Large language models (LLMs) achieved great success in multiple application domains and attracted huge attention from different research communities recently. Unfortunately, even for the best LLM, there still exist many faults that LLM cannot correctly predict. Such faults will harm the usability of LLMs. How to quickly reveal them in LLMs is important, but challenging. The reasons are twofold, 1) the heavy labeling effort for preparing the test data, and 2) accessing closed-source LLMs such as GPT4 is money-required. To handle this problem, in the traditional deep learning testing field, test selection methods have been proposed for efficiently testing deep learning models by prioritizing faults. However, the usefulness of these methods on LLMs is unclear and under exploration. In this paper, we first study the effectiveness of existing fault detection methods for LLMs. Experimental results on four different tasks~(including both code tasks and natural language processing tasks) and four LLMs (e.g., LLaMA and GPT4) demonstrated that existing fault detection methods cannot perform well on LLMs (e.g., seven out of eight methods perform worse than random selection on LLaMA). To enhance existing fault detection methods, we propose MuCS, a prompt Mutation-based prediction Confidence Smoothing method for LLMs. Concretely, we mutate the prompts and compute the average prediction confidence of all mutants as the input of fault detection methods. The results show that our proposed solution significantly enhances existing methods with the improvement of test relative coverage by up to 97.64%.

The reliable operation of automatic systems is heavily dependent on the ability to detect faults in the underlying dynamical system. While traditional model-based methods have been widely used for fault detection, data-driven approaches have garnered increasing attention due to their ease of deployment and minimal need for expert knowledge. In this paper, we present a novel principal component analysis (PCA) method that uses occupation kernels. Occupation kernels result in feature maps that are tailored to the measured data, have inherent noise-robustness due to the use of integration, and can utilize irregularly sampled system trajectories of variable lengths for PCA. The occupation kernel PCA method is used to develop a reconstruction error approach to fault detection and its efficacy is validated using numerical simulations.