3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data
This work addresses the need for models that inherently handle 3D symmetries in tasks like protein analysis, offering a novel approach for domain-specific applications in computational biology.
The paper tackles the problem of learning rotationally equivariant features in volumetric data by introducing 3D Steerable CNNs, which are equivariant to rigid body motions, and demonstrates their effectiveness with applications in amino acid propensity prediction and protein structure classification.
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.