Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal Approximation with Certified Networks   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.

23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex