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Verifying and explaining the behavior of neural networks is becomingincreasingly important, especially when they are deployed in safety-criticalapplications. In this paper, we study verification problems for BinarizedNeural Networks (BNNs), the 1-bit quantization of general real-numbered neuralnetworks. Our approach is to encode BNNs into Binary Decision Diagrams (BDDs),which is done by exploiting the internal structure of the BNNs. In particular,we translate the input-output relation of blocks in BNNs to cardinalityconstraints which are then encoded by BDDs. Based on the encoding, we develop aquantitative verification framework for BNNs where precise and comprehensiveanalysis of BNNs can be performed. We demonstrate the application of ourframework by providing quantitative robustness analysis and interpretabilityfor BNNs. We implement a prototype tool BDD4BNN and carry out extensiveexperiments which confirm the effectiveness and efficiency of our approach.

BDD4BNN: A BDD-based Quantitative Analysis Framework for Binarized Neural Networks