However,existing algorithms lack universality in the sense that they can only handle one type of convex functions and need apriori knowledge of parameters.

Our initial investigation identifies which distributions accurately characterize the feature space, subsequently leveraging this priori to guide the alignment of the weakly supervised embeddings. Specifically, we analyze the superiority of the mixture of von Mises-Fisher distributions (moVMF) among several common distribution candidates.

In addition, we examine two common computation frameworks for this problem, i.e., population-based training (PBT) and iterative learning

Numerical experiments are conducted tosupport our theoretical results.

Numerical experiments are conducted tosupport our theoretical results.