arXiv:2609.23094v1 Announce Type: cross
Abstract: We study the number of prototypes needed to represent Boolean functions by nearest-neighbour classification. There are two distinct settings: the pro...
By Martin Anthony
arXiv:2609. 29756v1 Announce Type: cross Abstract: How much information can a single neuron remember?
By Xinyuan Xie
arXiv:2607. 21761v1 Announce Type: cross Abstract: We prove function-theoretic analogues of a quantitative result of Hodges on extracting the order property from a sufficiently large 2-tree coded in a binary relation.
By G Conant, C Terry
arXiv:2602. 16807v2 Announce Type: replace Abstract: A collection of hyperplanes $\mathcal{H}$ slices all edges of the $n$-dimensional hypercube $Q_n$ with vertex set $\{-1,1\}^n$ if, for every edge $e$ in the hypercube, there exists a hyperplane in $\mathcal{H}$ intersecting $e$ in its interior.
By Duncan Soiffer, Nathaniel Itty, Christopher D. Rosin, Blake Bruell, Mason DiCicco, G\'abor N. S\'ark\"ozy, Ryan Offstein, Daniel Reichman
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:2607. 03815v1 Announce Type: cross Abstract: For compact convex sets $L,K \subset \mathbb{R}^n$, denote by $\lambda_K(L)$ the smallest size of a homothet of $K$ that contains $L$.
By Egor Bakaev, Amir Yehudayoff