HOMRS: High Order Metamorphic Relations Selector for Deep Neural Networks

Deep Neural Networks (DNN) applications are increasingly becoming a part of our everyday life, from medical applications to autonomous cars. Traditional validation of DNN relies on accuracy measures, however, the existence of adversarial examples has highlighted the limitations of these accuracy measures, raising concerns especially when DNN are integrated into safety-critical systems. In this paper, we present HOMRS, an approach to boost metamorphic testing by automatically building a small optimized set of high order metamorphic relations from an initial set of elementary metamorphic relations. HOMRS' backbone is a multi-objective search; it exploits ideas drawn from traditional systems testing such as code coverage, test case, and path diversity. We applied HOMRS to LeNet5 DNN with MNIST dataset and we report evidence that it builds a small but effective set of high order transformations achieving a 95% kill ratio. Five raters manually labeled a pool of images before and after high order transformation; Fleiss' Kappa and statistical tests confirmed that they are metamorphic properties. HOMRS built-in relations are also effective to confront adversarial or out-of-distribution examples; HOMRS detected 92% of randomly sampled out-of-distribution images. HOMRS transformations are also suitable for online real-time use.