  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).
