Can LLMs capture stable human-generated sentence entropy measures?

Abstract: Predicting upcoming words is a core mechanism of language comprehension and may be quantified using Shannon entropy. There is currently no empirical consensus on how many human responses are required to obtain stable and unbiased entropy estimates at the word level. Moreover, LLMs are increasingly used as substitutes for human norming data, yet their ability to reproduce stable human entropy remains unclear. Here, we address both issues using two large publicly available cloze datasets in German 1 and English 2. We implemented a bootstrap-based convergence analysis that tracks how entropy estimates stabilize as a function of sample size. Across both languages, more than 97% of sentences reached stable entropy estimates within the available sample sizes. 90% of sentences converged after 111 responses in German and 81 responses in English, while low-entropy sentences (<1) required as few as 20 responses and high-entropy sentences (>2.5) substantially more. These findings provide the first direct empirical validation for common norming practices and demonstrate that convergence critically depends on sentence predictability. We then compared stable human entropy values with entropy estimates derived from several LLMs, including GPT-4o, using both logit-based probability extraction and sampling-based frequency estimation, GPT2-xl/german-GPT-2, RoBERTa Base/GottBERT, and LLaMA 2 7B Chat. GPT-4o showed the highest correspondence with human data, although alignment depended strongly on the extraction method and prompt design. Logit-based estimates minimized absolute error, whereas sampling-based estimates were better in capturing the dispersion of human variability. Together, our results establish practical guidelines for human norming and show that while LLMs can approximate human entropy, they are not interchangeable with stable human-derived distributions.