Isometric Transformation Invariant and Equivariant Graph Convolutional Networks

By Masanobu Horie, Naoki Morita, Yushi Ihara, Naoto Mitsume. 2020

25 citations recorded by the source corpus.

Graphs are one of the most important data structures for representing pairwise relations between objects. Specifically, a graph embedded in a Euclidean space is essential to solving real problems, such as object detection, structural chemistry analyses, and physical simulation. A crucial requirement to applying a graph in a Euclidean space is learning the isometric transformation invariant and equivariant features. In the present paper, we propose a set of transformation invariant and equivariant models based on graph convolutional networks (GCNs), called IsoGCNs. We demonstrate that the proposed model outperforms state-of-the-art methods on tasks related with geometrical and physical data. Moreover, the proposed model can scale up to the graphs with 1M vertices and conduct an inference faster than a conventional finite element analysis.

Subfields: Computer Vision and Pattern Recognition, Graph Learning

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Citations in the corpus

E(n) Equivariant Graph Neural Networks (2021, background): “Horie et al. (2020) proposes a set of isometric invariant and equivairant transformations for Graph Neural Networks.”