Interval Universal Approximation for Neural Networks

Understand

To verify safety and robustness of neural networks, researchers have successfully applied abstract interpretation, primarily using the interval abstract domain.

• In this paper, we study the theoretical power and limits of the interval domain for neural-network verification.
• First, we introduce the interval universal approximation (IUA) theorem.
• IUA shows that neural networks not only can approximate any continuous function $f$ (universal approximation) as we have known for decades, but we can find a neural network, using any well-behaved activation function, whose interval bounds are an arbitrarily close approximation of the set semantics of $f$ (the result of applying $f$ to a set of inputs).