A Robust Prototype-Based Network with Interpretable RBF Classifier Foundations

Prototype-based classification learning methods are known to be inherently interpretable. However, this paradigm suffers from major limitations compared to deep models, such as lower performance. This led to the development of the socalled deep Prototype-Based Networks (PBNs), also known as prototypical parts models. In this work, we analyze these models with respect to different properties, including interpretability. In particular, we focus on the Classification-by-Components (CBC) approach, which uses a probabilistic model to ensure interpretability and can be used as a shallow or deep architecture. We show that this model has several shortcomings, like creating contradicting explanations. Based on these findings, we propose an extension of CBC that solves these issues. Moreover, we prove that this extension has robustness guarantees and derive a loss that optimizes robustness. Additionally, our analysis shows that most (deep) PBNs are related to (deep) RBF classifiers, which implies that our robustness guarantees generalize to shallow RBF classifiers. The empirical evaluation demonstrates that our deep PBN yields state-of-the-art classification accuracy on different benchmarks while resolving the interpretability shortcomings of other approaches. Further, our shallow PBN variant outperforms other shallow PBNs while being inherently interpretable and exhibiting provable robustness guarantees. Backbone Latent Proto. Similarity Linear Layer Constraints Single Loss Main Contribution LeNet5 single yes RBF none no CNN with RBF head ProtoPNet* single yes* RBF (log) l 1 reg. no (deep) NN with prototype classification head CBC* Siamese* no RBF or ReLU-cosine probabilistic yes negative/positive/indefinite reasoning Hier. ProtoPNet single yes* RBF (log) l 1 reg. no hierarchical classification ProtoAttend* Siamese no relational attention none no attention for prototype selection ProtoTree single yes* RBF (soft) tree* yes tree upon similarities ProtoPShare single yes* RBF (log) l 1 reg. no prototype sharing between classes TesNet single yes* dot-product l 1 reg. no orthogonal prototypes