  Tensor network decomposition, originated from quantum physics to model
entangled many-particle quantum systems, turns out to be a promising
mathematical technique to efficiently represent and process big data in
parsimonious manner. In this study, we show that tensor networks can
systematically partition structured data, e.g. color images, for distributed
storage and communication in privacy-preserving manner. Leveraging the sea of
big data and metadata privacy, empirical results show that neighbouring
subtensors with implicit information stored in tensor network formats cannot be
identified for data reconstruction. This technique complements the existing
encryption and randomization techniques which store explicit data
representation at one place and highly susceptible to adversarial attacks such
as side-channel attacks and de-anonymization. Furthermore, we propose a theory
for adversarial examples that mislead convolutional neural networks to
misclassification using subspace analysis based on singular value decomposition
(SVD). The theory is extended to analyze higher-order tensors using
tensor-train SVD (TT-SVD); it helps to explain the level of susceptibility of
different datasets to adversarial attacks, the structural similarity of
different adversarial attacks including global and localized attacks, and the
efficacy of different adversarial defenses based on input transformation. An
efficient and adaptive algorithm based on robust TT-SVD is then developed to
detect strong and static adversarial attacks.
