# Deep-RBF Networks Revisited: Robust Classification with Rejection

arXiv: https://arxiv.org/abs/1812.03190 · HTML: https://mlsanity.com/paper/1812.03190/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2018.

## Built on by (most cited first, 10 of 10)

- [Two Coupled Rejection Metrics Can Tell Adversarial Examples Apart](https://mlsanity.com/paper/2105.14785/) (2021)
- [Survey on Leveraging Uncertainty Estimation Towards Trustworthy Deep Neural Networks: The Case of Reject Option and Post-training Processing](https://mlsanity.com/paper/2304.04906/) (2023)
- [Synaptic Plasticity Models and Bio-Inspired Unsupervised Deep Learning: A Survey](https://mlsanity.com/paper/2307.16236/) (2023)
- [Multi-Branch Deep Radial Basis Function Networks for Facial Emotion Recognition](https://mlsanity.com/paper/2109.03336/) (2021)
- [Variational Meta Reinforcement Learning for Social Robotics](https://mlsanity.com/paper/2206.03211/) (2022)
- [Deep-RBF Networks for Anomaly Detection in Automotive Cyber-Physical Systems](https://mlsanity.com/paper/2103.14172/) (2021)
- [Finite Gaussian Neurons: Defending against adversarial attacks by making neural networks say "I don't know"](https://mlsanity.com/paper/2306.07796/) (2023)
- [Introducing One Sided Margin Loss for Solving Classification Problems in Deep Networks](https://mlsanity.com/paper/2206.01002/) (2022)
- [Multi-layer Radial Basis Function Networks for Out-of-distribution Detection](https://mlsanity.com/paper/2501.02616/) (2025)
- [Radial Basis Function Networks as Projection Heads in Self-Supervised Learning](https://mlsanity.com/paper/2606.21590/) (2026)

## Abstract (arXiv)

One of the main drawbacks of deep neural networks, like many other classifiers, is their vulnerability to adversarial attacks. An important reason for their vulnerability is assigning high confidence to regions with few or even no feature points. By feature points, we mean a nonlinear transformation of the input space extracting a meaningful representation of the input data. On the other hand, deep-RBF networks assign high confidence only to the regions containing enough feature points, but they have been discounted due to the widely-held belief that they have the vanishing gradient problem. In this paper, we revisit the deep-RBF networks by first giving a general formulation for them, and then proposing a family of cost functions thereof inspired by metric learning. In the proposed deep-RBF learning algorithm, the vanishing gradient problem does not occur. We make these networks robust to adversarial attack by adding the reject option to their output layer. Through several experiments on the MNIST dataset, we demonstrate that our proposed method not only achieves significant classification accuracy but is also very resistant to various adversarial attacks.