Quantization replaces floating point arithmetic with integer arithmetic in deep neural network models, providing more efficient on-device inference with less power and memory. In this work, we propose a framework for formally verifying the properties of quantized neural networks. Our baseline technique is based on integer linear programming which guarantees both soundness and completeness. We then show how efficiency can be improved by utilizing gradient-based heuristic search methods and also bound-propagation techniques. We evaluate our approach on perception networks quantized with PyTorch. Our results show that we can verify quantized networks with better scalability and efficiency than the previous state of the art.

The operation of trimming data sets is heavily used in AI systems. Trimming is useful to make AI systems more robust against adversarial or common perturbations. At the core of robust AI systems lies the concept that outliers in a data set occur with low probability, and therefore can be discarded with little loss of precision in the result. The statistical argument that formalizes this concept of robustness is based on an extension of the Chebyshev’s inequality first proposed by Tukey in 1960.