Chain of Functions: A Programmatic Pipeline for Fine-Grained Chart Reasoning Data

Visual reasoning is crucial for multimodal large language models (MLLMs) to address complex chart queries, yet high-quality rationale data remains scarce. Existing methods leveraged (M)LLMs for data generation, but direct prompting often yields limited precision and diversity. In this paper, we propose textitChain of Functions (CoF), a novel programmatic reasoning data generation pipeline that utilizes freely-explored reasoning paths as supervision to ensure data precision and diversity. Specifically, it starts with human-free exploration among the atomic functions (e.g., maximum data and arithmetic operations) to generate diverse function chains, which are then translated into linguistic rationales and questions with only a moderate open-sourced LLM. textitCoF provides multiple benefits: 1) Precision: function-governed generation reduces hallucinations compared to freeform generation; 2) Diversity: enumerating function chains enables varied question taxonomies; 3) Explainability: function chains serve as built-in rationales, allowing fine-grained evaluation beyond overall accuracy; 4) Practicality: eliminating reliance on extremely large models. Employing textitCoF, we construct the textitChartCoF dataset, with 1.4k complex reasoning Q&A for fine-grained analysis and 50k Q&A for reasoning enhancement. The fine-grained evaluation on textitChartCoF reveals varying performance across question taxonomies for each MLLM, and the experiments also show that finetuning with textitChartCoF achieves state-of-the-art performance among same-scale MLLMs on widely used benchmarks. Furthermore, the novel paradigm of function-governed rationale generation in textitCoF could inspire broader applications beyond charts.