We present a vehicle self-localization method using point-based deep neural networks. Our approach processes measurements and point features, i.e. landmarks, from a high-definition digital map to infer the vehicles pose. To learn the best association and incorporate local information between the point sets, we propose an attention mechanism that matches the measurements to the corresponding landmarks. Finally, we use this representation for the point-cloud registration and the subsequent pose regression task. Furthermore, we introduce a training simulation framework that artificially generates measurements and landmarks to facilitate the deployment process and reduce the cost of creating extensive datasets from real-world data. We evaluate our method on our dataset, as well as an adapted version of the Kitti odometry dataset, where we achieve superior performance compared to related approaches; and additionally show dominant generalization capabilities.