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The No-Clash Teaching Dimension is Bounded by VC Dimension

Information Theory 2026-04-02 v3 Machine Learning math.IT

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. However, whether No-Clash Teaching Dimension is upper-bounded by Vapnik-Chervonenkis dimension remains unknown. In this paper, for any finite concept class, we construct fragments of size equals to its Vapnik-Chervonenkis dimension which identify concepts through an ordered compression scheme. Naturally, these fragments are used as teaching sets, one can easily see that they satisfy the non-clashing condition, i.e., this open question is resolved for finite concept classes.

Keywords

Cite

@article{arxiv.2603.23561,
  title  = {The No-Clash Teaching Dimension is Bounded by VC Dimension},
  author = {Jiahua Liu and Benchong Li},
  journal= {arXiv preprint arXiv:2603.23561},
  year   = {2026}
}
R2 v1 2026-07-01T11:36:03.551Z