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

This paper presents UniFast-HGR, a scalable surrogate for Hirschfeld--Gebelein--R\'enyi (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.

Many AI systems need to learn from several kinds of information at the same time, such as images, text, audio, or satellite data. A key challenge is to find what these sources truly share, while ignoring noise or details that only appear in one source. Existing methods that measure such shared information can be powerful, but they often become too expensive or unstable when used in modern large models. This paper introduces a simpler training method that keeps the useful idea of measuring shared dependence, but avoids the costly calculations that usually make it hard to scale. It also removes unhelpful self-comparisons that can dominate the training signal. A faster version further reduces memory use for large batches. Experiments on image recognition, text-image and video-text retrieval, remote-sensing segmentation, and emotion recognition show that the method improves accuracy while remaining efficient for very large feature dimensions.