13 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…
Fully analogue in-memory neural computing via quantum tunneling effect
Songyuan Li, Teng Wang, Jinrong Tang +7
Fully analogue neural computation requires hardware that can implement both linear and nonlinear transformations without digital assistance. While analogue in-memory computing effi…
Variational analysis of determinantal varieties
Yan Yang, Bin Gao, Ya-xiang Yuan
Determinantal varieties -- the sets of bounded-rank matrices or tensors -- have attracted growing interest in low-rank optimization. The tangent cone to low-rank sets is widely stu…
Optimization without Retraction on the Random Generalized Stiefel Manifold
Simon Vary, Pierre Ablin, Bin Gao +1
Optimization over the set of matrices that satisfy , referred to as the generalized Stiefel manifold, appears in many applications involving sampled covarianc…
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…