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

arXiv: https://arxiv.org/abs/2503.16260 · HTML: https://mlsanity.com/paper/2503.16260/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 31 of its 54 references that are in the map.
- First posted on arXiv 20 Mar 2025.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)
- Multimodal LLMs / vision-language models / [Chart understanding and anomaly detection](https://mlsanity.com/mllm/chart-understanding-and-anomaly-detection/)

## Builds on (most cited first, 30 of 31)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023)
- [Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling](https://mlsanity.com/paper/2412.05271/) (2024)
- [A Survey on Multimodal Large Language Models](https://mlsanity.com/paper/2306.13549/) (2023)
- [DeepSeek-VL: Towards Real-World Vision-Language Understanding](https://mlsanity.com/paper/2403.05525/) (2024)
- [DeepSeek-VL2: Mixture-of-Experts Vision-Language Models for Advanced Multimodal Understanding](https://mlsanity.com/paper/2412.10302/) (2024)
- [CogVLM2: Visual Language Models for Image and Video Understanding](https://mlsanity.com/paper/2408.16500/) (2024)
- [InternLM-XComposer-2.5: A Versatile Large Vision Language Model Supporting Long-Contextual Input and Output](https://mlsanity.com/paper/2407.03320/) (2024)
- [ChartLlama: A Multimodal LLM for Chart Understanding and Generation](https://mlsanity.com/paper/2311.16483/) (2023)
- [Improve Vision Language Model Chain-of-thought Reasoning](https://mlsanity.com/paper/2410.16198/) (2024)
- [ChartX & ChartVLM: A Versatile Benchmark and Foundation Model for Complicated Chart Reasoning](https://mlsanity.com/paper/2402.12185/) (2024)
- [ChartBench: A Benchmark for Complex Visual Reasoning in Charts](https://mlsanity.com/paper/2312.15915/) (2023)
- [Insight-V: Exploring Long-Chain Visual Reasoning with Multimodal Large Language Models](https://mlsanity.com/paper/2411.14432/) (2024)
- [ChartAssisstant: A Universal Chart Multimodal Language Model via Chart-to-Table Pre-training and Multitask Instruction Tuning](https://mlsanity.com/paper/2401.02384/) (2024)
- [ChartGemma: Visual Instruction-tuning for Chart Reasoning in the Wild](https://mlsanity.com/paper/2407.04172/) (2024)
- [ChartInstruct: Instruction Tuning for Chart Comprehension and Reasoning](https://mlsanity.com/paper/2403.09028/) (2024)
- [TinyChart: Efficient Chart Understanding with Visual Token Merging and Program-of-Thoughts Learning](https://mlsanity.com/paper/2404.16635/) (2024)
- [ChartMoE: Mixture of Diversely Aligned Expert Connector for Chart Understanding](https://mlsanity.com/paper/2409.03277/) (2024)
- [EvoChart: A Benchmark and a Self-Training Approach Towards Real-World Chart Understanding](https://mlsanity.com/paper/2409.01577/) (2024)
- [Distill Visual Chart Reasoning Ability from LLMs to MLLMs](https://mlsanity.com/paper/2410.18798/) (2024)
- [On Pre-training of Multimodal Language Models Customized for Chart Understanding](https://mlsanity.com/paper/2407.14506/) (2024)
- [DOMINO: A Dual-System for Multi-step Visual Language Reasoning](https://mlsanity.com/paper/2310.02804/) (2023)

## Built on by (most cited first, 2 of 2)

- [PixelCraft: A Multi-Agent System for High-Fidelity Visual Reasoning on Structured Images](https://mlsanity.com/paper/2509.25185/) (2025)
- [Chart Specification: Structural Representations for Incentivizing VLM Reasoning in Chart-to-Code Generation](https://mlsanity.com/paper/2602.10880/) (2026)

## Abstract (arXiv)

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.