We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of categories and even marked filtrations, where one descends not only admissible subcategories but also preferred objects.

Inspired by the recent paper (L. Ying, Journal of Scientific Computing, 84, 1–14 (2020), we explore relationship between mirror descent and variable metric method. When in decent is induced a convex function, whose Hessian close to objective this method enjoys both robustness from superlinear convergence for Newton type methods. applied linearly constrained minimization problem, prove global lo...

Several recent empirical studies demonstrate that important machine learning tasks such as training deep neural networks, exhibit a low-rank structure, where most of the variation in loss function occurs only few directions input space. In this paper, we leverage structure to reduce high computational cost canonical gradient-based methods gradient descent (GD). Our proposed Low-Rank Gradient De...