Product quantization is a key strategy in compact dictionary learning for the transmission of 3D point clouds, producing quantization codes of varying lengths. This paper presents a moment-preserving thresholding neural network designed to expedite dictionary learning for progressive 3D point cloud compression. The proposed moment-preserving product quantization neural network (MPPQNet) allows for simultaneous training across different code lengths without additional coding or transmission costs. By progressively refining 3D models, we optimize similarity ranking, enhancing reconstruction quality and generating efficient quantization codes. Experimental results demonstrate that our approach outperforms state-of-the-art methods in search accuracy for 3D point cloud compression.