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Extracting point-to-point correspondences from overlapping point clouds is essential for accurate registration of LiDAR point clouds. This task is generally addressed through a four-step pipeline: keypoint detection, keypoint description, descriptor matching, and outlier rejection. A critical step in this process is computing distinctive point descriptors that are robust to noise and occlusions. This study investigates the use of various neural network architectures to learn 3D descriptors and assesses their performance on real-world datasets. We explore different training objectives, including self-supervision, metric learning, and a hybrid approach. The learned descriptors are evaluated on two single-source aerial LiDAR datasets for the ratio of inlier correspondences in point matching. The best-performing model is further tested on a cross-source LiDAR-photogrammetry dataset to evaluate its generalization across sensor modalities. Results showthat metric learning yields superior descriptor quality, and a modified PointNet architecture achieves the highest performance in both single-source and cross-source settings. Future work should prioritize improving generalization to more challenging cross-source matching scenarios.