2 papers
math.AC2026
Sums of squares on curves and surfaces
BartÅomiej Bychawski, Bartosz GÅowacki, Tomasz Kowalczyk
We study sums of higher even powers in the coordinate rings of singular planar curves for coprime positive integers . We then show that the -Pythagoras number of…
math.PR2026
Convergence of Stochastic Gradient Descent with mini-batching and infinite variance
Bartosz Glowacki, Rafal Kulik, Philippe Soulier
Stochastic gradient descent (SGD) with mini-batching is a standard tool in large-scale optimization, yet its theoretical properties under heavy-tailed gradient noise remain largely…