Visual Sufficiency Landscapes: Understanding Query-Conditioned Reliability in Visual Token Pruning

Different visual token pruning strategies retain different subsets while maintaining similar task performance. This motivates a combinatorial question: how many visual subsets can preserve model behavior, and how does their abundance depend on the query? We introduce visual sufficiency landscapes to characterize this abundance. At a fixed layer and budget, visual sufficiency probability is the fraction of uniformly sampled subsets that jointly preserve the dense model's answer, reference-answer likelihood, and output distribution. Independent sampling replicates separate input variation from estimation noise. Across Qwen2.5-VL-7B, InternVL2-8B, and LLaVA-v1.5-7B, differences between inputs on GQA and TextVQA exceed replication error, and different questions about the same GQA image produce distinct landscapes. Sufficiency probability also improves failure prediction for full pruning methods. On LLaVA, adding this probability increases AUC by 0.1151 for FastV, 0.0683 for VisionZip, and 0.1401 for SparseVLM, while reducing log loss and Brier score. Several architecture-adapted configurations on the other two models reproduce these gains. Under controlled selection rules, predictors trained on the original images reduce log loss on new images by 9.0%, 13.0%, and 14.1%, respectively. These results establish successful-subset abundance as a measurable dimension of local prunability and connect it to the identification of high-risk pruning conditions.