4 papers
Rank One Completion for Higher Order Tensors
Linghao Zhang, Ioana Dumitriu, Jiawang Nie
We study the rank one completion problem for tensors of arbitrary orders. The notion of rank one determinable tensors is introduced. We explore its properties and propose a recursi…
Learning Polynomial Activation Functions for Deep Neural Networks
Linghao Zhang, Jiawang Nie, Tingting Tang
Activation functions are crucial for deep neural networks. This novel work frames the problem of training neural network with learnable polynomial activation functions as a polynom…
Sparse Polynomial Optimization with Matrix Constraints
Jiawang Nie, Zheng Qu, Xindong Tang +1
This paper studies the hierarchy of sparse matrix Moment-SOS relaxations for solving sparse polynomial optimization problems with matrix constraints. First, we prove a sufficient a…
A Characterization for Tightness of the Sparse Moment-SOS Hierarchy
Jiawang Nie, Zheng Qu, Xindong Tang +1
This paper studies the sparse Moment-SOS hierarchy of relaxations for solving sparse polynomial optimization problems. We show that this sparse hierarchy is tight if and only if th…