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

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arxiv 2302.03655 v2 pith:RFNBYO57 submitted 2023-02-07 cs.LG physics.chem-phphysics.comp-ph

Saro Passaro , C. Lawrence Zitnick This is my paper
classification cs.LGphysics.chem-phphysics.comp-ph
keywords equivariantconvolutionscomplexitycomputationalgraphnetworknetworksneural
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Cited by 4 Pith papers

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  1. Fast contracted Clebsch--Gordan tensor products for equivariant graph neural networks

    physics.comp-ph 2026-05 unverdicted novelty 7.0 of 10

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  2. Velocityformer: Broken-Symmetry-Matched Equivariant Graph Transformers for Cosmological Velocity Reconstruction

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    Velocityformer achieves 35% higher velocity correlation than linear theory by matching graph transformer inductive bias to the line-of-sight broken symmetry and conditioning on long-wavelength physics, while training ...

  3. Interpretable Nanoporous Materials Design with Symmetry-Aware Networks

    cond-mat.mtrl-sci 2025-09 conditional novelty 6.0 of 10

    An equivariant transformer with periodic space sampling predicts nanoporous properties and attributes each prediction to local structural sites.

  4. Hot-Ham: an accurate and efficient E(3)-equivariant machine-learning electronic structures calculation framework

    physics.comp-ph 2025-09 conditional novelty 6.0 of 10

    Hot-Ham combines Gaunt tensor products with a local-coordinate SO(2) convolution to predict DFT Hamiltonians accurately and efficiently across several material classes.

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