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We consider Graph Anisotropic Diffusion (GAD), a recently proposed [4] model of graph neural networks, that can be trained to predict desired properties of the graph by performing learnable diffusion of node features on it. In contrast with similar methods, GAD introduces anisotropy of said diffusion by incorporating filters built from the graph’s Fiedler vector. In present work we attempt to improve this approach by increasing the dimension of the space in which GAD runs – that is, adding filters built from other low-frequency eigenmodes of the graph (eigenvectors of its Laplacian). We report the performance of such “dimension-augmented” GAD in predicting the chemical properties of small organic molecules from the ZINC dataset [5].

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Dimension-Augmented Anisotropy in Graph Neural Diffusion

  • 会议论文

  • 发表日期：

    2026年

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  • Tatiana Sycheva,
  • Maxim Beketov,
  • Ivan Smolyar

摘要

We consider Graph Anisotropic Diffusion (GAD), a recently proposed [4] model of graph neural networks, that can be trained to predict desired properties of the graph by performing learnable diffusion of node features on it. In contrast with similar methods, GAD introduces anisotropy of said diffusion by incorporating filters built from the graph’s Fiedler vector. In present work we attempt to improve this approach by increasing the dimension of the space in which GAD runs – that is, adding filters built from other low-frequency eigenmodes of the graph (eigenvectors of its Laplacian). We report the performance of such “dimension-augmented” GAD in predicting the chemical properties of small organic molecules from the ZINC dataset [5].