Juanjuan Sun

Li-Lin Ji, Juanjuan Sun, Jun-Feng Yin

Tensor linear systems widely arise from high-dimensional data mining and computing, for instance, natural language processing and machine learning. A class of residual-based tensor Kaczmarz method is proposed for tensor linear equations with t-product. Theoretical analyses prove the convergence and give an upper bound of the convergence rate of the proposed method. Furthermore, an accelerated residual-based Kaczmarz method with heavy ball momentum is developed. Numerical experiments verify the efficiency of the proposed methods and demonstrate that they are faster than the existing tensor Kaczmarz methods.

Qizhi Zhang, Lichun Li, Shan Yin et al.

Secure comparison and secure selection are two fundamental MPC (secure Multi-Party Computation) protocols. One important application of these protocols is the secure ReLU and DReLU computation in privacy preserving deep learning. In this paper, we introduce G-module, a mathematics tool, to re-design such protocols. In mathematics, given a group G, a G-module is an abelian group M on which G acts compatibly with the abelian group structure on M. We design three secure protocols for three G-module operations. i.e. "G-module action", "Cross G-module action" and "G-module recover". As far as we know, this is the first work on secure G-module operations. Based on them, we design secure comparison, selection, ReLU and DReLU protocols, which improve communication efficiency by 2X to 10X compared with state of arts. Our protocols are very computation efficient too. They do not require public key operations or any other expensive operations.