6 papers
First-order methods on bounded-rank tensors converging to stationary points
Bin Gao, Renfeng Peng, Ya-xiang Yuan
Provably finding stationary points on bounded-rank tensors turns out to be an open problem [E. Levin, J. Kileel, and N. Boumal, Math. Program., 199 (2023), pp. 831--864] due to the…
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…
Optimization on product manifolds under a preconditioned metric
Bin Gao, Renfeng Peng, Ya-xiang Yuan
Since optimization on Riemannian manifolds relies on the chosen metric, it is appealing to know that how the performance of a Riemannian optimization method varies with different m…
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…