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

TL;DR

This paper introduces 3D Steerable CNNs that are designed to learn features invariant to rotations and translations in volumetric data, improving tasks like protein structure analysis by leveraging SE(3)-equivariant convolutions.

Contribution

The paper develops a novel SE(3)-equivariant convolutional framework using steerable kernels, providing a mathematically rigorous approach for rotationally equivariant feature learning in 3D data.

Findings

Effective in amino acid propensity prediction

Improves protein structure classification accuracy

Kernel basis derived analytically for equivariance

Abstract

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.