Related papers: On Generation in Metric Spaces
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…
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…
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…
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 investigate language generation in the limit - a model by Kleinberg and Mullainathan [NeurIPS 2024] and extended by Li, Raman, and Tewari [COLT 2025]. While Kleinberg and Mullainathan proved generation is possible for all countable…
The magnitude of a metric space is a novel invariant that provides a measure of the 'effective size' of a space across multiple scales, while also capturing numerous geometrical properties, such as curvature, density, or entropy. We develop…
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…
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]…
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…
Language models have demonstrated remarkable capabilities on standard benchmarks, yet they struggle increasingly from mode collapse, the inability to generate diverse and novel outputs. Our work introduces NoveltyBench, a benchmark…
We propose a simple and effective modeling framework for controlled generation of multiple, diverse outputs. We focus on the setting of generating the next sentence of a story given its context. As controllable dimensions, we consider…
In this work, we propose to study the global geometrical properties of generative models. We introduce a new Riemannian metric to assess the similarity between any two data points. Importantly, our metric is agnostic to the parametrization…
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…
Generation novelty is a key indicator of an LLM's ability to generalize, yet measuring it against full pretraining corpora is computationally challenging. Existing evaluations often rely on lexical overlap, failing to detect paraphrased…
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…
Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator…
We continue to study the learning-theoretic foundations of generation by extending the results from Kleinberg and Mullainathan [2024] and Li et al. [2024] to account for noisy example streams. In the noiseless setting of Kleinberg and…
Every formal grammar defines a language and can in principle be used in three ways: to generate strings (production), to recognize them (parsing), or -- given only examples -- to infer the grammar itself (grammar induction). Generation and…
The purpose of unconditional text generation is to train a model with real sentences, then generate novel sentences of the same quality and diversity as the training data. However, when different metrics are used for comparing the methods…
Precision and Recall are two prominent metrics of generative performance, which were proposed to separately measure the fidelity and diversity of generative models. Given their central role in comparing and improving generative models,…