arXiv:2608.19608 2026 Regularization 2 ideas extracted · analyzed Sep 1, 2026
The paper gives an explicit, low-dimensional family of dependence-preserving couplings built from piecewise-linear monotonic surjections (PLMS), together with exact formulas for Kendall's tau, Spearman's rho, and tail dependence. The transferable asset is not the statistical interpretation itself, but the ability to generate pairs of uniform variables with prescribed asymmetric dependence while retaining exact marginals and cheap sampling. These couplings can become differentiable latent-data augmentation layers or dependence-controlled regularizers, avoiding Gaussian-copula assumptions and allowing separate control of concordance and tail behavior. The strongest initial test is a PLMS coupling layer inserted into contrastive or multimodal training and compared against independent, Gaussian, and rank-shuffle augmentations.
Use PLMS endpoint parameters to impose an explicit penalty or constraint on lower- and upper-tail dependence between learned representation coordinates. This targets rare-event co-activation directly, rather than relying on covariance or average correlation to control extreme latent behavior.
Generate pairs of latent variables with exactly uniform marginals but non-Gaussian, asymmetric dependence by applying a randomly chosen PLMS map to one uniform latent coordinate. The coupling can expose a model to controlled concordant, discordant, or piecewise-dependent examples without changing either marginal distribution.