## 1 Introduction  
With the rapid advancement of industrial automation and informatization, fault diagnosis technology increasingly plays a pivotal role in ensuring the reliable operation of equipment and the safety of industrial systems [1]. Particularly in complex industrial environments, such as chemical, manufacturing, and energy sectors, the ability to accurately and swiftly identify and address faults is key to enhancing production efficiency and preventing accidents [2; 3; 4]. The recent surge in big data and Internet of Things (IoT) technologies has catalyzed the extensive deployment of sensors in industrial systems, resulting in a massive influx of data [5; 6]. This data serve not only to record the operational status of equipment, but also to offer unparalleled opportunities for fault diagnosis. However, the high reliability of industrial equipment renders fault data relatively rare in comparison with data from normal operations, leading to a significant data imbalance, particularly in the context of few-shot fault diagnosis [7; 8]. Given these circumstances, traditional machine learning and deep learning methods, which generally depend on abundant labeled data to train effective models, face substantial challenges [9; 10; 11; 12]. Consequently, investigating potent few-shot learning techniques capable of accurately diagnosing faults in data-scarce environments has emerged as a crucial research area in industrial intelligence. In the realm of few-shot learning, notable advancements and representative technologies or papers have emerged, particularly for addressing challenges in data-scarceenvironments. Methods such as data augmentation [13], synthetic data generation [14], transfer learning [15], self-supervised learning [16], and meta-learning [17] have been instrumental. These methods have demonstrated success in various fields, including object detection, image segmentation, and image classification, subsequently influencing fault diagnosis practices. Focusing on the domain of fault diagnosis, few-shot learning has seen significant technological progress. Data augmentation techniques, particularly sampling methods and synthetic data generation, have been primarily employed to enhance fault data. Research in the field of rolling bearing fault diagnosis has shown that the use of compressed sensing for limited fault data augmentation can significantly improve diagnostic accuracy [18]. Furthermore, several studies have demonstrated that combining data augmentation with deep learning can effectively diagnose faults in rotating machinery [19; 20], thereby enhancing both the precision and robustness of the diagnosis. Beyond data augmentation, alterations in model architecture have shown promise. Noteworthy among these is the development of a novel bidirectional gated recurrent unit (BGRU) for effective and efficient fault diagnosis [21]. Additionally, research has introduced few-shot fault diagnosis methods based on attention mechanisms, utilizing spectral kurtosis filtering and particle swarm optimization in conjunction with stacked sparse autoencoders [22]. The Siamese neural network, which learns through sample pair comparisons, is another innovative approach to the few-shot problem [23]. Transfer learning has played a significant role in enhancing the efficiency and accuracy of machine fault diagnosis, especially in cases where there are a scarcity of labeled data or low-precision sensors are utilized for data collection. Transfer learning has played a significant role in enhancing the efficiency and accuracy of machine fault diagnosis, especially in cases where there is a scarcity of labeled data or low-precision sensors are utilized for data collection [24; 25]. However, these methods often require retraining the entire network for new tasks, limiting their practical adaptability in industrial settings. Additionally, varying operational conditions in practical engineering can diminish the effectiveness of these diagnostic methods under new circumstances.