  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.
