## 1 Introduction  
Text classification [1; 2] is a fundamental and crucial part of the NLP community. With the growth of deep neural networks, researchers have begun to focus on how to extend good classification performance to scenarios with only a small amount of labeled data. Inspired by the advances of few-shot learning in CV [3; 4], many studies [5; 6] have leveraged the meta-learning based framework to tackle few-shot text classification (FSTC). [PERSON] et al. [7] proposed a self-attention based encoder and a mutual information based loss function to obtain high-quality prototype representation. [PERSON] et al. [8] proposed a data augmentation algorithm, which randomly generates instances within the smallest enclosing ball, to promote meta-learning methods. Unlike methods that learn directly from words, [PERSON] et al. [9] proposed DS-FSL, which learns word importance via distributional signatures of texts. Distributional signatures mean characteristics of text distribution. A well-known instance of using these signatures is TF-IDF, which models the weights of words by their frequencies--a kind of explicit distributional signatures. These characteristics of text distribution imply underlying semantic knowledge, and their behaviors are consistent across classes. [PERSON] et al. [9] suggest that learning from distributional signature is much more effective to generalize across different classes than directly learning from words. However, the above approaches follow the in-domain setting. This setting assumes that the meta-training and meta-testing data are in the same data distribution, which is not feasible in real-world applications. Consequently, some researchers have begun to extend FSTC to a cross-domain setting. [PERSON] et al. [10] presented cross-domain few-shot text classification (CD-FSTC). In CD-FSTC, meta-training is conducted on one dataset in a single domain, and meta-testing on another in a different domain. [PERSON] et al. [11] supposed that a meta-training dataset with only a single domain in CD-FSTC limits the generalization ability of the model, and proposed domain-generalized few-shot text classification (DG-FSTC). DG-FSTC replaces the single-domain dataset with a multi-domain dataset as the base dataset for meta-training. The meta-learning framework enables models to learn how to learn across different domains. Compared with conventional FSTC and CD-FSTC, DG-FSTC effectively improves the domain adaptability of the model, and is much closer to real application scenarios. Currently, the DG-FSTC problem is still challenging for previous FSTC methods. Directly applying the FSTC methods to DG-FSTC will inevitably suffer from performance degradation. This is because the feature distribution changes significantly as the domain varies. The distribution variation makes those methods that learn directly from words struggle to capture discriminative features in specific domains under a domain shift. Therefore, we attempt to enhance the domain adaptability of the model by utilizing features that reflect specific domain information, such as distributional signatures. We find that in multi-domain data, the distributional signatures of different domains are highly domain-related. As shown in Figure 1, we utilize word frequency, an explicit distributional signature, to estimate word importance. The results show that, in a specific domain, the most informative words are highly domain-related. For instance, in travel domain, 'flight' and 'translate' are two of the most informative words. In a nutshell, the distributional signatures of texts are solid and annotation-free to reflect the word importance in specific domains. Consequently, this study introduces the distributional signature to solve DG-FSTC problem and propose a model based on Multi-level Distributional Signatures, namely MultiDS.