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The recent successes of large language models (LLMs) have led to a surge of theoretical research into language generation. A recent line of work proposes an abstract view, called language generation in the limit, where generation is seen as…

Combinatorics · Mathematics 2025-04-22 Jon Kleinberg , Fan Wei

Although current large language models are complex, the most basic specifications of the underlying language generation problem itself are simple to state: given a finite set of training samples from an unknown language, produce valid new…

Data Structures and Algorithms · Computer Science 2024-04-11 Jon Kleinberg , Sendhil Mullainathan

We study language generation in the limit under bounded memory. In this task, a learner observes examples from an unknown target language one at a time and must eventually output only new valid examples. Prior work assumes access to the…

Data Structures and Algorithms · Computer Science 2026-05-29 Jon Kleinberg , Anay Mehrotra , Amin Saberi , Grigoris Velegkas

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]…

Machine Learning · Statistics 2025-11-11 Anay Mehrotra , Grigoris Velegkas , Xifan Yu , Felix Zhou

We study language generation in the limit - introduced by Kleinberg and Mullainathan [KM24] - building on classical works of Gold [Gol67] and Angluin [Ang79]. [KM24]'s main result is an algorithm for generating from any countable language…

Machine Learning · Computer Science 2025-07-04 Alkis Kalavasis , Anay Mehrotra , Grigoris Velegkas

We study the problem of language identification in the limit, where given a sequence of examples from a target language, the goal of the learner is to output a sequence of guesses for the target language such that all the guesses beyond…

Computation and Language · Computer Science 2025-11-07 Moses Charikar , Chirag Pabbaraju , Ambuj Tewari

The recent work of Kleinberg & Mullainathan [KM24] provides a concrete model for language generation in the limit: given a sequence of examples from an unknown target language, the goal is to generate new examples from the target language…

Data Structures and Algorithms · Computer Science 2024-12-25 Moses Charikar , Chirag Pabbaraju

Kleinberg and Mullainathan showed that language generation in the limit is always possible at the level of computability: given enough positive examples, a learner can eventually generate data indistinguishable from a target language.…

Computation and Language · Computer Science 2026-01-30 Marcelo Arenas , Pablo Barceló , Luis Cofré , Alexander Kozachinskiy

As scaling laws push the training of frontier large language models (LLMs) toward ever-growing data requirements, training pipelines are approaching a regime where much of the publicly available online text may be consumed. At the same…

Machine Learning · Computer Science 2026-03-13 Giorgio Racca , Michal Valko , Amartya Sanyal

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…

Machine Learning · Computer Science 2026-05-12 Jon Kleinberg , Charlotte Peale , Omer Reingold

Large Language Models (LLMs) have demonstrated a powerful ability for text generation. However, achieving optimal results with a given prompt or instruction can be challenging, especially for billion-sized models. Additionally, undesired…

Computation and Language · Computer Science 2024-10-07 Lifu Tu , Semih Yavuz , Jin Qu , Jiacheng Xu , Rui Meng , Caiming Xiong , Yingbo Zhou

Kleinberg and Mullainathan (2024) recently proposed a formal framework called language generation in the limit and showed that given a sequence of example strings from an unknown target language drawn from any countable collection, an…

Data Structures and Algorithms · Computer Science 2026-02-09 Yannan Bai , Debmalya Panigrahi , Ian Zhang

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…

Computation and Language · Computer Science 2026-01-14 Antonios Anastasopoulos , Giuseppe Ateniese , Evgenios M. Kornaropoulos

Kleinberg and Mullainathan (2024) recently proposed an interesting model for language generation in the limit: Given a countable collection of languages, and an adversary enumerating the strings of some language $L$ from the collection, the…

Data Structures and Algorithms · Computer Science 2025-10-06 Moses Charikar , Chirag Pabbaraju

Specifying all desirable properties of a language model is challenging, but certain requirements seem essential. Given samples from an unknown language, the trained model should produce valid strings not seen in training and be expressive…

Machine Learning · Computer Science 2025-10-16 Alkis Kalavasis , Anay Mehrotra , Grigoris Velegkas

Advancements in natural language generation (NLG) and large language models (LLMs) have led to proficient text generation in various tasks. However, integrating intricate constraints into neural text generation, due to LLMs' opacity,…

Computation and Language · Computer Science 2024-03-22 Xiang Chen , Xiaojun Wan

Some consider large-scale language models that can generate long and coherent pieces of text as dangerous, since they may be used in misinformation campaigns. Here we formulate large-scale language model output detection as a hypothesis…

Computation and Language · Computer Science 2020-02-11 Lav R. Varshney , Nitish Shirish Keskar , Richard Socher

Today's probabilistic language generators fall short when it comes to producing coherent and fluent text despite the fact that the underlying models perform well under standard metrics, e.g., perplexity. This discrepancy has puzzled the…

Computation and Language · Computer Science 2025-06-06 Clara Meister , Tiago Pimentel , Gian Wiher , Ryan Cotterell

Kleinberg and Mullainathan recently proposed a formal framework for studying the phenomenon of language generation, called language generation in the limit. In this model, an adversary gives an enumeration of example strings from an unknown…

Data Structures and Algorithms · Computer Science 2026-01-30 Aaron Li , Ian Zhang

An ideal detection system for machine generated content is supposed to work well on any generator as many more advanced LLMs come into existence day by day. Existing systems often struggle with accurately identifying AI-generated content…

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