UniFast-HGR: Scalable and Efficient Maximal Correlation for Multimodal Models

This paper presents UniFast-HGR, a scalable surrogate for Hirschfeld--Gebelein--Rényi (HGR) maximal correlation in high-dimensional multimodal learning. The method replaces explicit covariance whitening with centered and $\ell_2$-normalized cosine alignment, rewrites the covariance interaction in local-batch Gram space, and removes invariant diagonal self-correlation through Trivial Spectrum Suppression (TSS). This reformulation preserves the standardized dependence-maximization target of HGR-style learning while replacing the finite-sample whitening estimator with a differentiable local-batch objective whose dominant structural cost is $O(m^2K)$ for local batch size $m$ and feature dimension $K$. OptFast-HGR further reduces the practical memory burden by estimating the off-diagonal structural term through stochastic projection. Experiments across retrieval, image classification, remote sensing segmentation, and multimodal emotion recognition show consistent gains over covariance-based HGR/CCA variants and contrastive or neural MI-estimator objectives on strong multimodal backbones, while microbenchmarks confirm stable behavior at extreme feature dimensions.