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Context: In every iteration of the training phase,the computation costsof our proposed methodare mainly fromthe E-step estimation of Q(\cdot) and M-step optimization of \thetawith multi-tasks training.For the E-step,the time complexity is O(|U|mKd) from clustering, where d is the dimensionalityof the embedding and m is themaximum iteration number in clustering (m=20 in this paper).For the M-step,since we have three objectivesto optimize the network f_{\theta}(\cdot),the time complexity is O(3⋅(|U|2d+|U|d2)O(3\cdot(|U|^{2}d+|U|d^{2})italic_O ( 3 ⋅ ( | italic_U | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d + | italic_U | italic_d start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ).The overall complexity is dominated by the term O(3\cdot(|U|^{2}d)),which is 3 times of Transformer-based SR with only next item prediction objective, e.g., SASRec.Fortunately,the model can be effectively parallelized becausef_{\theta} is Transformer and we leave it in future work.In the testing phase,the proposed ICL as wellas the SeqCL objectivesare no longer needed, which yields themodel to have the sametime complexity as SASRec (O(d|V|)).The empirical time spending comparisonsare reported in Sec. 5.2.The convergence of ICL is guaranteedunder the generalized EM framework.Proof is provided in Appendix B.

Question: Does the parallelization of transformer part of the proposed method reduce time complexity effectively?
Logically, yes. Empirically, no.