Tensor-valued data arise frequently from a wide variety of scientific
applications, and many among them can be translated into an alteration
detection problem of tensor dependence structures. In this article, we
formulate the problem under the popularly adopted tensor-normal distributions
and aim at two-sample correlation/partial correlation comparisons of
tensor-valued observations. Through decorrelation and centralization, a
separable covariance structure is employed to pool sample information from
different tensor modes to enhance the power of the test. Additionally, we
propose a novel Sparsity-Exploited Reranking Algorithm (SERA) to further
improve the multiple testing efficiency. The algorithm is approached through
reranking of the p-values derived from the primary test statistics, by
incorporating a carefully constructed auxiliary tensor sequence. Besides the
tensor framework, SERA is also generally applicable to a wide range of
two-sample large-scale inference problems with sparsity structures, and is of
independent interest. The asymptotic properties of the proposed test are
derived and the algorithm is shown to control the false discovery at the
pre-specified level. We demonstrate the efficacy of the proposed method through
intensive simulations and two scientific applications