arXiv:2606. 18306v1 Announce Type: new Abstract: Gaussian width is a central geometric complexity measure in high-dimensional probability, compressed sensing, convex optimization, and learning theory.
By Vu Khac Ky
arXiv:2606. 20469v1 Announce Type: new Abstract: A widely held intuition in deep learning is that stochastic gradient descent (SGD) implicitly favors flat minima and that flat minima generalize better, but standard Euclidean measures of flatness such as the trace or maximum eigenvalue of the loss Hessian are not invariant under reparametrizations that preserve the network function, which undermines the theoretical foundations of this narrative.
By Md Sakir Ahmed, Kumaresh Sarmah, Hemen Dutta
arXiv:2609. 20687v1 Announce Type: cross Abstract: We study first-order black-box convex optimization over an $\ell_p$-ball for objectives Lipschitz in the $\ell_q$-norm, solving in the affirmative the nonsmooth version of the COLT open question (Guz15b) on whether the geometry of a smaller feasible set ($p < q$) can improve convergence rates in convex optimization, and matching prior lower bounds up to logarithmic factors.
By David Mart\'inez-Rubio, Brian Bullins, Crist\'obal Guzm\'an, Mathieu Molina
arXiv:2609. 30105v1 Announce Type: new Abstract: For an arbitrary isotropic log-concave distribution $P$ on $\mathbb{R}^d$, we prove that the polynomial $(Cm)^m\|v\|_2^m - \mathbb{E}_{X\sim P}\langle X,v\rangle^m$ is a sum of squares for every even $m\ge2$, where $C>0$ is a universal constant.
By Aleksandr Storozhenko
arXiv:2411. 15067v2 Announce Type: replace-cross Abstract: We investigate proximal descent methods, inspired by the minimizing movement scheme introduced by Jordan, Kinderlehrer and Otto, for optimizing entropy-regularized functionals on the Wasserstein space.
By Razvan-Andrei Lascu, Mateusz B. Majka, David \v{S}i\v{s}ka, {\L}ukasz Szpruch
arXiv:2609.38834v1 Announce Type: cross
Abstract: Contrastive learning is a successful paradigm for learning $d$-dimensional geometric representations from a collection of ``anchor--positive--negativ...
By Dionysis Arvanitakis, Vaggos Chatziafratis, Yiyuan Luo, Konstantin Makarychev