Can Hybrid Weight-Space Stochasticity Advance Adversarial Robustness in Multimodal Fusion?

We introduce Hybrid Weight-Space Convolutional Stochasticity (HyWeCS), a unified randomized defense for multimodal fusion that closes the long-standing gap between provable ℓ2 certification and empirical robustness against strong ℓ∞ attacks, while preserving generalization on natural- and medical data. Specifically, we formulate two complementary mechanisms at disjoint weight locations within every filter: Orthogonally Retracted Random-Projection Weights (ORaW) and Stochastic Hybrid-Space Attention-Noise Weights (SHANW), jointly exploiting projection diversity and self-modulated attention noise during training and inference. Reciprocal intermediate cross fusion reuses terminal stochastic weights without a separate feature-space stochastic module, thereby saving computational cost, with parameters and GFLOPs reduced by up to ≈ 60.5% and ≈ 91.1%, respectively. Shared Lipschitz calibration establishes a uniform 2-Lipschitz score bound for formal certification. Across eight multimodal benchmarks, HyWeCS improves certified and empirical robustness by up to ≈ 12.4% and ≈ 12.8%, respectively, over the strongest competing defenses, with improvements persisting under adaptive attacks.