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Cloud computing platforms are becoming increasingly prevalent and readily available nowadays, providing us alternative and economic services for resource-constrained clients to perform large-scale computation. In this work, we address the problem of secure outsourcing of large-scale nonnegative matrix factorization (NMF) to a cloud in a way that the client can verify the correctness of results with small overhead. The input matrix protection is achieved by a lightweight, permutation-based encryption mechanism. By exploiting the iterative nature of NMF computation, we propose a single-round verification strategy, which can be proved to be effective. Both theoretical and experimental results are given to demonstrate the superior performance of our scheme.

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Deep neural networks (DNNs) have been shown to be vulnerable against adversarial examples (AEs), which are maliciously designed to cause dramatic model output errors. In this work, we reveal that normal examples (NEs) are insensitive to the fluctuations occurring at the highly-curved region of the decision boundary, while AEs typically designed over one single domain (mostly spatial domain) exhibit exorbitant sensitivity on such fluctuations. This phenomenon motivates us to design another classifier (called dual classifier) with transformed decision boundary, which can be collaboratively used with the original classifier (called primal classifier) to detect AEs, by virtue of the sensitivity inconsistency. When comparing with the state-of-the-art algorithms based on Local Intrinsic Dimensionality (LID), Mahalanobis Distance (MD), and Feature Squeezing (FS), our proposed Sensitivity Inconsistency Detector (SID) achieves improved AE detection performance and superior generalization capabilities, especially in the challenging cases where the adversarial perturbation levels are small. Intensive experimental results on ResNet and VGG validate the superiority of the proposed SID.