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A Robust Prototype-Based Network with Interpretable RBF Classifier Foundations

Sascha Saralajew, Ashish Rana, Thomas Villmann, Ammar Shaker

TL;DR

This work addresses the interpretability gap in prototype-based classification by analyzing deep prototype-based networks (PBNs) and their relation to RBF classifiers, highlighting interpretability and robustness limitations. It introduces a robust Classification-by-Components (CBC) extension that removes indefinite reasoning in favor of class-specific priors and probabilistic negative reasoning, accompanied by a proven robustness bound and a loss that optimizes robustness. The authors show that deep PBNs are closely tied to deep RBF heads, but suffer interpretability issues, while shallow CBC offers inherent interpretability and provable robustness; empirically, the deep CBC achieves state-of-the-art accuracy on benchmarks and the shallow CBC demonstrates robustness advantages. The work provides a practical pathway to interpretable, robust prototype-based classification with strong empirical performance and theoretical guarantees, while outlining future work on extending to non-image domains and refining training stability.

Abstract

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 so-called 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.

A Robust Prototype-Based Network with Interpretable RBF Classifier Foundations

TL;DR

This work addresses the interpretability gap in prototype-based classification by analyzing deep prototype-based networks (PBNs) and their relation to RBF classifiers, highlighting interpretability and robustness limitations. It introduces a robust Classification-by-Components (CBC) extension that removes indefinite reasoning in favor of class-specific priors and probabilistic negative reasoning, accompanied by a proven robustness bound and a loss that optimizes robustness. The authors show that deep PBNs are closely tied to deep RBF heads, but suffer interpretability issues, while shallow CBC offers inherent interpretability and provable robustness; empirically, the deep CBC achieves state-of-the-art accuracy on benchmarks and the shallow CBC demonstrates robustness advantages. The work provides a practical pathway to interpretable, robust prototype-based classification with strong empirical performance and theoretical guarantees, while outlining future work on extending to non-image domains and refining training stability.

Abstract

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 so-called 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.

Paper Structure

This paper contains 42 sections, 7 theorems, 80 equations, 16 figures, 8 tables.

Table of Contents

  1. Motivation and Context
  2. Review of Deep Prototype-based Networks
  3. Differences between the architectures and their relation to RBF networks.
  4. On the interpretability of deep PBNs.
  5. On the OOD detection properties.
  6. The role of negative reasoning.
  7. Classification-by-Components Networks
  8. Review of the original CBC method.
  9. Our extension of the original CBC method.
  10. Learning the parameters in CBC models.
  11. The proven robustness of the CBC architecture.
  12. The robustness with alternative distance functions.
  13. Final remarks.
  14. Experiments
  15. Interpretability and performance assessment: Comparison with PIPNet.
  16. ...and 27 more sections

Key Result

Theorem 1

The robustness of a correctly classified sample $\mathbf{x}$ with class label $y$ is lower bounded by when $A_{c'}\neq0$, where and $\kappa=\sigma_{min}=\min_{k}\sigma_{k}$.

Figures (16)

  • Figure 1: General architecture of deep PBNs.
  • Figure 2: Probability tree diagram of the original CBC with the changes we propose for our extension in the gray box.
  • Figure 3: Fish crow gets incorrectly classified as common raven by PIPNet because of the overemphasis of weights.
  • Figure 4: The comparative analysis of PIPNet and CBC for the vermilion flycatcher, where negative reasoning is used.
  • Figure 5: Margin value hyperparameter search for different backbone architectures.
  • ...and 11 more figures

Theorems & Definitions (11)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Lemma 4
  • proof
  • Theorem
  • proof
  • Theorem 5
  • proof
  • Theorem
  • ...and 1 more