# Higher-arity PAC learning, VC dimension and packing lemma

arXiv: https://arxiv.org/abs/2510.02420 · HTML: https://mlsanity.com/paper/2510.02420/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 24 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Builds on (most cited first, 3 of 3)

- [High-arity PAC learning via exchangeability](https://mlsanity.com/paper/2402.14294/) (2024)
- [From learnable objects to learnable random objects](https://mlsanity.com/paper/2504.00847/) (2025)
- [Sample completion, structured correlation, and Netflix problems](https://mlsanity.com/paper/2509.20404/) (2025)

## Built on by (most cited first, 1 of 1)

- [Remarks on a recent preprint of Chernikov and Towsner](https://mlsanity.com/paper/2510.19665/) (2025)

## Abstract (arXiv)

The aim of this note is to overview some of our work in Chernikov, Towsner'20 (arXiv:2010.00726) developing higher arity VC theory (VCn dimension), including a generalization of Haussler packing lemma, and an associated tame (slice-wise) hypergraph regularity lemma; and to demonstrate that it characterizes higher arity PAC learning (PACn learning) in n-fold product spaces with respect to product measures introduced by Kobayashi, Kuriyama and Takeuchi'15. We also point out how some of the recent results in arXiv:2402.14294, arXiv:2505.15688, arXiv:2509.20404 follow from our work in arXiv:2010.00726.