# Mistake-Bounded Language Generation

arXiv: https://arxiv.org/abs/2605.10809 · HTML: https://mlsanity.com/paper/2605.10809/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 19 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 14 of 14)

- [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)
- [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)
- [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)
- [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)
- [Language Generation with Infinite Contamination](https://mlsanity.com/paper/2511.07417/) (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)
- [Learning to Answer from Correct Demonstrations](https://mlsanity.com/paper/2510.15464/) (2025)

## Built on by (most cited first, 5 of 5)

- [Multiscale Reward Hedging from Correct Demonstrations](https://mlsanity.com/paper/2608.06825/) (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)
- [Polynomial-Time Mistake-Bounded Language Generation](https://mlsanity.com/paper/2606.16077/) (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 investigate the learning task of language generation in the limit, but shift focus from the traditional time-of-last-mistake metric of a generator's success to a new notion of "mistake-bounded generation." While existing results for language generation in the limit focus on guaranteeing eventual consistency, they are blind to the cumulative error incurred during the learning process. We address this by shifting the goal to minimizing the total number of invalid elements output by a generation algorithm. We establish a formal reduction to the Learning from Correct Demonstrations framework of Joshi et al. (2025), enabling a general recipe for deriving mistake bounds via weighted update rules. For finite classes, we provide an algorithm that simultaneously achieves an optimal last-mistake time of mathsfCdim(L) and a mistake bound of lfloor log2 |L| rfloor, whereas for the non-uniform setting of countably infinite streams of languages, we prove a fundamental trade-off: achieving logarithmic mistakes O(log i) necessarily precludes convergence guarantees established in prior work. Finally, we show that our framework can be extended to accommodate noisy adversaries and guarantee mistake bounds that scale with the adversary's suboptimality.