EuLearn: A 3D database for learning Euler characteristics
This work addresses the challenge of topological feature recognition in 3D data for machine learning researchers, though it appears incremental as it builds on existing architectures with adaptations.
The authors tackled the problem of training machine learning systems to discern topological features by introducing EuLearn, the first 3D database equitably representing diverse topological types, and found that incorporating topological information significantly improves performance on these datasets.
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.