Beyond Points: Spherical Distributional Part Prototypes for Interpretable Classification

2026-06-25

AI Summary

Existing point prototypes in normalized embedding spaces suffer from redundancy or instability due to high intra-class variability of semantic parts, degrading both explanation quality and robustness. This work proposes vMFProto, the first framework to incorporate spherical von Mises-Fisher (vMF) distributions into interpretable classification by modeling each class as a mixture of distributions on the hypersphere, enabling prototypes to adaptively learn concentration parameters that capture part-specific variability. Structured assignment of image patches to prototypes is achieved via entropy-regularized optimal transport, while a distribution-aware diversity regularizer enhances prototype discriminability. A two-stage training strategy facilitates effective prototype discovery followed by end-to-end optimization. Evaluated on CUB-200-2011, Stanford Dogs, and Cars, the method achieves state-of-the-art performance in explanation consistency, stability, and distinctiveness, while maintaining competitive classification accuracy.

Abstract

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.

Problem

• prototype-based interpretability
• intra-class variability
• directional embedding spaces
• redundant prototypes
• explanation quality

Innovation

• distributional prototypes
• von Mises-Fisher
• optimal transport
• interpretable classification
• hyperspherical embeddings