Hierarchical Copula-Gumbel-Top-\texorpdfstring{$K$}{K} Routing: Two-Sided Dependence Control for Frozen Mixture-of-Experts at Fixed Per-Token Routing Laws

arXiv:2607.28670v1 Announce Type: new Abstract: A stochastic Gumbel-Top-$K$ router defines, for every token of a mixture-of-experts (MoE) model, a \emph{routing law}: a distribution over ordered expert lists and mixture weights. We ask which \emph{joint} distributions over the routing choices of different tokens are reachable while every individual token's complete routing law is held exactly fixed. We give a two-sided construction, \emph{Hierarchical Copula-Gumbel-Top-$K$} (\CGA{}). Within a gr...