Let the exact homogeneous hard-margin support vector machine be trained on \(m\) independent observations from a Borel probability law on a real Hilbert space. We prove that, with score zero counted a...
arXiv:2607. 10751v1 Announce Type: new Abstract: Following Alon, Hanneke, Holzman, and Moran (FOCS 2021), we define a partial concept class (PCC) as a family of partial functions \(f: V\to\{0,1,\ast\}\); equivalently, its concepts partition the ground set into black ($f^{-1}(1)$), grey ($f^{-1}(\ast)$), and white parts ($f^{-1}(0)$).
By Grigory Ivanov, Attila Jung, M\'arton Nasz\'odi
arXiv:2608.30254v1 Announce Type: new
Abstract: We resolve the threshold part of Question 4 of the COLT 2025 open problem "Data Selection for Regression Tasks" of Hanneke, Moran, Shlimovich and Yehud...
By Guangjian Zhang
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:2609.38834v1 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
arXiv:2602. 19172v2 Announce Type: replace Abstract: Realizable online regression can behave very differently from online classification.
By Ilan Doron-Arad, Idan Mehalel, Elchanan Mossel