通过离散的里奇曲率在图形变压器中更深入地利用图形结构信息
Xin Lai1,2, Yang Liu2, Rui Qian3
1School of Mathematics, Renmin University of China, Beijing 100872, China.
Entropy (Basel, Switzerland)
|June 28, 2023
概括
本研究介绍了Curvphormer,这是一种使用离散里奇曲率 (DRC) 来更好地理解图形结构的新型图形变压器. 这种方法显著提高了各种图表级任务的性能.
科学领域:
- 图形神经网络的神经网络
- 几何深度学习 几何深度学习
- 拓数据分析 拓数据分析
背景情况:
- 图形结构数据无处不在,但充分利用其固有的结构仍然具有挑战性.
- 现有的图形表示学习方法可能无法捕获所有相关的拓信息.
- 需要新的几何描述符来增强图形模型的表达力.
研究的目的:
- 介绍一个新的图形变压器模型,Curvphormer,它包含几何信息.
- 为了利用离散的里奇曲率 (DRC) 作为发现更深层次的图形结构的描述符.
- 提高图形神经网络在复杂的图形级任务上的性能.
主要方法:
- 开发了Curvphormer,一个拓意识的图形变压器.
- 集成离散里奇曲率 (DRC) 作为量化图形连接的关键特征.
- 在大规模数据集 (PCQM4M-LSC,ZINC,MolHIV) 上进行了广泛的实验.
主要成果:
- 在各种图表级和微调任务中取得了显著的性能提升.
- 证明了DRC在捕获基本图形结构信息方面的有效性.
- 展示了Curvphormer在同质图表中提取固有的社区结构的能力.
结论:
- 使用离散的里奇曲率的Curvphormer增强了图形表示学习.
- 几何描述符的集成为未来的图形神经网络研究提供了一个有希望的方向.
- 这种方法为量化图形连接和提取结构信息提供了一种更加清晰的方法.
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