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

A stochastic Gumbel-Top-K router defines, for every token of a mixture-of-experts (MoE) model, a routing law: a distribution over ordered expert lists and mixture weights. We ask which 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, 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 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.

Towards Diverse and Comprehensive Benchmarks for Mutual Information Estimation

Mutual information (MI) estimation is a central problem in machine learning and statistics; however, existing benchmarks typically evaluate estimators on simplified, low-dimensional distributions, leaving their performance on complex, realistic data largely unexplored. We address this gap with a comprehensive benchmarking framework grounded in a unified copula-theoretic perspective that subsumes existing benchmarks as special cases. Within this framework, we propose two complementary families of tests: a copula-first family that systematically varies ground-truth MI, dimensionality, and marginal complexity using synthetic and flow-based transformations; and a marginals-first family that couples real-world image data with controlled dependency structures, extending the classic same-class-pairing paradigm. We use this suite to extensively evaluate three classes of estimators: non-parametric, discriminative, and generative. Contrary to prevailing assumptions, our results indicate that there is no universal winner: each category can systematically outperform all other estimators under specific setups. By analyzing these cases, we identify fundamental estimation barriers and propose new tests that more effectively stress these specific limitations. We share the open source code at https://github.com/VanessB/mutinfo.

BSTabDiff: Block-Subunit Diffusion Priors for High-Dimensional Tabular Data Generation

High-Dimensional Low-Sample Size (HDLSS) tabular domains (e.g., omics) are characterized by $n \ll m$, where $n$ = number of samples, and $m$ = number of features. Such domains often exhibit strong local correlation groups, sparse cross-group dependencies, heavy-tailed non-Gaussian marginals, heteroscedastic noise, and structured missingness, making direct density learning in $\mathbb{R}^m$ ill-conditioned since $n \ll m$. We propose BSTabDiff, a block-subunit generative framework that partitions the $m$ observed features into $M$ latent blocks ($M \ll m$) and generates each block via a shared low-dimensional subunit variable, concentrating global dependence learning in the compact block-latent space $\mathbb{R}^M$ while decoding to the full feature space with copula-driven dependence, flexible per-feature marginals, and explicit missingness mechanisms. BSTabDiff supports modern deep priors on block latents, including diffusion and normalizing flows, enabling stable synthesis and controllable benchmark generation in the HDLSS regime. Empirically, BSTabDiff produces more realistic and stable high-dimensional synthetic data when compared with unstructured tabular generators on HDLSS data.