## 1 Introduction
MultiDS utilizes hierarchical distributional signatures to generate knowledge from three aspects, which are domain-agnostic, domain-specific, and class-specific, to improve the classification performance of the model under domain shift. Firstly, we argue that even textual representations of different domains have a kind of general and domain-agnostic  
Figure 1: Word importance estimation on multi-domain data (Clinc150 [12]) using word frequency [13]. We list the top two words for each domain. The darker the color, the more important the word. features. Inspired by pretrained language models, we compute distributional signatures on a large news dataset containing information from multiple domains. The computed distributional signatures are used as the domain-agnostic features. Secondly, since the distributional signatures of different domains indicate specific domain information, we compute distributional signatures from texts of the same domain in each episode. These distributional signatures are treated as the domain-specific features. Thirdly, distributional signatures of different categories also show class-level differences, which can be used to model class-level word importance. In each episode, we calculate the distributional signatures of each class as class-specific features. After obtaining multi-level distributional signatures, we apply neural networks to translate them into word-level attention weights, which is able to help the model focus on informative features in different domains. In addition to utilizing distributional signatures to generate word importance, information indicated by distributional signatures are also beneficial in correcting feature distributions of different domains. Concretely, we think that domain-specific distributional signatures are also beneficial for neural networks to fit the feature distribution of specific domains. Therefore, we fuse domain-specific distributional signatures and word embeddings to generate instance-level calibration vectors. These calibration vectors effectively enable the model to adapt to different feature distributions. MultiDS thus obtains strong domain adaptability based on multi-level distributional signatures. In summary, the main contributions of this study are as follows:  
* We propose a simple yet powerful method based on multi-level distributional signatures to produce high-quality word-level attention values under domain shift. A large news corpus is firstly used to calculate domain-agnostic distributional signatures. Secondly, we compute domain-specific and class-specific distributional signatures from texts of the same domain and category, respectively. As a result, domain-adaptive word-level attentions are derived by translating multi-level distributional signatures using deep neural networks;
* We propose a domain calibration method based on domain-specific distributional signatures. By modeling the domain information indicated by domain-specific distributional signatures, the calibration method generates instance-level calibration vectors that are used to help the model fit the feature distributions of specific domains;
* We conduct extensive experiments on four datasets. The experimental results illustrate that our method outperforms the state-of-the-art method in DG-FSTC by 1.41% on average. Our method achieves the best average performance compared to five competitive baseline methods. Compared with DS-FSL [9], our method achieves an average improvement of 4.79%.