Quantifying Noise in Language Generation

2026-01-29

AI Summary

This study investigates the impact of adversarial noise—specifically, inserted irrelevant strings—on the generative capacity of formal language systems, with a focus on whether a single noise string can strictly reduce the class of generable languages. Leveraging formal language theory, computational learning theory, and adversarial enumeration models, the work employs constructive proofs and reduction techniques to establish, for the first time, that even a single adversarial noise string suffices to strictly shrink the set of generable languages. Moreover, it demonstrates the equivalence in generative power between a single noise and any finite collection of noises, thereby resolving an open problem posed by Raman and Raman (2025). The paper also provides the first complete characterization of generability under non-uniform noise dependencies, transcending existing hierarchical frameworks of noise tolerance.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Natural Language Processing: Generation
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• language generation
• noise
• adversarial strings
• generatability
• formal language theory

Innovation

• noisy language generation
• uniform generation
• non-uniform generation
• noise robustness
• generatability characterization