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2020年5月13日

Isometric Transformation Invariant and Equivariant Graph Convolutional Networks

  • Masanobu Horie
  • ,
  • Naoki Morita
  • ,
  • Toshiaki Hishinuma
  • ,
  • Yu Ihara
  • ,
  • Naoto Mitsume

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 physical
simulations. A crucial requirement for applying graphs in Euclidean spaces to
physical simulations is learning and inferring the isometric transformation
invariant and equivariant features in a computationally efficient manner. In
this paper, we propose a set of transformation invariant and equivariant models
based on graph convolutional networks, called IsoGCNs. We demonstrate that the
proposed model has a competitive performance compared to state-of-the-art
methods on tasks related to geometrical and physical simulation data. Moreover,
the proposed model can scale up to graphs with 1M vertices and conduct an
inference faster than a conventional finite element analysis, which the
existing equivariant models cannot achieve.

リンク情報
arXiv
http://arxiv.org/abs/arXiv:2005.06316
URL
http://arxiv.org/abs/2005.06316v3
URL
http://arxiv.org/pdf/2005.06316v3 本文へのリンクあり

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