# Challenges in 3D Data Synthesis for Training Neural Networks on Topological Features

arXiv: https://arxiv.org/abs/2511.04972 · HTML: https://mlsanity.com/paper/2511.04972/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 19 references that are in the map.
- First posted on arXiv 7 Nov 2025.

## Builds on (most cited first, 6 of 6)

- [3DCTN: 3D Convolution-Transformer Network for Point Cloud Classification](https://mlsanity.com/paper/2203.00828/) (2022)
- [RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds](https://mlsanity.com/paper/2202.01725/) (2022)
- [PI-Net: A Deep Learning Approach to Extract Topological Persistence Images](https://mlsanity.com/paper/1906.01769/) (2019)
- [A persistent homology approach to heart rate variability analysis with an application to sleep-wake classification](https://mlsanity.com/paper/1908.06856/) (2019)
- [Repulsive Surfaces](https://mlsanity.com/paper/2107.01664/) (2021)
- [Synthetic Data Generation and Deep Learning for the Topological Analysis of 3D Data](https://mlsanity.com/paper/2309.16968/) (2023)

## Abstract (arXiv)

Topological Data Analysis (TDA) involves techniques of analyzing the underlying structure and connectivity of data. However, traditional methods like persistent homology can be computationally demanding, motivating the development of neural network-based estimators capable of reducing computational overhead and inference time. A key barrier to advancing these methods is the lack of labeled 3D data with class distributions and diversity tailored specifically for supervised learning in TDA tasks. To address this, we introduce a novel approach for systematically generating labeled 3D datasets using the Repulsive Surface algorithm, allowing control over topological invariants, such as hole count. The resulting dataset offers varied geometry with topological labeling, making it suitable for training and benchmarking neural network estimators. This paper uses a synthetic 3D dataset to train a genus estimator network, created using a 3D convolutional transformer architecture. An observed decrease in accuracy as deformations increase highlights the role of not just topological complexity, but also geometric complexity, when training generalized estimators. This dataset fills a gap in labeled 3D datasets and generation for training and evaluating models and techniques for TDA.