拓扑神经网络的可微提升
Differentiable Lifting for Topological Neural Networks
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中文总结 AI 辅助
针对拓扑神经网络（TNNs）图提升操作先验识别的缺陷，提出可微提升框架DiffLift，实验显示其在多基准分类任务上优于现有方法，最高提升45%。
中文摘要 AI 辅助
拓扑神经网络（TNNs）能够利用图上的高阶结构（如环和团）来提升消息传递神经网络的表达能力。然而，这些结构通常是通过无监督的图提升操作先验识别的，这种选择至关重要，可能对TNN在下游任务上的性能产生重大影响。为规避该问题，我们提出$\boldsymbol{\nabla}$lift（DiffLift），这是一个以端到端方式学习图到超图、胞腔复形和单纯复形提升的通用框架。具体而言，我们的方法利用学习到的顶点级潜在表示来识别和参数化候选高阶单元的包含分布，从而得到一个可扩展的模型，可轻松集成到任何TNN中。实验表明，在多个图和节点分类基准（涵盖不同TNN架构）上，$\boldsymbol{\nabla}$lift的性能优于现有提升方法，值得注意的是，相较于静态提升方法（包括基于连通性和特征的提升方法），我们的方法可带来最高达45%的性能提升。
英文摘要
Topological neural networks (TNNs) enable leveraging high-order structures on graphs (e.g., cycles and cliques) to boost the expressive power of message-passing neural networks. In turn, however, these structures are typically identified a priori through an unsupervised graph lifting operation. Notwithstanding, this choice is crucial and may have a drastic impact on a TNN's performance on downstream tasks. To circumvent this issue, we propose $\partial$lift (DiffLift), a general framework for learning graph liftings to hypergraphs and cellular- and simplicial complexes in an end-to-end fashion. In particular, our approach leverages learned vertex-level latent representations to identify and parameterize distributions over candidate higher-order cells for inclusion. This results in a scalable model which can be readily integrated into any TNN. Our experiments show that $\partial$lift outperforms existing lifting methods on multiple benchmarks for graph and node classification across different TNN architectures. Notably, our approach leads to gains of up to 45% over static liftings, including both connectivity- and feature-based ones.
发表机构
- University of São Paulo（圣保罗大学）
- Instituto Curvelo（库尔韦洛研究所）
- Federal Institute of Ceará（塞阿拉联邦学院）
- Aalto University（阿尔托大学）
- Getulio Vargas Foundation（热图利奥·瓦加斯基金会）
机构由 AI 辅助整理，请以论文原文为准。
