Visual Programmability: A Guide for Code-as-Thought in Chart
  Understanding
Authors: name: Bohao Tang, name: Yan Ma, name: Fei Zhang, name: Jiadi Su, name: Ethan Chern, name: Zhulin Hu, name: Zhixin Wang, name: Pengfei Liu, name: Ya Zhang

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.