9 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…
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…
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…
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…
A space-decoupling framework for optimization on bounded-rank matrices with orthogonally invariant constraints
Yan Yang, Bin Gao, Ya-xiang Yuan
Imposing additional constraints on low-rank optimization has garnered growing interest. However, the geometry of coupled constraints hampers the well-developed low-rank structure a…
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…
Bilevel reinforcement learning via the development of hyper-gradient without lower-level convexity
Yan Yang, Bin Gao, Ya-xiang Yuan
Bilevel reinforcement learning (RL), which features intertwined two-level problems, has attracted growing interest recently. The inherent non-convexity of the lower-level RL proble…
LancBiO: dynamic Lanczos-aided bilevel optimization via Krylov subspace
Yan Yang, Bin Gao, Ya-xiang Yuan
Bilevel optimization, with broad applications in machine learning, has an intricate hierarchical structure. Gradient-based methods have emerged as a common approach to large-scale…
Low-rank optimization on Tucker tensor varieties
Bin Gao, Renfeng Peng, Ya-xiang Yuan
In the realm of tensor optimization, the low-rank Tucker decomposition is crucial for reducing the number of parameters and for saving storage. We explore the geometry of Tucker te…