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The VC-Dimension of Axis-Parallel Boxes on the Torus

Combinatorics 2020-04-30 v1 Discrete Mathematics Machine Learning

Abstract

We show in this paper that the VC-dimension of the family of dd-dimensional axis-parallel boxes and cubes on the dd-dimensional torus are both asymptotically dlog2(d)d \log_2(d). This is especially surprising as the VC-dimension usually grows linearly with dd in similar settings.

Cite

@article{arxiv.2004.13861,
  title  = {The VC-Dimension of Axis-Parallel Boxes on the Torus},
  author = {Pierre Gillibert and Thomas Lachmann and Clemens Müllner},
  journal= {arXiv preprint arXiv:2004.13861},
  year   = {2020}
}
R2 v1 2026-06-23T15:10:08.337Z