Does a Large Language Model Really Speak in Human-Like Language?

Large Language Models (LLMs) have recently emerged, attracting considerable attention due to their ability to generate highly natural, human-like text. This study compares the latent community structures of LLM-generated text and human-written text within a hypothesis testing procedure. Specifically, we analyze three text sets: original human-written texts ($\mathcal{O}$), their LLM-paraphrased versions ($\mathcal{G}$), and a twice-paraphrased set ($\mathcal{S}$) derived from $\mathcal{G}$. Our analysis addresses two key questions: (1) Is the difference in latent community structures between $\mathcal{O}$ and $\mathcal{G}$ the same as that between $\mathcal{G}$ and $\mathcal{S}$? (2) Does $\mathcal{G}$ become more similar to $\mathcal{O}$ as the LLM parameter controlling text variability is adjusted? The first question is based on the assumption that if LLM-generated text truly resembles human language, then the gap between the pair ($\mathcal{O}$, $\mathcal{G}$) should be similar to that between the pair ($\mathcal{G}$, $\mathcal{S}$), as both pairs consist of an original text and its paraphrase. The second question examines whether the degree of similarity between LLM-generated and human text varies with changes in the breadth of text generation. To address these questions, we propose a statistical hypothesis testing framework that leverages the fact that each text has corresponding parts across all datasets due to their paraphrasing relationship. This relationship enables the mapping of one dataset's relative position to another, allowing two datasets to be mapped to a third dataset. As a result, both mapped datasets can be quantified with respect to the space characterized by the third dataset, facilitating a direct comparison between them. Our results indicate that GPT-generated text remains distinct from human-authored text.