Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNs

• URL: http://arxiv.org/abs/2302.03655v2
• Date: Wed, 14 Jun 2023 14:07:05 GMT
• Title: Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNs
• Authors: Saro Passaro, C. Lawrence Zitnick
• Abstract summary: equivariant convolutions increase significantly in computational complexity as higher-order tensors are used. We propose a graph neural network utilizing our novel approach to equivariant convolutions, which achieves state-of-the-art results on the large-scale OC-20 and OC-22 datasets.
• Score: 3.1618838742094457
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph neural networks that model 3D data, such as point clouds or atoms, are typically desired to be $SO(3)$ equivariant, i.e., equivariant to 3D rotations. Unfortunately equivariant convolutions, which are a fundamental operation for equivariant networks, increase significantly in computational complexity as higher-order tensors are used. In this paper, we address this issue by reducing the $SO(3)$ convolutions or tensor products to mathematically equivalent convolutions in $SO(2)$ . This is accomplished by aligning the node embeddings' primary axis with the edge vectors, which sparsifies the tensor product and reduces the computational complexity from $O(L^6)$ to $O(L^3)$, where $L$ is the degree of the representation. We demonstrate the potential implications of this improvement by proposing the Equivariant Spherical Channel Network (eSCN), a graph neural network utilizing our novel approach to equivariant convolutions, which achieves state-of-the-art results on the large-scale OC-20 and OC-22 datasets.

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