# On a Combinatorial Problem Arising in Machine Teaching

arXiv: https://arxiv.org/abs/2402.04907 · HTML: https://mlsanity.com/paper/2402.04907/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 23 references that are in the map.
- First posted on arXiv 7 Feb 2024.

## Builds on (most cited first, 5 of 5)

- [An Overview of Machine Teaching](https://mlsanity.com/paper/1801.05927/) (2018)
- [Teaching an Active Learner with Contrastive Examples](https://mlsanity.com/paper/2110.14888/) (2021)
- [Preference-based Teaching](https://mlsanity.com/paper/1702.02047/) (2017)
- [Mitigating belief projection in explainable artificial intelligence via Bayesian Teaching](https://mlsanity.com/paper/2102.03919/) (2021)
- [When Redundancy Matters: Machine Teaching of Representations](https://mlsanity.com/paper/2401.12711/) (2024)

## Abstract (arXiv)

We study a model of machine teaching where the teacher mapping is constructed from a size function on both concepts and examples. The main question in machine teaching is the minimum number of examples needed for any concept, the so-called teaching dimension. A recent paper [7] conjectured that the worst case for this model, as a function of the size of the concept class, occurs when the consistency matrix contains the binary representations of numbers from zero and up. In this paper we prove their conjecture. The result can be seen as a generalization of a theorem resolving the edge isoperimetry problem for hypercubes [12], and our proof is based on a lemma of [10].