Hierarchical Cross-Class Part Alignment for Prototypical Part Networks via Hyperbolic Entailment

In fine-grained image recognition, semantic parts (e.g., wings, head) recur across classes while discriminative cues lie in within-part features (e.g., yellow wings, striped wings). The prototypical part network (ProtoPNet) is an interpretable model that provides case-based explanations for image recognition by measuring similarities between local patches in an images and their closest prototypes representing patches in a training set. However, existing ProtoPNet variants do not explicitly model this two-level structure, causing prototypes for the same anatomical part to fragment across classes. We propose a hierarchical prototype learning framework that separates shared prototypes capturing cross-class part concepts from class-specific prototypes capturing intra-part features. To model this hierarchy geometrically, prototypes are embedded in hyperbolic space and an entailment loss constrains each class-specific prototype to lie within the cone of its corresponding shared prototype. To prevent degenerate trivial solutions such as redundant prototypes, we introduce a patch-level contrastive learning using pseudo patch IDs from a vision foundation model, used only at training time, leaving the backbone choice free at inference. Unlike prior hyperbolic prototype methods where prototype hierarchies are uncontrolled, our framework defines explicit shared part to intra-part feature correspondences. Across four ProtoPNet variants and four backbones on CUB-200-2011 and Stanford Cars, our method improves classification accuracy by up to 10 points, raises hierarchical part hierarchy IoU from 11\% to 75\%, and consistently improves four interpretability metrics on CUB-200-2011.