语言生成中的幻觉率

中文摘要 AI 辅助

语言生成极限是Kleinberg和Mullainathan引入的优雅模型，用于研究仅基于示例字符串学习的算法的语言生成。在该模型中，若算法在有限时间后不再出错，则称其能从一种语言中正确生成。然而，实际中即使复杂语言模型也常产生幻觉。本文研究有（无限）幻觉的语言生成极限，即算法可能无限次生成错误字符串，但错误以有限速率出现。首先表明，即使幻觉率为0，也使极限生成更强大，存在有限错误无法生成但无限错误可生成的语言集合。还展示了由幻觉率表征的语言集合严格层次结构，该层次结构扩展到生成目标语言的比例。最后研究无重复的极限生成，再次证明在各幻觉率和比例下的严格层次结构。这些结果揭示了有幻觉的极限语言生成集合的丰富结构，并确立幻觉率为语言生成理论研究的重要参数。

英文摘要

Language generation in the limit is an elegant model introduced by Kleinberg and Mullainathan [KM24] to formally study language generation by an algorithm that learns solely based on example strings. In this model, an algorithm is said to correctly generate from a language if it never makes an error after some finite time. In contrast, even sophisticated language models are known to regularly hallucinate in practice. In this paper, we initiate the study of language generation in the limit with (infinite) hallucination, i.e., the algorithm may generate incorrect strings infinitely often, but the errors occur at a limited rate (possibly even with 0-measure). We first show that hallucination, even at rate 0, makes generation in the limit strictly more powerful: there are language collections that cannot be generated with finite error but can be generated with infinite error, even when errors occur on a 0-measure set of time-steps. Furthermore, while all countable collections are generatable with finite error, we show a strict hierarchy of (uncountable) language collections characterized by the hallucination rate. This hierarchy extends to breadth, the fraction of the target language generated. While all countable collections can attain the optimal breadth of 1/2 [KW26b], we show strict separation at every breadth and hallucination rate. Finally, we study generation in the limit without repetition, where the algorithm may not repeat strings. This lets us compare the sets of correct and incorrect strings generated, rather than the fractions of correct and incorrect time-steps. Once again, we demonstrate a strict hierarchy at every hallucination rate and breadth. Taken together, these results reveal rich structure in language collections generatable in the limit with hallucination and establish hallucination rate as an important parameter in the theoretical study of language generation.

发表机构

• Duke University（杜克大学）

机构由 AI 辅助整理，请以论文原文为准。