Quantifying Noise in Language Generation

TL;DR

This paper investigates the impact of noise on language generation models, showing that even a single extraneous string can significantly restrict generability and establishing equivalence between finite and unlimited noise scenarios.

Contribution

It provides the first characterization of noise-dependent generatability and demonstrates that a single noisy string has a profound effect, contrasting previous hierarchical results.

Findings

A single noisy string reduces the set of generatable collections.

Generation with one noisy string is equivalent to any finite amount of noise.

First characterization of noise-dependent generatability in language generation.

Abstract

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 target language, and the algorithm is tasked with correctly generating unseen strings from the target language within finite time. Refined notions of non-uniform and uniform generation were later introduced by Li, Raman, and Tewari (2025), and a noisy model was introduced by Raman and Raman (2025), which allows the adversary to insert extraneous strings. A natural question in the noisy model is to quantify the effect of noise, by studying the impact of each additional extraneous string. We show two complementary results in this setting. We first show that for both uniform and non-uniform generation, a single noisy string strictly reduces the set of collections that can be generated, thus answering an open question in Raman and Raman (2025). Then, we show for both uniform and non-uniform generation that generation with a single noisy string is equivalent to generation with any finite amount of noise, sharply contrasting with the strict hierarchy for noisy generation in the limit shown by Bai, Panigrahi, and Zhang (2026). Finally, we leverage our previous results to provide the first known characterization for non-uniform noise-dependent generatability.