Formal Verification of Deep Neural Networks

Deep neural networks are among the most successful artificial intelligence technologies making impact in a variety of practical applications. However, many concerns were raised about the `magical' power of these networks. It is disturbing that we are really lacking of understanding of the decision making process behind this technology. Therefore, a natural question is whether we can trust decisions that neural networks make. One way to address this issue is to define properties that we want a neural network to satisfy. Verifying whether a neural network fulfills these properties sheds light on the properties of the function that it represents. In this tutorial, we overview several approaches to verifying neural networks properties. The first set of methods encode neural networks into Integer Linear Programs or Satisfiability Modulo Theory formulas. They come up with domain-specific algorithms to solve verification problems. The second approach is to treat the neural network as a non-linear function and to use global optimization techniques for verification. The third line of work uses abstract interpretation to certify neural networks. Finally, we consider a special class of neural networks - Binarized Neural Networks - that can be represented and analyzed using Boolean Satisfiability. We discuss how we can take advantage of the structure of neural networks in the search procedure.