EnergyMIL: Multiple Instance Learning as Strongly Convex Energy Minimization for Whole-Slide Image Classification

Multiple instance learning (MIL) is the dominant framework for whole slide image (WSI) classification, where each slide becomes a bag of thousands of patch features supervised only by a slide label. Contextual MIL enriches these features through interactions among patches. Current designs specify the operations that compute context, while the target representation remains implicit. Making that target explicit gives contextual aggregation a principled endpoint. We design EnergyMIL to assign each WSI a unique contextual state defined over the entire slide. First, factorized anchor coupling connects tissue evidence across thousands of patches with storage linear in bag size. Then, a strongly convex contextual energy defines the state, and proximal refinement approaches it through a memory efficient learning path. Finally, complementary focal and global readouts produce the slide prediction. Across four datasets, EnergyMIL ranks first outright in eleven of the twelve dataset by metric comparisons and ties for first in the remaining one. Together, the formulation and results show how a well defined contextual state can provide a stable and scalable basis for integrating heterogeneous tissue evidence in WSI classification.