3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

Bibtex Metadata Paper Reviews Supplemental


Maurice Weiler, Mario Geiger, Max Welling, Wouter Boomsma, Taco S. Cohen


We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations. These SE(3)-equivariant convolutions utilize kernels which are parameterized as a linear combination of a complete steerable kernel basis, which is derived analytically in this paper. We prove that equivariant convolutions are the most general equivariant linear maps between fields over R^3. Our experimental results confirm the effectiveness of 3D Steerable CNNs for the problem of amino acid propensity prediction and protein structure classification, both of which have inherent SE(3) symmetry.