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Intensive research has been conducted on the verification and validation ofdeep neural networks (DNNs), aiming to understand if, and how, DNNs can beapplied to safety critical applications. However, existing verification andvalidation techniques are limited by their scalability, over both the size ofthe DNN and the size of the dataset. In this paper, we propose a novelabstraction method which abstracts a DNN and a dataset into a Bayesian network(BN). We make use of dimensionality reduction techniques to identify hiddenfeatures that have been learned by hidden layers of the DNN, and associate eachhidden feature with a node of the BN. On this BN, we can conduct probabilisticinference to understand the behaviours of the DNN processing data. Moreimportantly, we can derive a runtime monitoring approach to detect inoperational time rare inputs and covariate shift of the input data. We can alsoadapt existing structural coverage-guided testing techniques (i.e., based onlow-level elements of the DNN such as neurons), in order to generate test casesthat better exercise hidden features. We implement and evaluate the BNabstraction technique using our DeepConcolic tool available athttps://github.com/TrustAI/DeepConcolic.

Abstraction and Symbolic Execution of Deep Neural Networks with Bayesian Approximation of Hidden Features