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Tag: lower

  • A Gapped Scale-Sensitive Dimension and Lower Bounds for Offset Rademacher Complexity

    A Gapped Scale-Sensitive Dimension and Lower Bounds for Offset Rademacher Complexity arXiv:2509.20618v1 Announce Type: new Abstract: We study gapped scale-sensitive dimensions of a function class in both sequential and non-sequential settings. We demonstrate that covering numbers for any uniformly bounded class are controlled above by these gapped dimensions, generalizing the results of cite{anthony2000function,alon1997scale}. Moreover, we…

  • Lower Bounds for Greedy Teaching Set Constructions

    Lower Bounds for Greedy Teaching Set Constructions arXiv:2505.03223v1 Announce Type: new Abstract: A fundamental open problem in learning theory is to characterize the best-case teaching dimension $operatorname{TS}_{min}$ of a concept class $mathcal{C}$ with finite VC dimension $d$. Resolving this problem will, in particular, settle the conjectured upper bound on Recursive Teaching Dimension posed by [Simon…