# Safe Language Generation in the Limit

arXiv: https://arxiv.org/abs/2601.08648 · HTML: https://mlsanity.com/paper/2601.08648/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 30 references that are in the map.
- First posted on arXiv 13 Jan 2026.

## Builds on (most cited first, 16 of 16)

- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- ["Do Anything Now": Characterizing and Evaluating In-The-Wild Jailbreak Prompts on Large Language Models](https://mlsanity.com/paper/2308.03825/) (2023)
- [ToxiGen: A Large-Scale Machine-Generated Dataset for Adversarial and Implicit Hate Speech Detection](https://mlsanity.com/paper/2203.09509/) (2022)
- [Agentic Misalignment: How LLMs Could Be Insider Threats](https://mlsanity.com/paper/2510.05179/) (2025)
- [The State of Multilingual LLM Safety Research: From Measuring the Language Gap to Mitigating It](https://mlsanity.com/paper/2505.24119/) (2025)
- [Language Generation in the Limit](https://mlsanity.com/paper/2404.06757/) (2024)
- [Generation through the lens of learning theory](https://mlsanity.com/paper/2410.13714/) (2024)
- [Security Concerns for Large Language Models: A Survey](https://mlsanity.com/paper/2505.18889/) (2025)
- [Exploring Facets of Language Generation in the Limit](https://mlsanity.com/paper/2411.15364/) (2024)
- [The Scales of Justitia: A Comprehensive Survey on Safety Evaluation of LLMs](https://mlsanity.com/paper/2506.11094/) (2025)
- [Density Measures for Language Generation](https://mlsanity.com/paper/2504.14370/) (2025)
- [Generation from Noisy Examples](https://mlsanity.com/paper/2501.04179/) (2025)
- [On Union-Closedness of Language Generation](https://mlsanity.com/paper/2506.18642/) (2025)
- [Language Generation in the Limit: Noise, Loss, and Feedback](https://mlsanity.com/paper/2507.15319/) (2025)
- [Language Generation and Identification From Partial Enumeration: Tight Density Bounds and Topological Characterizations](https://mlsanity.com/paper/2511.05295/) (2025)
- [Language Generation with Infinite Contamination](https://mlsanity.com/paper/2511.07417/) (2025)

## Built on by (most cited first, 9 of 9)

- [Mistake-Bounded Language Generation](https://mlsanity.com/paper/2605.10809/) (2026)
- [Characterizing the Effect of Noise in Language Generation in the Limit](https://mlsanity.com/paper/2601.21237/) (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)
- [Differentially Private Language Generation and Identification in the Limit](https://mlsanity.com/paper/2604.08504/) (2026)
- [On Language Generation in the Limit with Bounded Memory](https://mlsanity.com/paper/2605.30324/) (2026)
- [Flood and Harvest: The Provable Necessity of Trivia for Generating Valuable Mathematics via the Lens of Language Generation in the Limit](https://mlsanity.com/paper/2606.14688/) (2026)
- [Hallucination Rates in Language Generation](https://mlsanity.com/paper/2607.23361/) (2026)

## Abstract (arXiv)

Recent results in learning a language in the limit have shown that, although language identification is impossible, language generation is tractable. As this foundational area expands, we need to consider the implications of language generation in real-world settings. This work offers the first theoretical treatment of safe language generation. Building on the computational paradigm of learning in the limit, we formalize the tasks of safe language identification and generation. We prove that under this model, safe language identification is impossible, and that safe language generation is at least as hard as (vanilla) language identification, which is also impossible. Last, we discuss several intractable and tractable cases.