Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of applications in machine learning, data science and statistics. Classically, such problems are solved via constrained Euclidean optimization, where the domain is viewed as a Euclidean space and the structure of the matrices (e.g., positive definiteness) enters as constraints. More recently, geometric approaches that leverage parametrizations of the problem as unconstrained tasks on the corresponding matrix manifold have been proposed. While they exhibit algorithmic benefits in many settings, they cannot directly handle additional constraints, such as inequality or sparsity constraints. A remedy comes in the form of constrained Riemannian optimization methods, notably, Riemannian Frank-Wolfe and Projected Gradient Descent. However, both algorithms require potentially expensive subroutines that can introduce computational bottlenecks in practise. To mitigate these shortcomings, we introduce a class of structured regularizers, based on symmetric gauge functions, which allow for solving constrained optimization on the SPD manifold with faster unconstrained methods. We show that our structured regularizers can be chosen to preserve or induce desirable structure, in particular convexity and "difference of convex" structure. We demonstrate the effectiveness of our approach in numerical experiments.
Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising
School of Mathematics, University of Birmingham（伯明翰大学数学学院）；Department of Mathematical Sciences, University of Bath（巴斯大学数学科学系）；DAMTP, University of Cambridge（剑桥大学应用数学与理论物理系）
本文提出凸三复合优化的随机原始-对偶三算子分裂算法 TOS-SPDHG，证明 O(1/K) 遍历收敛率，并结合 RED 与等变扩展用于成像逆问题。
LEAP: Learnable Pruning for Transformer-based Models
Microsoft（微软）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of California, Berkeley（加州大学伯克利分校）；International Computer Science Institute（国际计算机科学研究所）
Deep Neural Networks pruning via the Structured Perspective Regularization
CERC, Polytechnique Montréal（蒙特利尔理工学院计算与工程研究中心）；University of Pisa（比萨大学）；Huawei Montreal Research Centre（华为蒙特利尔研究中心）；Jacobs Technion-Cornell Institute（雅各布斯泰克尼翁-康奈尔研究所）；Cornell Tech（康奈尔理工学院）；Technion - IIT（以色列理工学院）
