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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…
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…
In his pioneering work in the field of Inductive Inference, Gold (1967) proved that a set containing all finite languages and at least one infinite language over the same fixed alphabet is not learnable in the exact sense. Within the same…
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…
Is automated hallucination detection possible? In this work, we introduce a theoretical framework to analyze the feasibility of automatically detecting hallucinations produced by large language models (LLMs). Inspired by the classical…
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…
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…
A statistical classification algorithm and its application to language identification from noisy input are described. The main innovation is to compute confidence limits on the classification, so that the algorithm terminates when enough…
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…
Large text corpora are increasingly important for a wide variety of Natural Language Processing (NLP) tasks, and automatic language identification (LangID) is a core technology needed to collect such datasets in a multilingual context.…
Knowing the language of an input text/audio is a necessary first step for using almost every NLP tool such as taggers, parsers, or translation systems. Language identification is a well-studied problem, sometimes even considered solved; in…
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…
Attributing outputs from Large Language Models (LLMs) in adversarial settings-such as cyberattacks and disinformation campaigns-presents significant challenges that are likely to grow in importance. We approach this attribution problem from…
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…
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…
We study a family of problems, called \prob{Maximum Solution}, where the objective is to maximise a linear goal function over the feasible integer assignments to a set of variables subject to a set of constraints. When the domain is Boolean…
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.…
We consider the problem of inferring the probability distribution associated with a language, given data consisting of an infinite sequence of elements of the languge. We do this under two assumptions on the algorithms concerned: (i) like a…
A classical problem in grammatical inference is to identify a language from a set of examples. In this paper, we address the problem of identifying a union of languages from examples that belong to several different unknown languages.…
This work is concerned with regular languages defined over large alphabets, either infinite or just too large to be expressed enumeratively. We define a generic model where transitions are labeled by elements of a finite partition of the…