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

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--> [Submitted on 25 Jul 2026] Title:Hierarchical Copula-Gumbel-Top-\texorpdfstring{$K$}{K} Routing: Two-Sided Dependence Control for Frozen Mixture-of-Experts at Fixed Per-Token Routing Laws View a PDF of the paper titled Hierarchical Copula-Gumbel-Top-\texorpdfstring{$K$}{K} Routing: Two-Sided Dependence Control for Frozen Mixture-of-Experts at Fixed Per-Token Routing Laws, by Richard Yi Da Xu View PDF HTML (experimental) 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 group of related tokens, an exchangeable Gaussian copula positively correlates the Gumbel perturbations at each expert coordinate, which can increase within-group expert-set coherence. Across disjoint pairs of groups, a tunable antithetic construction introduces a selectable amount of negative dependence. We prove that both operations leave each token's ordered Top-$K$ sample, mixture weights, and inclusion probabilities identical in distribution to independent routing \emph{at a routing layer conditioned on its pre-routing logits}; conditional expected expert traffic is preserved as a consequence. We characterize the resulting trade-off: positive within-group coupling can only inflate the variance of realized expert loads relative to independent routing, while nonnegative cross-group opposition can only reduce it relative to flat coupling at the same within-group strength. Coherence and load dispersion are thus controlled by two complementary dependence dials on the invariance constraint surface. Because the base model is untouched, the dials can be driven by a small controller over frozen features, trainable with a score-function estimator: the frozen network is evaluated only in the forward direction, and gradients are confined to the controller. An initial small-scale pilot validates the mechanism and the training route, but does not establish task-level fine-tuning gains. Subjects: Machine Learning (cs.LG) Cite as: arXiv:2607.28670 [cs.LG] (or arXiv:2607.28670v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2607.28670 arXiv-issued DOI via DataCite (pending registration) Submission history From: Richard Yi Da Xu Professor [view email] [v1] Sat, 25 Jul 2026 12:43:47 UTC (20 KB) Full-text links: Access Paper: View a PDF of the paper titled Hierarchical Copula-Gumbel-Top-\texorpdfstring{$K$}{K} Routing: Two-Sided Dependence Control for Frozen Mixture-of-Experts at Fixed Per-Token Routing Laws, by Richard Yi Da Xu View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-07 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)