Point Cloud Synthesis Using Inner Product Transforms

Ernst Röell; Bastian Rieck

NeurIPS 2025poster0 citations

Point Cloud Synthesis Using Inner Product Transforms

Abstract

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.

Topological Data AnalysisTDATopologyTopological Deep LearningGeometric Deep Learning

BibTeX

@inproceedings{
roell2025point,
title={Point Cloud Synthesis Using Inner Product Transforms},
author={Ernst R{\"o}ell and Bastian Rieck},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=pceKiO7cEr}
}