A Theory of Time-Sensitive Language Generation: Sparse Hallucination Beats Mode Collapse

2026-05-11

AI Summary

This study addresses the challenge of generating high-ranked text promptly under a global string preference ordering while avoiding mode collapse and uncontrolled hallucination. To this end, the authors propose a sparse hallucination mechanism that circumvents impossibility results inherent to traditional consistent generators by allowing the hallucination rate to decay over time. Drawing on formal language theory, preference ranking models, and asymptotic analysis, they design a generator under relaxed consistency conditions and establish theoretical bounds linking timely generation to cutoff functions. The work proves that optimal-density timely generation is achievable under superlinear cutoff functions, whereas it is infeasible under linear cutoffs combined with decaying hallucination rates.

Abstract

We study language generation in the limit under a global preference ordering on strings, as introduced by Kleinberg and Wei. As in [arXiv:2504.14370, arXiv:2511.05295], we aim for \emph{breadth}, but impose an additional requirement of timeliness: higher-ranked strings should be generated earlier. A string is then only credited if it is generated before a deadline, where its deadline is defined by a function that maps a string's rank in the target language to the time by which it must be produced. This is in keeping with a central consideration in machine learning, where inductive bias favors ``simpler'' or ``more plausible'' outputs, all else being equal. We show that timely generation is impossible in a strong sense for eventually consistent generators -- the protagonists of most prior related work. Under what is perhaps the mildest natural relaxation of consistency, a hallucination rate that vanishes over time, we show that we can circumvent our impossibility result. In particular, we can achieve optimal density with respect to any superlinear deadline function. We also show this is tight by ruling out timely generation with linear deadlines and vanishing hallucination rate.

Problem

• time-sensitive generation
• language generation
• global preference ordering
• deadline function
• hallucination rate

Innovation

• time-sensitive generation
• vanishing hallucination rate
• global preference ordering
• deadline function
• mode collapse