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The success of large language models (LLMs) has motivated formal theories of language generation and learning. We study the framework of \emph{language generation in the limit}, where an adversary enumerates strings from an unknown language…

Data Structures and Algorithms · Computer Science 2025-11-10 Jon Kleinberg , Fan Wei

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

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

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

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

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

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 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

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

For open-ended language generation tasks such as storytelling and dialogue, choosing the right decoding algorithm is critical to controlling the tradeoff between generation quality and diversity. However, there presently exists no consensus…

Computation and Language · Computer Science 2020-04-23 Hugh Zhang , Daniel Duckworth , Daphne Ippolito , Arvind Neelakantan

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

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

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

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

Large language models (LLMs) have demonstrated impressive capabilities in natural language generation. However, their output quality can be inconsistent, posing challenges for generating natural language from logical forms (LFs). This task…

Computation and Language · Computer Science 2023-09-22 Levon Haroutunian , Zhuang Li , Lucian Galescu , Philip Cohen , Raj Tumuluri , Gholamreza Haffari

Language Confusion is a phenomenon where Large Language Models (LLMs) generate text that is neither in the desired language, nor in a contextually appropriate language. This phenomenon presents a critical challenge in text generation by…

Computation and Language · Computer Science 2025-02-11 Yiyi Chen , Qiongxiu Li , Russa Biswas , Johannes Bjerva

Algorithms for text-generation in dialogue can be misguided. For example, in task-oriented settings, reinforcement learning that optimizes only task-success can lead to abysmal lexical diversity. We hypothesize this is due to poor…

Computation and Language · Computer Science 2022-10-17 Anthony Sicilia , Malihe Alikhani

The development and evaluation of Large Language Models (LLMs) has primarily focused on their task-solving capabilities, with recent models even surpassing human performance in some areas. However, this focus often neglects whether…

Computation and Language · Computer Science 2025-07-29 Yanzhu Guo , Guokan Shang , Chloé Clavel

Although current state-of-the-art language models have achieved impressive results in numerous natural language processing tasks, still they could not solve the problem of producing repetitive, dull and sometimes inconsistent text in…

Computation and Language · Computer Science 2021-08-10 An Nguyen

Large Language Models (LLMs) have revolutionised the field of Natural Language Processing (NLP) and have achieved state-of-the-art performance in practically every task in this field. However, the prevalent approach used in text generation,…

Computation and Language · Computer Science 2024-08-12 Nicolo Micheletti , Samuel Belkadi , Lifeng Han , Goran Nenadic
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