Verifying the provenance of content is crucial to the function of many organizations, e.g., educational institutions, social media platforms, firms, etc. This problem is becoming increasingly difficult as text generated by Large Language Models (LLMs) becomes almost indistinguishable from human-generated content. In addition, many institutions utilize in-house LLMs and want to ensure that external, non-sanctioned LLMs do not produce content within the institution. In this paper, we answer the following question: Given a piece of text, can we identify whether it was produced by LLM $A$ or $B$ (where $B$ can be a human)? We model LLM-generated text as a sequential stochastic process with complete dependence on history and design zero-shot statistical tests to distinguish between (i) the text generated by two different sets of LLMs $A$ (in-house) and $B$ (non-sanctioned) and also (ii) LLM-generated and human-generated texts. We prove that the type I and type II errors for our tests decrease exponentially in the text length. In designing our tests, we derive concentration inequalities on the difference between log-perplexity and the average entropy of the string under $A$. Specifically, for a given string, we demonstrate that if the string is generated by $A$, the log-perplexity of the string under $A$ converges to the average entropy of the string under $A$, except with an exponentially small probability in string length. We also show that if $B$ generates the text, except with an exponentially small probability in string length, the log-perplexity of the string under $A$ converges to the average cross-entropy of $B$ and $A$. Lastly, we present preliminary experimental results to support our theoretical results. By enabling guaranteed (with high probability) finding of the origin of harmful LLM-generated text with arbitrary size, we can help fight misinformation.

本研究针对识别由大型语言模型（LLMs）生成的文本是否由特定模型或人类创作的挑战，提出了一种零-shot统计检验的方法。这一新颖的思路通过建立文本的顺序随机过程模型，并证明了检验的错误率随文本长度指数下降，展示了在识别危害性LLM生成内容方面的重要潜在影响。

谁写的？基于有限样本集中不等式的零-shot统计检验用于LLM生成文本检测