构建可控制拓扑特征的3D合成数据集，用于训练神经网络估计曲面复杂度。
Challenges in 3D Data Synthesis for Training Neural Networks on Topological Features
- 用排斥表面算法生成可控孔洞数的3D标签数据
- 模型在几何形变增大时准确率下降，揭示几何复杂性影响学习效果
- 适合研究拓扑数据分析中神经网络泛化能力的研究者
拓扑数据分析（TDA）通过分析数据的结构与连通性来揭示深层模式。传统方法如持久同调计算成本高，促使基于神经网络的估算器发展以降低计算开销和推理时间。然而，当前主要障碍在于缺乏专为有监督学习设计、具备类别分布与多样性标注的3D数据集。为此，本文提出一种新方法，利用排斥表面算法系统生成3D数据集，可调控拓扑不变量（如孔洞数量）。该数据集包含多样几何形态并带有拓扑标签，适用于训练与评估神经网络估算器。本研究使用该合成数据集训练了一个基于3D卷积变换器架构的亏格估算网络。实验发现，随着形变程度增加，模型准确率下降，表明在训练通用估算器时，不仅拓扑复杂性，几何复杂性同样起关键作用。该数据集填补了有标签3D数据生成与训练评估在TDA领域的空白。
原文摘要 · Abstract (English)
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.
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