Beyond Points: Spherical Distributional Part Prototypes for Interpretable Classification
For interpretable classification, vMFProto improves explanation quality and robustness over point prototypes, addressing redundancy and instability in directional embedding spaces.
vMFProto models each class as a mixture of von Mises-Fisher components to capture intra-class variability, achieving state-of-the-art explanation quality (consistency, stability, distinctiveness) with competitive accuracy on CUB-200-2011, Stanford Dogs, and Stanford Cars.
Prototype-based neural networks aim to provide intrinsic interpretability by grounding predictions in a small set of part prototypes. However, modern vision backbones typically operate in normalized, directional embedding spaces where each semantic part exhibits substantial intra-class variability. As a result, point prototypes often become redundant or unstable, hurting both explanation quality and robustness. We propose vMFProto, a distributional part-prototype framework that models each class as a mixture of von Mises-Fisher components on the hypersphere. Each prototype learns its own concentration, capturing part-specific variability, and we use entropic optimal transport (OT) to obtain structured patch-to-prototype assignments. A two-stage training schedule performs OT-driven prototype discovery followed by end-to-end refinement with patch-level distillation and distribution-aware diversity regularization. Experiments on CUB-200-2011, Stanford Dogs, and Stanford Cars with frozen DINO backbones show that vMFProto achieves state-of-the-art explanation quality (consistency, stability, and distinctiveness) with competitive accuracy. Qualitative results confirm that vMFProto yields localized, non-redundant part evidence.