Constructing Invariant and Equivariant Operations by Symmetric Tensor Network

Meng Zhang, Chao Wang, Hao Zhang, Shaojun Dong, Lixin He

Keywords: Invariance, Equivariance, Tensor network, Geometry graph neural network

TL;DR: This work developed a systematic tool capable of constructing invariance and equivariance operations given the specified forms of input and output, which include tuples of various rank Cartesian tensors and various types spherical tensors.

Abstract: Design of neural networks that incorporate symmetry is crucial for geometric deep learning. Central to this effort is the development of invariant and equivariant operations. This work presents a systematic method for constructing valid invariant and equivariant operations. It can handle inputs and outputs in the form of Cartesian tensors with different ranks, as well as spherical tensors with different types. In addition, our method features a graphical representation utilizing the symmetric tensor network, which simplifies both the proofs and constructions related to invariant and equivariant functions. We also show how to apply this method to design the equivariant interaction message for the geometry graph neural network and general neural network models incorporating symmetry.

Primary Area: learning on graphs and other geometries & topologies

Submission Number: 8588