Sign and Basis Invariant Networks for Spectral Graph Representation Learning-猫眼课题宝

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发表时间：

2022-02

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ArXiv

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其他

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作者：

Derek Lim;Joshua Robinson;Lingxiao Zhao;T. Smidt;S. Sra;Haggai Maron;S. Jegelka

我们介绍SignNet和BasisNet -新的神经架构，它们对特征向量显示的两个关键对称性是不变的：（i）符号翻转，因为如果$v$是特征向量，那么$-v$也是;（ii）更一般的基础对称性，它发生在具有无限多基础特征向量选择的高维特征空间中。我们证明了在一定条件下，我们的网络是普遍的，即，它们可以近似具有期望的不变性的特征向量的任何连续函数。当与拉普拉斯特征向量一起使用时，我们的网络可以证明比图上现有的谱方法更具表现力;例如，它们将所有谱图卷积，某些谱图不变量和先前提出的图位置编码作为特例。实验表明，我们的网络在分子图回归、学习表达性图形表示和学习三角形网格上的神经域方面的性能明显优于现有基线。我们的代码可在https://github.com/cptq/SignNet-BasisNet上获得。

We introduce SignNet and BasisNet -- new neural architectures that are invariant to two key symmetries displayed by eigenvectors: (i) sign flips, since if $v$ is an eigenvector then so is $-v$; and (ii) more general basis symmetries, which occur in higher dimensional eigenspaces with infinitely many choices of basis eigenvectors. We prove that under certain conditions our networks are universal, i.e., they can approximate any continuous function of eigenvectors with the desired invariances. When used with Laplacian eigenvectors, our networks are provably more expressive than existing spectral methods on graphs; for instance, they subsume all spectral graph convolutions, certain spectral graph invariants, and previously proposed graph positional encodings as special cases. Experiments show that our networks significantly outperform existing baselines on molecular graph regression, learning expressive graph representations, and learning neural fields on triangle meshes. Our code is available at https://github.com/cptq/SignNet-BasisNet .

Sign and Basis Invariant Networks for Spectral Graph Representation Learning

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