Universal Approximation with Certified NetworksDownload PDF

Published: 20 Dec 2019, Last Modified: 22 Oct 2023ICLR 2020 Conference Blind SubmissionReaders: Everyone
Keywords: adversarial robustness, universal approximation, certified network, interval bound propagation
TL;DR: We prove that for a large class of functions f there exists an interval certified robust network approximating f up to arbitrary precision.
Abstract: Training neural networks to be certifiably robust is critical to ensure their safety against adversarial attacks. However, it is currently very difficult to train a neural network that is both accurate and certifiably robust. In this work we take a step towards addressing this challenge. We prove that for every continuous function $f$, there exists a network $n$ such that: (i) $n$ approximates $f$ arbitrarily close, and (ii) simple interval bound propagation of a region $B$ through $n$ yields a result that is arbitrarily close to the optimal output of $f$ on $B$. Our result can be seen as a Universal Approximation Theorem for interval-certified ReLU networks. To the best of our knowledge, this is the first work to prove the existence of accurate, interval-certified networks.
Code: https://github.com/eth-sri/UniversalCertificationTheory
Community Implementations: [![CatalyzeX](/images/catalyzex_icon.svg) 1 code implementation](https://www.catalyzex.com/paper/arxiv:1909.13846/code)
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