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The VC-Dimension of Axis-Parallel Boxes on the Torus (2004.13861v1)
Published 28 Apr 2020 in math.CO, cs.DM, and cs.LG
Abstract: We show in this paper that the VC-dimension of the family of $d$-dimensional axis-parallel boxes and cubes on the $d$-dimensional torus are both asymptotically $d \log_2(d)$. This is especially surprising as the VC-dimension usually grows linearly with $d$ in similar settings.
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