Increased availability of open-source software repositories and recent advances in code analysis using large language models (LLMs) has triggered a wave of new work to automate software engineering tasks that were previously very difficult to automate. In this paper, we investigate a recent line of work that hypothesises that comparing the probability of code generated by LLMs with the probability the current code would have had can indicate potential quality problems. We investigate the association between the cross-entropy of code generated by ten different models (based on GPT2 and Llama2) and the following quality aspects: readability, understandability, complexity, modularisation, and overall maintainability assessed by experts and available in an benchmark dataset. Our results show that, controlling for the number of logical lines of codes (LLOC), cross-entropy computed by LLMs is indeed a predictor of maintainability on a class level (the higher the cross-entropy the lower the maintainability). However, this relation is reversed when one does not control for LLOC (e.g., comparing small classes with longer ones). Furthermore, while the complexity of LLMs affects the range of cross-entropy (smaller models tend to have a wider range of cross-entropy), this plays a significant role in predicting maintainability aspects. Our study limits itself on ten different pretrained models (based on GPT2 and Llama2) and on maintainability aspects collected by Schnappinger et al. When controlling for logical lines of code (LLOC), cross-entropy is a predictor of maintainability. However, while related work has shown the potential usefulness of cross-entropy at the level of tokens or short sequences, at the class level this criterion alone may prove insufficient to predict maintainability and further research is needed to make best use of this information in practice.

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