (2024)
- [InternLM-XComposer2: Mastering Free-form Text-Image Composition and Comprehension in Vision-Language Large Model](https://mlsanity.com/paper/2401.16420/) (2024)
- [SPHINX: The Joint Mixing of Weights, Tasks, and Visual Embeddings for Multi-modal Large Language Models](https://mlsanity.com/paper/2311.07575/) (2023)
- [We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?](https://mlsanity.com/paper/2407.01284/) (2024)

## Built on by (most cited first, 10 of 10)

- [Perception, Reason, Think, and Plan: A Survey on Large Multimodal Reasoning Models](https://mlsanity.com/paper/2505.04921/) (2025)
- [MathCanvas: Intrinsic Visual Chain-of-Thought for Multimodal Mathematical Reasoning](https://mlsanity.com/paper/2510.14958/) (2025)
- [VL-Cogito: Progressive Curriculum Reinforcement Learning for Advanced Multimodal Reasoning](https://mlsanity.com/paper/2507.22607/) (2025)
- [GeoSense: Evaluating Identification and Application of Geometric Principles in Multimodal Reasoning](https://mlsanity.com/paper/2504.12597/) (2025)
- [CogFlow: Bridging Perception and Reasoning through Knowledge Internalization for Visual Mathematical Problem Solving](https://mlsanity.com/paper/2601.01874/) (2026)
- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)
- [VidVec: Unlocking Video MLLM Embeddings for Video-Text Retrieval](https://mlsanity.com/paper/2602.08099/) (2026)
- [MathSight: A Benchmark Exploring Have Vision-Language Models Really Seen in University-Level Mathematical Reasoning?](https://mlsanity.com/paper/2511.23112/) (2025)
- [A Survey of Multimodal Mathematical Reasoning: From Perception, Alignment to Reasoning](https://mlsanity.com/paper/2603.08291/) (2026)
- [Seeing and Solving Are Not Enough for Vision-Language Models](https://mlsanity.com/paper/2609.33694/) (2026)

## Abstract (arXiv)

Despite strong results on many tasks, multimodal large language models (MLLMs) still underperform on visual mathematical problem solving, especially in reliably perceiving and interpreting diagrams. Inspired by human problem-solving, we hypothesize that the ability to extract meaningful information from diagrams is pivotal, as it directly conditions subsequent inference. Hence, we introduce FlowVerse, a comprehensive benchmark that provides a fine-grained evaluation of MLLMs' perception and reasoning capabilities. Our preliminary results on FlowVerse reveal that existing MLLMs exhibit substantial limitations when extracting essential information and reasoned properties from diagrams and performing complex reasoning based on these visual inputs. In response, we introduce MathFlow, a modular problem-solving pipeline that decouples perception and inference into distinct stages, thereby optimizing each independently. Given the perceptual limitations observed in current MLLMs, we trained MathFlow-P-7B as a dedicated perception model. Experimental results indicate that MathFlow-P-7B yields substantial performance gains when integrated with various closed-source and open-source inference models. This demonstrates the effectiveness of the MathFlow pipeline and its compatibility with diverse inference frameworks. Project page: https://github.com/MathFlow-zju/MathFlow.