  Multimodal fusion emerges as an appealing technique to improve model
performances on many tasks. Nevertheless, the robustness of such fusion methods
is rarely involved in the present literature. In this paper, we propose a
training-free robust late-fusion method by exploiting conditional independence
assumption and Jacobian regularization. Our key is to minimize the Frobenius
norm of a Jacobian matrix, where the resulting optimization problem is relaxed
to a tractable Sylvester equation. Furthermore, we provide a theoretical error
bound of our method and some insights about the function of the extra modality.
Several numerical experiments on AV-MNIST, RAVDESS, and VGGsound demonstrate
the efficacy of our method under both adversarial attacks and random
corruptions.
