Whole-slide multiple-instance learning (MIL) observes only the patches admitted by its selector. Deployment can alter this selector through compute limits, tissue masking, or regional workflows, even when the patch count is unchanged. We introduce BagShift, a paired protocol that changes the selector for the same case while holding its features and predictor fixed, thereby isolating selector response from case mix. With equal 128-patch budgets, sampling across the tissue or concentrating around one coordinate exposes markedly different evidence: on PANDA, the two views reduce quadratic weighted kappa by 1.57 and 17.96 points, respectively (QWK reported on the $\times100$ scale). On CAMELYON16, lesion annotations withheld from model development show that localized views retain tumor in only 10.0\% of micrometastatic observations, and matched exposure does not consistently recover the loss. The same fixed-count stressor produces a much smaller response on external lung subtyping, although differences in relative coverage make cross-task severity descriptive. When repeated localized observations are available, unioning their patches before one nonlinear MIL pass improves PANDA QWK by 7.87 points over averaging regional predictions. Patch count specifies computation, not observed evidence; deployment evaluations should report both what a selector preserves and how repeated observations are aggregated.
Each WSI slide contains thousands of candidate tissue patches, while supervision is usually available only at slide level. Existing bag-construction strategies like Uniform extraction and handcrafted heuristics do not control redundancy while attention-based multiple-instance models couple patch importance to a particular downstream classifier, and coreset methods optimise embedding-space coverage without modelling task-relevant patch quality. We introduce InfoDPP-PAC, a principled patch-selection framework that combines teacher-seeded Gaussian process relevance modelling, determinantal log-determinant diversity,submodular greedy optimisation, and a concentration-based adaptive stopping rule. The main theoretical result shows that the log-determinant diversity term used in DPP-style selection is the Gaussian process mutual information between a selected subset and the latent relevance function. We further derive a PAC-style certificate for residual information gain, allowing the number of retained patches to vary by slide rather than being fixed a priori. The empirical study evaluates whether the selected subset is diverse, spatially and morphologically covering, non-redundant, and enriched for the teacher-derived relevance signal. It does not claim end-to-end diagnostic improvement after retraining a downstream MIL model. On 202 HISTAI gastrointestinal whole-slide images, the adaptive rule uses 83.7% fewer patches on average than a fixed full budget while retaining 97.9% of full-budget composite selection quality. At a matched budget, InfoDPP-PAC achieves the highest mean teacher-derived relevance score among fourteen baselines, with diversity and composite scores close to the strongest coreset methods. The results support InfoDPP-PAC as a controlled quality-diversity-cardinality selection framework, rather than as a downstream clinical predictor.