# EuLearn: A 3D database for learning Euler characteristics

arXiv: https://arxiv.org/abs/2505.13539 · HTML: https://mlsanity.com/paper/2505.13539/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 78 references that are in the map.
- First posted on arXiv 18 May 2025.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Datasheets for Datasets](https://mlsanity.com/paper/1803.09010/) (2018)
- [What Does BERT Look At? An Analysis of BERT's Attention](https://mlsanity.com/paper/1906.04341/) (2019)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [Point-BERT: Pre-training 3D Point Cloud Transformers with Masked Point Modeling](https://mlsanity.com/paper/2111.14819/) (2021)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [A Survey of Visual Transformers](https://mlsanity.com/paper/2111.06091/) (2021)
- [MeshNet: Mesh Neural Network for 3D Shape Representation](https://mlsanity.com/paper/1811.11424/) (2018)
- [Shape Completion Enabled Robotic Grasping](https://mlsanity.com/paper/1609.08546/) (2016)
- [Transformers in 3D Point Clouds: A Survey](https://mlsanity.com/paper/2205.07417/) (2022)
- [SimJEB: Simulated Jet Engine Bracket Dataset](https://mlsanity.com/paper/2105.03534/) (2021)
- [Euler Characteristic Tools For Topological Data Analysis](https://mlsanity.com/paper/2303.14040/) (2023)
- [EdgeConv with Attention Module for Monocular Depth Estimation](https://mlsanity.com/paper/2106.08615/) (2021)
- [Neural Poisson Surface Reconstruction: Resolution-Agnostic Shape Reconstruction from Point Clouds](https://mlsanity.com/paper/2308.01766/) (2023)

## Built on by (most cited first, 1 of 1)

- [FILTR: Extracting Topological Features from Pretrained 3D Models](https://mlsanity.com/paper/2604.22334/) (2026)

## Abstract (arXiv)

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.