4 papers
Quotient geometry of tensor ring decomposition
Bin Gao, Renfeng Peng, Ya-xiang Yuan
Differential geometries derived from tensor decompositions have been extensively studied and provided the foundations for a variety of efficient numerical methods. Despite the prac…
Normalized tensor train decomposition
Renfeng Peng, Chengkai Zhu, Bin Gao +2
Tensors with unit Frobenius norm are fundamental objects in many fields, including scientific computing and quantum physics, which are able to represent normalized eigenvectors and…
Riemannian Optimization for Holevo Capacity
Chengkai Zhu, Renfeng Peng, Bin Gao +1
Computing the classical capacity of a noisy quantum channel is crucial for understanding the limits of communication over quantum channels. However, its evaluation remains challeng…
Desingularization of bounded-rank tensor sets
Bin Gao, Renfeng Peng, Ya-xiang Yuan
Low-rank tensors appear to be prosperous in many applications. However, the sets of bounded-rank tensors are non-smooth and non-convex algebraic varieties, rendering the low-rank o…