When Seeing Becomes Saying: Nonmonotonic Answer Dependence in Visual Chain-of-Thought

A numerical value can continue to influence a vision-language model after its written positions have been blocked. In visual chain-of-thought, separate and joint masks test answer dependence, while numerical substitutions and state transfer trace the value that remains influential. Individual masks miss joint dependencies on 51 of 119 Qwen and 73 of 119 InternVL TabMWP traces under blank-image continuation. Enlarging a mask can also restore an answer, with complete-answer controls showing how recovery changes across intervention operators. Replacing the source value while blocking all digit positions tests which number still reaches the answer. Across 800 controlled scenes, nonnumeric-state transfer favors the used replacement over its unused alternative by 3.56 points for Qwen and 0.94 for InternVL. Access to a written number and the influence of its value therefore require different tests. These findings motivate Gate, which chooses between retaining CoT computation and answering afresh. Gate improves over voting by 1.57 points across development benchmarks. On 600 new ChartQA images, frozen Gate reaches 85.00%, matching candidate scoring and improving over voting by 1.67 points.