SAGG: Sample-Adaptive Gradient Gating for Robust Multimodal Learning under Heterogeneous Corruption

Multimodal gradient balancing methods modulate encoder gradients with a shared scalar per modality, implicitly assuming that corruption is uniform across the training batch. In practice, corruption is sample-heterogeneous: within a single mini-batch, different samples may have different modalities corrupted. We prove that under this heterogeneous corruption model, any batch-level sample-agnostic linear estimator with a shared modulation parameter incurs an irreducible bias with respect to the clean-data gradient, and that sample-level all-or-nothing gating is the unique unbiased strategy within a natural distribution-free estimator class. Motivated by this result, we propose Sample-Adaptive Gradient Gating (SAGG), which makes a binary retain-or-discard decision per sample via an online feature-norm quality test and incorporates a truncation mechanism for variance control. We prove that SAGG-based SGD converges at the standard O(1/sqrt(T)) rate to stationary points of the clean loss without a corruption-dependent error floor, and derive a certified robustness radius for the independent-encoder architecture that connects per-modality Lipschitz constants to the classification margin. Experiments on Kinetics-Sounds and UCF-101 under Gaussian noise injection, partial modality missing, and natural contribution imbalance show that SAGG consistently outperforms ten existing methods, with the largest gains in high-corruption regimes where batch-level bias is most severe.