Two AI Models Supercharge Math Diagram Solving with Vision-to-Code Alignment

Systems capable of multimodal mathematical reasoning integrate text analysis and visual interpretation to tackle problems combining written descriptions with diagrams or figures. They merge language-processing modules with vision networks to interpret equations, shapes and annotations in complex contexts. Such technology supports applications in education—powering intelligent tutoring systems that guide students through geometry proofs—as well as in document analysis tools that must decode technical content containing both prose and graphics. Beyond geometry, these systems help analyze calculus graphs, probability charts and algebraic structures embedded in lecture slides or research articles.

One significant barrier lies in the insufficient mapping between mathematical illustrations and related text or symbolic notation. Existing multimodal collections typically use generic captions that omit fine-grained details like angle measures or segment labels. Common omissions include curvature labels, region shading and axis ticks. Systems trained on that data struggle with geometry drawings, technical schematics or function plots that demand exact visual reasoning and reliable linkage to algebraic expressions or step-by-step instructions.

Past solutions either improved visual encoders or assembled handcrafted datasets, but these methods produced limited image variety because they relied on fixed templates and manual designs. Efforts such as Math-LLaVA and MAVIS created synthetic data based on predefined categories, yet they could not generate diverse math visuals dynamically. They also lack variety in bar graphs and statistical plots. This limitation leaves models underprepared for tackling complex or unconventional problems that fall outside the scope of their training examples.

A research team at The Chinese University of Hong Kong’s Multimedia Laboratory and CPII under InnoHK introduced MathCoder-VL, a framework combining FigCodifier—a vision-to-code model—with a synthetic data engine. They created ImgCode-8.6M by iteratively generating and validating figures, producing the largest image-code dataset to date. In parallel, they released MM-MathInstruct-3M, a set of multimodal instructions matched with newly generated diagrams. MathCoder-VL undergoes mid-training on ImgCode-8.6M to learn visual-to-text alignment and then fine-tunes on MM-MathInstruct-3M to enhance reasoning performance. Their pipeline outputs both TikZ and Python renderings for format flexibility. Their database covers topics from basic topology to statistical analysis plots.

FigCodifier translates each math illustration into code that regenerates the figure precisely, ensuring exact alignment unlike caption-based approaches. The initial seed of 119,000 DaTikZ pairs expanded with diagrams from textbooks, K12 problems and arXiv papers. Python rendering complemented TikZ scripts, resulting in two balanced subsets of 4.3 million pairs each. A quality-control pipeline discards invalid code, duplicates and irrelevant samples, leaving a rich collection spanning arithmetic charts, geometric constructions, topology diagrams and three-dimensional plots. It introduces varied styles, including color schemes and line widths. It handles both matrix diagrams and circuit graphs.

Training proceeds in two steps. First, mid-training on ImgCode-8.6M teaches the model to bind visual input with symbolic output. Next, fine-tuning on MM-MathInstruct-3M reinforces reasoning skills by exposing the system to step-by-step multimodal instructions. Over several cycles, over two million new figure-code pairs were validated per round. On MathVista Geometry Problem Solving, the 8B-parameter MathCoder-VL achieves 73.6% accuracy, outpacing GPT-4o and Claude 3.5 Sonnet by 8.9% and 9.2%. The model registers 26.1% on MATH-Vision and 46.5% on MathVerse. These results underscore the benefit of high-quality synthetic datasets aligned with precise figure code.

On Chinese benchmarks, MathCoder-VL records 51.2% on GAOKAO-MM. In We-Math tests it solves two-step challenges at 58.6%, slightly ahead of GPT-4o’s 58.1%, and three-step tasks at 52.1%, compared with GPT-4o’s 43.6%. Relative to its base model InternVL2-8B, it posts gains of 6.1% on MATH-Vision and 11.6% on MathVista geometry items. Early tests on symbolic algebra benchmarks show notable accuracy gains. By addressing the lack of precise visual-text alignment with a code-driven data strategy, MathCoder-VL advances the state of the art in multimodal math reasoning.

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