Stable Spectral Copula Alignment for Robust Multimodal Learning

Multimodal alignment fails under deployment shift because standard objectives entangle cross-modal dependence with marginal-sensitive geometry. Stable Spectral Copula Alignment (SSCA) provides a deployment protocol targeting copula-stable dependence under strictly monotone marginal distortions, with auditable, label-free diagnostics for monitoring and mitigation. SSCA combines (i) clipped soft-rank Gaussianization suppressing marginal effects while tracking tie/approximation errors, (ii) dependence-weighted sliced Wasserstein hub coupling for globally coherent multiway alignment with cycle auditing, and (iii) diagonal-stabilized block-spectral learning with eigengap-normalized Davis--Kahan diagnostics, yielding an actionable subspace-risk inequality. A calibrated gate maps diagnostic proxies to a reliability signal with controlled false-alarm/miss rates, enabling safe activation, budgeted remediation, and conservative fallback for out-of-scope drift. Evaluations on MOSEI/MELD, MSCOCO, and CC3M-500K demonstrate improved performance under perturbation and substantially reduced degradation under both monotone and realistic drifts.