Detecting sharp features in raw point clouds is an essential step in designing efficient priors in several 3D Vision applications. This paper presents a deep learning-based approach that learns to detect and consolidate sharp feature points on raw 3D point clouds. We devise a multi-task neural network architecture that identifies points near sharp features and predicts displacement vectors toward the local sharp features. The so-detected points are thus consolidated via relocation. Our approach is robust against noise by utilizing a dynamic labeling oracle during the training phase. The approach is also flexible and can be combined with several popular point-based network architectures. Our experiments demonstrate that our approach outperforms the previous work in terms of detection accuracy measured on the popular ABC dataset. We show the efficacy of the proposed approach by applying it to several 3D Vision tasks.