Universal Approximation with Certified Networks
arXiv:1909.13846
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 , there exists a network such that: (i) approximates arbitrarily close, and (ii) simple interval bound propagation of a region through yields a result that is arbitrarily close to the optimal output of on . 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.
arXiv commentICLR 2020
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