Developers of machine learning applications often apply post-training neural network optimizations, such as quantization and pruning, that approximate a neural network to speed up inference and reduce energy consumption, while maintaining high accuracy and robustness.

Despite a recent surge in techniques for the robustness verification of neural networks, a major limitation of almost all state-of-the-art approaches is that the verification needs to be run from scratch every time the network is even slightly modified. Running precise end-to-end verification from scratch for every new network is expensive and impractical in many scenarios that use or compare multiple approximate network versions, and the robustness of all the networks needs to be verified efficiently.

We present FANC, the first general technique for transferring proofs between a given network and its multiple approximate versions without compromising verifier precision. To reuse the proofs obtained when verifying the original network, FANC generates a set of templates – connected symbolic shapes at intermediate layers of the original network – that capture the proof of the property to be verified. We present novel algorithms for generating and transforming templates that generalize to a broad range of approximate networks and reduce the verification cost.

We present a comprehensive evaluation demonstrating the effectiveness of our approach. We consider a diverse set of networks obtained by applying popular approximation techniques such as quantization and pruning on fully-connected and convolutional architectures and verify their robustness against different adversarial attacks such as adversarial patches, L0, rotation and brightening. Our results indicate that FANC can significantly speed up verification with state-of-the-art verifier, DeepZ by up to 4.1x.