# Language Generation with Infinite Contamination

arXiv: https://arxiv.org/abs/2511.07417 · HTML: https://mlsanity.com/paper/2511.07417/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2025.

## Built on by (most cited first, 10 of 10)

- [Safe Language Generation in the Limit](https://mlsanity.com/paper/2601.08648/) (2026)
- [Language Generation with Replay: A Learning-Theoretic View of Model Collapse](https://mlsanity.com/paper/2603.11784/) (2026)
- [Mistake-Bounded Language Generation](https://mlsanity.com/paper/2605.10809/) (2026)
- [Agnostic Language Identification and Generation](https://mlsanity.com/paper/2601.23258/) (2026)
- [On Generation in Metric Spaces](https://mlsanity.com/paper/2602.07710/) (2026)
- [Contrastive Identification and Generation in the Limit](https://mlsanity.com/paper/2605.06211/) (2026)
- [On the Price of Privacy for Language Identification and Generation](https://mlsanity.com/paper/2604.07238/) (2026)
- [On Language Generation in the Limit with Bounded Memory](https://mlsanity.com/paper/2605.30324/) (2026)
- [Hallucination Rates in Language Generation](https://mlsanity.com/paper/2607.23361/) (2026)
- [GenLimitLib: A Formal Library for Language Generation in the Limit and AI-Assisted Mathematical Research](https://mlsanity.com/paper/2609.36663/) (2026)

## Abstract (arXiv)

We study language generation in the limit, where an algorithm observes an adversarial enumeration of strings from an unknown target language K and must eventually generate new, unseen strings from K. Kleinberg and Mullainathan [KM24] proved that generation is achievable in surprisingly general settings. But their generator suffers from ``mode collapse,'' producing from an ever-smaller subset of the target. To address this, Kleinberg and Wei [KW25] require the generator's output to be ``dense'' in the target language. They showed that generation with density, surprisingly, remains achievable at the same generality. Both results assume perfect data: no noisy insertions and no omissions. This raises a central question: how much contamination can generation tolerate? Recent works made partial progress on this question by studying (non-dense) generation with either finite amounts of noise (but no omissions) or omissions (but no noise). We characterize robustness under contaminated enumerations: 1. Generation under Contamination: Language generation in the limit is achievable for all countable collections iff the fraction of contaminated examples converges to zero. When this fails, we characterize which collections are generable. 2. Dense Generation under Contamination: Dense generation is strictly less robust to contamination than generation. As a byproduct, we resolve an open question of Raman and Raman [ICML25] by showing that generation is possible with only membership oracle access under finitely many contaminated examples. Finally, we introduce a beyond-worst-case model inspired by curriculum learning and prove that dense generation is achievable even with infinite contamination provided the fraction of contaminated examples converges to zero. This suggests curriculum learning may be crucial for learning from noisy web data.