# A Robust Prototype-Based Network with Interpretable RBF Classifier Foundations

arXiv: https://arxiv.org/abs/2412.15499 · HTML: https://mlsanity.com/paper/2412.15499/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 42 references that are in the map.
- First posted on arXiv 20 Dec 2024.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem](https://mlsanity.com/paper/1812.05720/) (2018)
- [Neural Prototype Trees for Interpretable Fine-grained Image Recognition](https://mlsanity.com/paper/2012.02046/) (2020)
- [Interpretable Image Recognition with Hierarchical Prototypes](https://mlsanity.com/paper/1906.10651/) (2019)
- [This Looks Like That... Does it? Shortcomings of Latent Space Prototype Interpretability in Deep Networks](https://mlsanity.com/paper/2105.02968/) (2021)
- [Interpretable Image Classification with Adaptive Prototype-based Vision Transformers](https://mlsanity.com/paper/2410.20722/) (2024)
- [LucidPPN: Unambiguous Prototypical Parts Network for User-centric Interpretable Computer Vision](https://mlsanity.com/paper/2405.14331/) (2024)
- [Generalizing the Convolution Operator in Convolutional Neural Networks](https://mlsanity.com/paper/1707.09864/) (2017)
- [What if Neural Networks had SVDs?](https://mlsanity.com/paper/2009.13977/) (2020)

## Built on by (most cited first, 2 of 2)

- [Geodesic Prototype Matching via Diffusion Maps for Interpretable Fine-Grained Recognition](https://mlsanity.com/paper/2509.17050/) (2025)
- [This Looks Distinctly Like That: Grounding Interpretable Recognition in Stiefel Geometry against Neural Collapse](https://mlsanity.com/paper/2603.08374/) (2026)

## Abstract (arXiv)

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.