TiltMIL: Learning Finite Statistics from Functional Bag Representations for Multiple Instance Learning

Multiple instance learning (MIL) predicts bag-level labels from multiple instances using only bag-level supervision and is widely applied to whole-slide image analysis in computational pathology. However, existing MIL methods typically compress an instance set directly into a finite-dimensional representation whose retained information form is predetermined by the representation mechanism, although different tasks may require different forms of compositional information. We propose TiltMIL, a Bag composition modeling framework based on finite cumulant-generating function (CGF) readouts. TiltMIL represents a bag as an empirical probability measure in a task-specific feature space, uses the CGF as a functional distributional representation, and learns task-relevant tilt locations to extract finite CGF function values and cumulant statistics for prediction. A lightweight hierarchical fusion mechanism combines these readouts, while empirical perturbation consistency improves stability to finite composition changes. Experiments on three WSI-MIL benchmarks with two feature encoders demonstrate consistent performance improvements across multiple pathology classification tasks.