Universal Approximation with Certified Networks
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Date
2020-04
Publication Type
Conference Paper
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yes
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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.
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published
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Publisher
International Conference on Learning Representations
Event
8th International Conference on Learning Representations (ICLR 2020) (virtual)
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Software
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Subject
Adversarial; Adversarial attacks; Interval bound propagation; Relu networks; Robustness; Universal approximation
Organisational unit
03948 - Vechev, Martin / Vechev, Martin
Notes
Due to the Coronavirus (COVID-19) the conference was conducted virtually.