Automated Synthesis of Certified Neural Networks

Neural networks find applications in many safety-critical systems that raise concerns about their deployment: Are we sure the network will never advise doing anything violating a set of safety constraints? Formal verification has been recently applied to prove whether an existing neural network is certified for some property (i.e., if it satisfies the property for all possible inputs) or not. Formal verification can prove that a network respects the property, but cannot fix a network that does not respect it. In this paper we focus on the automated synthesis of certified neural networks, that is, on how to automatically build a network that is guaranteed to respect some required properties. We exploit a Counter Example Guided Inductive Synthesis (CEGIS) loop that alternates Deep Learning, Formal Verification, and a novel data generation technique that augments the training data to synthesize certified networks in a fully automatic way. An application of a proof-of-concept implementation of the framework shows the feasibility of the approach.