Multimodal mathematical reasoning enables machines to solve problems involving textual information and visual components like diagrams and figures. This requires combining language understanding and visual interpretation to make sense of complex mathematical contexts. Such capabilities are vital in education, automated tutoring, and document analysis, where problems are often presented with a blend of text and images.
A major obstacle in this area is the lack of high-quality, precise alignment between math images and their textual or symbolic representations. Most datasets used to train large multimodal models are derived from image captions in natural settings, which often miss the detailed elements essential for mathematical accuracy. This creates problems for models that rely on these data sources, making them unreliable when dealing with geometry, figures, or technical diagrams. A model’s performance in mathematical reasoning depends heavily on its ability to correctly interpret and link these visual details with mathematical expressions or instructions.
In the past, some approaches tried to address this by either enhancing the visual encoders or using manually crafted datasets. However, these methods tend to produce low image diversity, relying on hand-coded or template-based generation, which limits their applicability. Some efforts, like Math-LLaVA and MAVIS, developed synthetic datasets and used templates or predefined categories. Still, they could not dynamically create a wide variety of math-related visuals. This shortfall restricts the learning scope of models and leaves them struggling with more complex or less structured mathematical problems.
Researchers from the Multimedia Laboratory at The Chinese University of Hong Kong and CPII under InnoHK introduced a novel approach called MathCoder-VL. This method combines a vision-to-code model named FigCodifier and a synthetic data engine. They constructed the ImgCode-8.6M dataset using a model-in-the-loop strategy, which allowed them to build the largest image-code dataset to date iteratively. Further, they developed MM-MathInstruct-3M, a multimodal instruction dataset enriched with newly synthesized images. The MathCoder-VL model is trained in two stages: mid-training on ImgCode-8.6M to improve visual-text alignment and fine-tuning on MM-MathInstruct-3M to strengthen reasoning abilities.
The FigCodifier model works by translating mathematical figures into code that can recreate those figures exactly. This code-image pairing ensures strict alignment and accuracy, unlike caption-based datasets. The process begins with 119K image-code pairs from DaTikZ and expands through iterative training using images collected from textbooks, K12 datasets, and arXiv papers. The final dataset includes 8.6 million code-image pairs and covers various mathematical topics. FigCodifier also supports Python-based rendering, which adds variety to image generation. The system filters low-quality data by checking code validity and removing redundant or unhelpful visuals, resulting in 4.3M high-quality TikZ and 4.3M Python-based pairs.
Performance evaluations show that MathCoder-VL outperforms multiple open-source models. The 8B version achieved 73.6% accuracy on the MathVista Geometry Problem Solving subset, surpassing GPT-4o and Claude 3.5 Sonnet by 8.9% and 9.2%, respectively. It also scored 26.1% on MATH-Vision and 46.5% on MathVerse. In Chinese-language benchmarks, it achieved 51.2% on GAOKAO-MM. On the We-Math benchmark, it solved two-step problems at 58.6%, outperforming GPT-4o’s 58.1%. Its performance on three-step problems reached 52.1%, again exceeding GPT-4o’s 43.6%. Compared to its base model InternVL2-8B, it showed gains of 6.1% on MATH-Vision and 11.6% on MathVista.
This work clearly defines the problem of insufficient visual-textual alignment in multimodal math reasoning and provides a scalable and innovative solution. The introduction of FigCodifier and synthetic datasets allows models to learn from accurate, diverse visuals paired with exact code, significantly boosting their reasoning abilities. MathCoder-VL represents a practical advancement in this field, demonstrating how thoughtful model design and high-quality data can overcome longstanding limitations in mathematical AI.
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Nikhil is an intern consultant at Marktechpost. He is pursuing an integrated dual degree in Materials at the Indian Institute of Technology, Kharagpur. Nikhil is an AI/ML enthusiast who is always researching applications in fields like biomaterials and biomedical science. With a strong background in Material Science, he is exploring new advancements and creating opportunities to contribute.
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