Abstract—There was significant recent progress in the field of deep learning, which has led to compelling advances in most tasks of semantic computer vision (e.g., classification, detection, and segmentation). Point cloud registration is a problem in which two or more different point clouds are aligned by estimation of the relative geometric transformation between them. This well-known problem plays an important role in many applications such as SLAM, 3D reconstruction, mapping, positioning, and localization. The complexity of the point cloud registration increases due to the difficulty of feature extraction related to a large difference in the appearances of a single object obtained by a laser scanner from different points of view. Millions of points created every second require high-efficiency algorithms and powerful computing devices. The well-known ICP algorithm for point cloud registration and its variants have relatively high computational efficiency, but are known to be immune to local minima and, therefore, rely on the quality of the initial rough alignment. Algorithm operation with the interference caused by noisy points on dynamic objects is usually critical for obtaining a satisfactory estimate, especially when using real LiDAR data. In this study, we propose a neural network algorithm to solve the problem of point cloud registration by estimating the soft alignment of the points of the source and target point clouds. The proposed algorithm efficiently works with incongruent noisy point clouds generated by LiDAR. Results of computer simulation are presented to illustrate the efficiency of the proposed algorithm.