# Visual Programmability: A Guide for Code-as-Thought in Chart Understanding

arXiv: https://arxiv.org/abs/2509.09286 · HTML: https://mlsanity.com/paper/2509.09286/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 35 of its 68 references that are in the map.
- First posted on arXiv 11 Sep 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 35)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [ChartQA: A Benchmark for Question Answering about Charts with Visual and Logical Reasoning](https://mlsanity.com/paper/2203.10244/) (2022)
- [Multimodal Chain-of-Thought Reasoning in Language Models](https://mlsanity.com/paper/2302.00923/) (2023)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [DeeBERT: Dynamic Early Exiting for Accelerating BERT Inference](https://mlsanity.com/paper/2004.12993/) (2020)
- [MM-Eureka: Exploring the Frontiers of Multimodal Reasoning with Rule-based Reinforcement Learning](https://mlsanity.com/paper/2503.07365/) (2025)
- [TALM: Tool Augmented Language Models](https://mlsanity.com/paper/2205.12255/) (2022)
- [Conditional Computation in Neural Networks for faster models](https://mlsanity.com/paper/1511.06297/) (2015)
- [ChartLlama: A Multimodal LLM for Chart Understanding and Generation](https://mlsanity.com/paper/2311.16483/) (2023)
- [OpenThinkIMG: Learning to Think with Images via Visual Tool Reinforcement Learning](https://mlsanity.com/paper/2505.08617/) (2025)
- [DePlot: One-shot visual language reasoning by plot-to-table translation](https://mlsanity.com/paper/2212.10505/) (2022)
- [UniChart: A Universal Vision-language Pretrained Model for Chart Comprehension and Reasoning](https://mlsanity.com/paper/2305.14761/) (2023)
- [ChartMimic: Evaluating LMM's Cross-Modal Reasoning Capability via Chart-to-Code Generation](https://mlsanity.com/paper/2406.09961/) (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)
- [ChartCoder: Advancing Multimodal Large Language Model for Chart-to-Code Generation](https://mlsanity.com/paper/2501.06598/) (2025)
- [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)
- [PyVision: Agentic Vision with Dynamic Tooling](https://mlsanity.com/paper/2507.07998/) (2025)
- [Modular Visual Question Answering via Code Generation](https://mlsanity.com/paper/2306.05392/) (2023)
- [ChartMoE: Mixture of Diversely Aligned Expert Connector for Chart Understanding](https://mlsanity.com/paper/2409.03277/) (2024)
- [Point-RFT: Improving Multimodal Reasoning with Visually Grounded Reinforcement Finetuning](https://mlsanity.com/paper/2505.19702/) (2025)
- [Are Large Vision Language Models up to the Challenge of Chart Comprehension and Reasoning? An Extensive Investigation into the Capabilities and Limitations of LVLMs](https://mlsanity.com/paper/2406.00257/) (2024)
- [One RL to See Them All: Visual Triple Unified Reinforcement Learning](https://mlsanity.com/paper/2505.18129/) (2025)

## Built on by (most cited first, 4 of 4)

- [Group Pattern Selection Optimization: Let LRMs Pick the Right Pattern for Reasoning](https://mlsanity.com/paper/2601.07238/) (2026)
- [Learning More from Less: Exploiting Counterfactuals for Data-Efficient Chart Understanding](https://mlsanity.com/paper/2605.10855/) (2026)
- [What You See Is What You Get: Observation-Aligned Supervision for Chart-to-Code Generation](https://mlsanity.com/paper/2607.04726/) (2026)
- [Code as Representation: A Compilable Parsing Paradigm for Academic Documents](https://mlsanity.com/paper/2608.17550/) (2026)

## Abstract (arXiv)

Chart understanding presents a critical test to the reasoning capabilities of Vision-Language Models (VLMs). Prior approaches face critical limitations: some rely on external tools, making them brittle and constrained by a predefined toolkit, while others fine-tune specialist models that often adopt a single reasoning strategy, such as text-based chain-of-thought (CoT). The intermediate steps of text-based reasoning are difficult to verify, which complicates the use of reinforcement-learning signals that reward factual accuracy. To address this, we propose a Code-as-Thought (CaT) approach to represent the visual information of a chart in a verifiable, symbolic format. Our key insight is that this strategy must be adaptive: a fixed, code-only implementation consistently fails on complex charts where symbolic representation is unsuitable. This finding leads us to introduce Visual Programmability: a learnable property that determines if a chart-question pair is better solved with code or direct visual analysis. We implement this concept in an adaptive framework where a VLM learns to choose between the CaT pathway and a direct visual reasoning pathway. The selection policy of the model is trained with reinforcement learning using a novel dual-reward system. This system combines a data-accuracy reward to ground the model in facts and prevent numerical hallucination, with a decision reward that teaches the model when to use each strategy, preventing it from defaulting to a single reasoning mode. Experiments demonstrate strong and robust performance across diverse chart-understanding benchmarks. Our work shows that VLMs can be taught not only to reason but also how to reason, dynamically selecting the optimal reasoning pathway for each task.