Repeated Sequences Reveal Gaps between Large Language Models and Natural Language

Evaluating whether large language models (LLMs) capture the structure of natural language beyond local fluency remains an open challenge. Existing evaluation methods, largely based on task performance or short-context behavior, provide limited insight into the long-range statistical organization of generated text. We propose a complementary evaluation framework based on repeated subsequences. By analyzing their distribution across scales and relating it to higher-order R'enyi entropies, we probe how texts reuse previously established structure under finite-length conditions. Experiments on human-written texts and length-matched GPT-generated texts show that, while power-law models can describe restricted ranges of block length, the observed entropy growth is often equally or better characterized by logarithmic--power forms. Across datasets, natural language exhibits stable entropy-growth patterns over accessible ranges, with consistent average behavior despite variability across individual texts. In contrast, GPT-generated texts show systematic and statistically significant shifts in estimated exponents with model size. These results demonstrate that repeated-subsequence entropy provides a quantitative structural diagnostic that reveals systematic differences in long-range organization, distinguishing natural language from state-of-the-art LLM outputs beyond surface-level fluency.