EuLearn: A 3D database for learning Euler characteristics

TL;DR

EuLearn introduces a diverse 3D surface dataset with varying topologies to improve machine learning models' ability to recognize topological features, addressing current limitations in genus classification.

Contribution

The paper presents EuLearn, a novel 3D dataset with diverse topologies, and develops new non-Euclidean sampling and architecture adaptations to enhance topological feature learning.

Findings

Standard neural networks perform poorly on genus classification.

Non-Euclidean sampling improves model performance.

Topology-aware architectures outperform vanilla models.

Abstract

We present EuLearn, the first surface datasets equitably representing a diversity of topological types. We designed our embedded surfaces of uniformly varying genera relying on random knots, thus allowing our surfaces to knot with themselves. EuLearn contributes new topological datasets of meshes, point clouds, and scalar fields in 3D. We aim to facilitate the training of machine learning systems that can discern topological features. We experimented with specific emblematic 3D neural network architectures, finding that their vanilla implementations perform poorly on genus classification. To enhance performance, we developed a novel, non-Euclidean, statistical sampling method adapted to graph and manifold data. We also introduce adjacency-informed adaptations of PointNet and Transformer architectures that rely on our non-Euclidean sampling strategy. Our results demonstrate that incorporating topological information into deep learning workflows significantly improves performance on these otherwise challenging EuLearn datasets.