We present a novel method for scalable and precise certification of deep neural networks. The key technical insight behind our approach is a new abstract domain which combines floating point polyhedra with intervals and is equipped with abstract transformers specifically tailored to the domain of neural networks. Concretely, we introduce new transformers for the affine transform, the rectified linear unit (ReLU) activation, sigmoid, tanh, and maxpool functions.

We implemented our method in a system called DeepPoly and evaluated it extensively on a range of datasets, neural architectures, and specifications. Our experimental results indicate that DeepPoly is more precise than prior work while scaling to large networks. We also show how to combine DeepPoly with abstraction refinement in order to prove, for the first time, robustness of the given input (e.g., an image) to complex perturbations such as rotations.