Point Cloud Synthesis Using Inner Product Transforms

Ernst Röell, Bastian Rieck

Keywords: Topological Data Analysis, TDA, Topology, Topological Deep Learning, Geometric Deep Learning

TL;DR: We develop a differentiable, invertible geometrical-topological encoding of point clouds based on inner products.

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.

Primary Area: Deep learning (e.g., architectures, generative models, optimization for deep networks, foundation models, LLMs)

Submission Number: 16988