# Generation through the lens of learning theory

arXiv: https://arxiv.org/abs/2410.13714 · HTML: https://mlsanity.com/paper/2410.13714/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 18 references that are in the map.
- First posted on arXiv 17 Oct 2024.

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

- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Transformers in Vision: A Survey](https://mlsanity.com/paper/2101.01169/) (2021)
- [Language Generation in the Limit](https://mlsanity.com/paper/2404.06757/) (2024)

## Built on by (most cited first, 30 of 31)

- [Exploring Facets of Language Generation in the Limit](https://mlsanity.com/paper/2411.15364/) (2024)
- [Density Measures for Language Generation](https://mlsanity.com/paper/2504.14370/) (2025)
- [Generation from Noisy Examples](https://mlsanity.com/paper/2501.04179/) (2025)
- [Representative Language Generation](https://mlsanity.com/paper/2505.21819/) (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)
- [(Im)possibility of Automated Hallucination Detection in Large Language Models](https://mlsanity.com/paper/2504.17004/) (2025)
- [On Characterizations for Language Generation: Interplay of Hallucinations, Breadth, and Stability](https://mlsanity.com/paper/2412.18530/) (2024)
- [Language Generation and Identification From Partial Enumeration: Tight Density Bounds and Topological Characterizations](https://mlsanity.com/paper/2511.05295/) (2025)
- [Pareto-optimal Non-uniform Language Generation](https://mlsanity.com/paper/2510.02795/) (2025)
- [A Characterization of List Language Identification in the Limit](https://mlsanity.com/paper/2511.04103/) (2025)
- [Language Generation: Complexity Barriers and Implications for Learning](https://mlsanity.com/paper/2511.05759/) (2025)
- [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)
- [Characterizing the Effect of Noise in Language Generation in the Limit](https://mlsanity.com/paper/2601.21237/) (2026)
- [Agnostic Language Identification and Generation](https://mlsanity.com/paper/2601.23258/) (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)
- [A Theory of Time-Sensitive Language Generation: Sparse Hallucination Beats Mode Collapse](https://mlsanity.com/paper/2605.11302/) (2026)
- [On Language Generation in the Limit with Bounded Memory](https://mlsanity.com/paper/2605.30324/) (2026)
- [The Homogenization Problem in LLMs: Towards Meaningful Diversity in AI Safety](https://mlsanity.com/paper/2601.06116/) (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)
- [Space-Efficient Language Generation in the Limit](https://mlsanity.com/paper/2606.25777/) (2026)
- [Characterizing Language Generation in the Limit: Finite Witnesses and a Separation-Width Hierarchy](https://mlsanity.com/paper/2609.10525/) (2026)
- [If generative AI is the answer, what is the question?](https://mlsanity.com/paper/2509.06120/) (2025)
- [Why Code, Why Now: An Information-Theoretic Perspective on the Limits of Machine Learning](https://mlsanity.com/paper/2602.13934/) (2026)
- [Hierarchical Domain Generalization](https://mlsanity.com/paper/2607.16528/) (2026)
- [Hallucination Rates in Language Generation](https://mlsanity.com/paper/2607.23361/) (2026)

## Abstract (arXiv)

We study generation through the lens of statistical learning theory. First, we abstract and formalize the results of Gold [1967], Angluin [1979], Angluin [1980] and Kleinberg and Mullainathan [2024] in terms of a binary hypothesis class defined over an abstract example space. Then, we extend the notion of "generation" from Kleinberg and Mullainathan [2024] to two new settings, we call "uniform" and "non-uniform" generation, and provide a characterization of which hypothesis classes are uniformly and non-uniformly generatable. As is standard in learning theory, our characterizations are in terms of the finiteness of a new combinatorial dimension termed the Closure dimension. By doing so, we are able to compare generatability with predictability (captured via PAC and online learnability) and show that these two properties of hypothesis classes are incompatible -- there are classes that are generatable but not predictable and vice versa. Finally, we extend our results to capture prompted generation and give a complete characterization of which classes are prompt generatable, generalizing some of the work by Kleinberg and Mullainathan [2024].