Optimization and Abstraction: A Synergistic Approach for Analyzing Neural Network Robustness

Greg Anderson, Shankara Pailoor, Isil Dillig, Swarat Chaudhuri

Abstract:

In recent years, the notion of local robustness (or robustness
for short) has emerged as a desirable property of deep neural
networks. Intuitively, robustness means that small perturba-
tions to an input do not cause the network to perform misclas-
sifications. In this paper, we present a novel algorithm for ver-
ifying robustness properties of neural networks. Our method
synergistically combines gradient-based optimization meth-
ods for counterexample search with abstraction-based proof
search to obtain a sound and (δ -)complete decision proce-
dure. Our method also employs a data-driven approach to
learn a verification policy that guides abstract interpretation
during proof search. We have implemented the proposed
approach in a tool called Charon and experimentally evalu-
ated it on hundreds of benchmarks. Our experiments show
that the proposed approach significantly outperforms three
state-of-the-art tools, namely AI2, Reluplex, and Reluval.