Cross-domain sequential recommendation (CDSR) aims to address the data sparsity problems that exist in traditional sequential recommendation (SR) systems. The existing approaches aim to design a specific cross-domain unit that can transfer and propagate information across multiple domains by relying on overlapping users with abundant behaviors. However, in real-world recommender systems, CDSR scenarios usually consist of a majority of long-tailed users with sparse behaviors and cold-start users who only exist in one domain. This leads to a drop in the performance of existing CDSR methods in the real-world industry platform. Therefore, improving the consistency and effectiveness of models in open-world CDSR scenarios is crucial for constructing CDSR models (\textit{1st} CH). Recently, some SR approaches have utilized auxiliary behaviors to complement the information for long-tailed users. However, these multi-behavior SR methods cannot deliver promising performance in CDSR, as they overlook the semantic gap between target and auxiliary behaviors, as well as user interest deviation across domains (\textit{2nd} CH).
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