# Training Provably Robust Models by Polyhedral Envelope Regularization

arXiv: https://arxiv.org/abs/1912.04792 · HTML: https://mlsanity.com/paper/1912.04792/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2019.

## Built on by (most cited first, 6 of 6)

- [On the Robustness of Bayesian Neural Networks to Adversarial Attacks](https://mlsanity.com/paper/2207.06154/) (2022)
- [Adversarial Attacks and Defenses in Machine Learning-Powered Networks: A Contemporary Survey](https://mlsanity.com/paper/2303.06302/) (2023)
- [The Fundamental Limits of Interval Arithmetic for Neural Networks](https://mlsanity.com/paper/2112.05235/) (2021)
- [Learning Better Certified Models from Empirically-Robust Teachers](https://mlsanity.com/paper/2602.02626/) (2026)
- [Understanding Adversarial Robustness from Feature Maps of Convolutional Layers](https://mlsanity.com/paper/2202.12435/) (2022)
- [On Continuity of Robust and Accurate Classifiers](https://mlsanity.com/paper/2309.17048/) (2023)

## Abstract (arXiv)

Training certifiable neural networks enables one to obtain models with robustness guarantees against adversarial attacks. In this work, we introduce a framework to bound the adversary-free region in the neighborhood of the input data by a polyhedral envelope, which yields finer-grained certified robustness. We further introduce polyhedral envelope regularization (PER) to encourage larger polyhedral envelopes and thus improve the provable robustness of the models. We demonstrate the flexibility and effectiveness of our framework on standard benchmarks; it applies to networks of different architectures and general activation functions. Compared with the state-of-the-art methods, PER has very little computational overhead and better robustness guarantees without over-regularizing the model.