In multimodal learning, dominant modalities often overshadow others, limiting generalization. We propose Modality-Aware Sharpness-Aware Minimization (M-SAM), a model-agnostic framework that applies to many modalities and supports early and late fusion scenarios. In every iteration, M-SAM in three steps optimizes learning. \textbf{First, it identifies the dominant modality} based on modalities' contribution in the accuracy using Shapley. \textbf{Second, it decomposes the loss landscape}, or in another language, it modulates the loss to prioritize the robustness of the model in favor of the dominant modality, and \textbf{third, M-SAM updates the weights} by backpropagation of modulated gradients. This ensures robust learning for the dominant modality while enhancing contributions from others, allowing the model to explore and exploit complementary features that strengthen overall performance. Extensive experiments on four diverse datasets show that M-SAM outperforms the latest state-of-the-art optimization and gradient manipulation methods and significantly balances and improves multimodal learning.

Recent studies on deep neural networks show that flat minima of the loss landscape correlate with improved generalization. Sharpness-aware minimization (SAM) efficiently finds flat regions by updating the parameters according to the gradient at an adversarial perturbation. The perturbation depends on the Euclidean metric, making SAM non-invariant under reparametrizations, which blurs sharpness and generalization. We propose Monge SAM (M-SAM), a reparametrization invariant version of SAM by considering a Riemannian metric in the parameter space induced naturally by the loss surface. Compared to previous approaches, M-SAM works under any modeling choice, relies only on mild assumptions while being as computationally efficient as SAM. We theoretically argue that M-SAM varies between SAM and gradient descent (GD), which increases robustness to hyperparameter selection and reduces attraction to suboptimal equilibria like saddle points. We demonstrate this behavior both theoretically and empirically on a multi-modal representation alignment task.