首个大规模高阶数据集，助力拓扑深度学习模型评测与改进。
MANTRA: The Manifold Triangulations Assemblage
- 构建包含超43,000个曲面和25万个体积流形三角剖分的数据集。
- 验证高阶模型在拓扑分类任务中优于传统图模型，但仍有局限。
- 适合拓扑机器学习、几何深度学习方向研究者使用。
复杂系统中高阶交互关系的兴起推动了更表达性强的模型发展，尤其在拓扑深度学习（TDL）领域，该领域致力于在单纯复形等高阶域上设计神经网络。然而，该领域的进展受限于缺乏用于基准测试的高质量数据集。为此，我们提出MANTRA，首个大规模、多样且本质高阶的数据集，涵盖超过43,000个曲面和250,000个三维流形的三角剖分。利用MANTRA，我们在三个拓扑分类任务上评估了基于图和单纯复形的多种模型。结果表明，单纯复形神经网络在捕捉简单拓扑不变量方面普遍优于图基模型，但仍存在性能瓶颈，提示需重新思考拓扑深度学习方法。MANTRA为评估和推进拓扑方法提供了重要基准，引领更高效的高阶模型发展。
原文摘要 · Abstract (English)
The rising interest in leveraging higher-order interactions present in complex systems has led to a surge in more expressive models exploiting higher-order structures in the data, especially in topological deep learning (TDL), which designs neural networks on higher-order domains such as simplicial complexes. However, progress in this field is hindered by the scarcity of datasets for benchmarking these architectures. To address this gap, we introduce MANTRA, the first large-scale, diverse, and intrinsically higher-order dataset for benchmarking higher-order models, comprising over 43,000 and 250,000 triangulations of surfaces and three-dimensional manifolds, respectively. With MANTRA, we assess several graph- and simplicial complex-based models on three topological classification tasks. We demonstrate that while simplicial complex-based neural networks generally outperform their graph-based counterparts in capturing simple topological invariants, they also struggle, suggesting a rethink of TDL. Thus, MANTRA serves as a benchmark for assessing and advancing topological methods, leading the way for more effective higher-order models.
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