English

Learning Functions of Halfspaces

Data Structures and Algorithms 2026-03-10 v1 Computational Complexity

Abstract

We give an algorithm that learns arbitrary Boolean functions of kk arbitrary halfspaces over Rn\mathbb{R}^n, in the challenging distribution-free Probably Approximately Correct (PAC) learning model, running in time 2n(logn)O(k)2^{\sqrt{n} \cdot (\log n)^{O(k)}}. This is the first algorithm that can PAC learn even intersections of two halfspaces in time 2o(n).2^{o(n)}.

Keywords

Cite

@article{arxiv.2603.08700,
  title  = {Learning Functions of Halfspaces},
  author = {Josh Alman and Shyamal Patel and Rocco A. Servedio},
  journal= {arXiv preprint arXiv:2603.08700},
  year   = {2026}
}
R2 v1 2026-07-01T11:10:49.123Z