Tootfinder

İlk domates kızardı. Ben bunu kakao domates sanıyordum. Sanırım komşum yanlış fide verdi.
#garden #gardening #garten

Pond Slider on a rock. Descanso Gardens, La Canada Flintridge, California, USA. March, 2021. #descansogardens #turtle #slider

Multilevel Stochastic Gradient Descent for Optimal Control Under Uncertainty
Niklas Baumgarten, David Schneiderhan
https://arxiv.org/abs/2506.02647 https:/…

Multilevel Stochastic Gradient Descent for Optimal Control Under Uncertainty
We present a multilevel stochastic gradient descent method for the optimal control of systems governed by partial differential equations under uncertain input data. The gradient descent method used to find the optimal control leverages a parallel multilevel Monte Carlo method as stochastic gradient estimator. As a result, we achieve precise control over the stochastic gradient's bias, introduced by numerical approximation, and its sampling error, arising from the use of incomplete gradients, wh…

@… The proper way to start the Monday and week ahead. Greetings from Saigon!

This https://arxiv.org/abs/2409.16662 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A new class of anisotropic double phase problems: exponents depending on solutions and their gradients
In this work, we introduce two novel classes of quasilinear elliptic equations, each driven by the double phase operator with variable exponents. The first class features a new double phase equation where exponents depend on the gradient of the solution. We delve into proving various properties of the corresponding Musielak-Orlicz Sobolev spaces, including the $Δ_2$ property, uniform convexity, density and compact embedding. Additionally, we explore the characteristics of the new double phase …

Locally finitely presented Grothendieck categories with a flat generator
Lorenzo Martini, Carlos E. Parra, Manuel Saor\'in, Simone Virili
https://arxiv.org/abs/2508.00670 ht…

Locally finitely presented Grothendieck categories with a flat generator
A problem raised by Cuadra and Simson in 2007 asks whether a locally finitely presented Grothendieck category with enough flat objects has enough projective objects. We prove that the categories involved in the statement are precisely the locally finitely presented Grothendieck categories with exact product functors. This enables reformulations of the problem that answer the latter in the negative and prove that it is related to a classical problem posed by Miller in 1975 and to the Telescope C…

Blue Dasher dragonfly resting on a blade of grass. Descanso Gardens, La Canada Flintridge, California, USA. June, 2024. #descansogardens #bluedasher #dragonfly

This https://arxiv.org/abs/2502.03701 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

First-ish Order Methods: Hessian-aware Scalings of Gradient Descent
Gradient descent is the primary workhorse for optimizing large-scale problems in machine learning. However, its performance is highly sensitive to the choice of the learning rate. A key limitation of gradient descent is its lack of natural scaling, which often necessitates expensive line searches or heuristic tuning to determine an appropriate step size. In this paper, we address this limitation by incorporating Hessian information to scale the gradient direction. By accounting for the curvatur…

This https://arxiv.org/abs/2502.16492 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Convergence of Clipped SGD on Convex $(L_0,L_1)$-Smooth Functions
We study stochastic gradient descent (SGD) with gradient clipping on convex functions under a generalized smoothness assumption called $(L_0,L_1)$-smoothness. Using gradient clipping, we establish a high probability convergence rate that matches the SGD rate in the $L$ smooth case up to polylogarithmic factors and additive terms. We also propose a variation of adaptive SGD with gradient clipping, which achieves the same guarantee. We perform empirical experiments to examine our theory and algor…

Muscovy Duck. Descanso Gardens, La Canada-Flintridge, California, USA. February, 2025. #descansogardens #duck #muscovyduck