This paper presents an end-to-end multi-modal learning approach for monocular Visual-Inertial Odometry (VIO), which is specifically designed to exploit sensor complementarity in the light of sensor degradation scenarios. The proposed network makes use of a multi-head self-attention mechanism that learns multiplicative interactions between multiple streams of information. Another design feature of our approach is the incorporation of the model uncertainty using scalable Laplace Approximation. We evaluate the performance of the proposed approach by comparing it against the end-to-end state-of-the-art methods on the KITTI dataset and show that it achieves superior performance. Importantly, our work thereby provides an empirical evidence that learning multiplicative interactions can result in a powerful inductive bias for increased robustness to sensor failures.