arXiv:2606. 18236v1 Announce Type: new Abstract: In learning theory, the sign rank of a binary concept class captures the smallest dimension in which it can be represented by points and halfspaces.
arXiv:2606. 06148v1 Announce Type: new Abstract: In recent years, list replicability has emerged as a framework for formalizing reproducibility in learning theory.
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.
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:2608. 02533v1 Announce Type: cross Abstract: We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $\Omega(n^2)$.
arXiv:2605.13684v2 Announce Type: replace Abstract: We study the optimal scale at which real-valued function classes exhibit uniform convergence and learnability. Our main result establishes a scale-...
arXiv:2609. 12259v1 Announce Type: new Abstract: Matrix-valued memories make rank the natural budget of a learned representation: the number of independent directions a state spans bounds what it can bind, compose, and track.
arXiv:2603. 23561v4 Announce Type: replace-cross Abstract: In the realm of machine learning theory, to prevent unnatural coding schemes between teacher and learner, No-Clash Teaching Dimension was introduced as provably optimal complexity measure for collusion-free teaching.
arXiv:2606. 11780v1 Announce Type: cross Abstract: We establish conditions for embedding a corpus of $N$ documents as $d$-dimensional vectors such that every $k$-subset $S \subseteq [N]$ is realizable as a result of top-$k$ retrieval by some query vector.
arXiv:2511. 02644v2 Announce Type: replace Abstract: We study computable probably approximately correct (CPAC) learning, where learners are required to be computable functions.
arXiv:2604. 02995v3 Announce Type: replace-cross Abstract: We introduce the penalised Saito functional $\mathfrak S_{\lambda,\beta}(\mathcal{A};d_1,d_2)$ for a reduced arrangement $\mathcal{A}$ of $n$ lines and a prescribed pair $d_1+d_2=n-1$.
arXiv:2605.20434v2 Announce Type: replace-cross Abstract: We study the contradiction graphs associated with a binary concept class. For a class $H\subseteq\{0,1\}^X$, the order-$m$ contradiction grap...
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...