Training Provably Robust Models by Polyhedral Envelope Regularization

doi:10.1109/TNNLS.2021.3111892

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Training Provably Robust Models by Polyhedral Envelope Regularization

2023-06-01

Chen Liu *

Mathieu Salzmann

Sabine Süsstrunk

DOI：10.1109/TNNLS.2021.3111892

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Abstract

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Training certifiable neural networks enables us to obtain models with robustness guarantees against adversarial attacks. In this work, we introduce a framework to obtain a provable adversarial-free region in the neighborhood of the input data by a polyhedral envelope, which yields more fine-grained certified robustness than existing methods. We further introduce polyhedral envelope regularization (PER) to encourage larger adversarial-free regions 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 with general activation functions. Compared with state of the art, PER has negligible computational overhead; it achieves better robustness guarantees and accuracy on the clean data in various settings.

Keywords:

Robustness

Training

Predictive models

Computational modeling

Standards

Smoothing methods

Recurrent neural networks

Adversarial training

provable robustness