LiDAR relocalization plays a crucial role in many fields, including robotics,autonomous driving, and computer vision. LiDAR-based retrieval from a databasetypically incurs high computation storage costs and can lead to globallyinaccurate pose estimations if the database is too sparse. On the other hand,pose regression methods take images or point clouds as inputs and directlyregress global poses in an end-to-end manner. They do not perform databasematching and are more computationally efficient than retrieval techniques. Wepropose HypLiLoc, a new model for LiDAR pose regression. We use two branchedbackbones to extract 3D features and 2D projection features, respectively. Weconsider multi-modal feature fusion in both Euclidean and hyperbolic spaces toobtain more effective feature representations. Experimental results indicatethat HypLiLoc achieves state-of-the-art performance in both outdoor and indoordatasets. We also conduct extensive ablation studies on the framework design,which demonstrate the effectiveness of multi-modal feature extraction andmulti-space embedding. Our code is released at:https://github.com/sijieaaa/HypLiLoc