Inside VLM Chart Reading: Tracing Value Reading from Vertical Bar Charts Across Space and Depth

Vision--language models (VLMs) can answer chart questions accurately, but output accuracy does not show how they combine the evidence needed to recover an exact value. We study vertical-bar value reading with controlled counterfactual activation patching in Qwen2.5VL-7B-Instruct and InternVL3.5-8B. The study connects three analyses: (1) The single-factor results show that the changed bar-top region restores much more answer preference than the unchanged bar body, despite containing fewer visual tokens. Legend- and series-related states also lose local recoverability earlier than bar-geometry and axis-scale states. (2) In the handoff analysis, restoration shifts from visual legend regions in early layers to prompt-series positions in middle layers. Resetting the prompt-series state selectively reduces legend-source rescue, supporting its role as a partial mediator. (3) In the factorial analysis, both models can use geometry and scale states from separate donors to favor the combined target. InternVL performs similarly when the states come from separate donors or one image, while Qwen shows lower restoration for separate donors which suggests higher context sensitivity. Together, these results provide preliminary causal evidence for localizing the internal computations that support exact bar-value reading.