# Remarks on a recent preprint of Chernikov and Towsner

arXiv: https://arxiv.org/abs/2510.19665 · HTML: https://mlsanity.com/paper/2510.19665/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 9 references that are in the map.
- First posted on arXiv 22 Oct 2025.

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

- [High-arity PAC learning via exchangeability](https://mlsanity.com/paper/2402.14294/) (2024)
- [Sample completion, structured correlation, and Netflix problems](https://mlsanity.com/paper/2509.20404/) (2025)
- [Higher-arity PAC learning, VC dimension and packing lemma](https://mlsanity.com/paper/2510.02420/) (2025)

## Abstract (arXiv)

In this brief note, we first give a counterexample to a theorem in Chernikov and Towsner, arXiv:2510.02420(1). In arXiv:2510.02420(2), the theorem has changed but as we explain the proof has a mistake. The change in the statement, due to changes in the underlying definition, affects the paper's claims. Since that theorem had been relevant to connecting the work of their paper to Coregliano-Malliaris high-arity PAC learning, a connection which now disappears, we also explain why their definitions miss crucial aspects that our work was designed to grapple with.