Point cloud synthesis, i.e. the generation of novel point clouds from an input distribution, remains a challenging task, for which numerous complex machine learning models have been devised. We develop a novel method that encodes geometrical-topological characteristics of point clouds using inner products, leading to a highly-efficient point cloud representation with provable expressivity properties. Integrated into deep learning models, our encoding exhibits high quality in typical tasks like reconstruction, generation, and interpolation, with inference times orders of magnitude faster than existing methods.
@article{arxiv.2410.18987,
title = {Point Cloud Synthesis Using Inner Product Transforms},
author = {Ernst Röell and Bastian Rieck},
journal= {arXiv preprint arXiv:2410.18987},
year = {2026}
}
Comments
Accepted at the 39th Conference on Neural Information Processing Systems (NeurIPS) 2025. Our code is available at https://github.com/aidos-lab/inner-product-transforms