We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $Ω(n^2)$. By utilizing the special structure of these DNFs, we prove a lifting theorem with a constant-sized gadget that lifts the DNF to a communication problem, while losslessly translating the separation in certificate complexity to a separation in communication complexity.
arXiv:2605. 03823v3 Announce Type: replace Abstract: We study strong universal Bayes-consistency in the realizable setting for learning with general metric losses, extending classical characterizations beyond $0$-$1$ classification (Bousquet et al.
By Dan Tsir Cohen, Steve Hanneke, Aryeh Kontorovich
arXiv:2608. 02533v1 Announce Type: cross Abstract: We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $\Omega(n^2)$.
By Chirag Pabbaraju
arXiv:2608. 01320v1 Announce Type: cross Abstract: Language generation in the limit is a theoretical framework for studying how a generator can learn to produce new valid strings from a stream of positive examples.
By Ziyi Cai, Shuangping Li, Yiheng Shen, Kangning Wang, Peng Zhang
arXiv:2509. 20848v2 Announce Type: replace-cross Abstract: In the classic point location problem, one is given an arbitrary dataset $X \subset \mathbb{R}^d$ of $n$ points with query access to an unknown halfspace $f : \mathbb{R}^d \to \{0,1\}$, and the goal is to learn the label of every point in $X$.
By Hadley Black, Kasper Green Larsen, Arya Mazumdar, Barna Saha, Geelon So
arXiv:2607. 05791v1 Announce Type: cross Abstract: Boosting is a fundamental technique for generically improving the accuracy of learning algorithms (Schapire 1989).
By Addison Prairie, Li-Yang Tan