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arxiv: 1807.02547 · v2 · submitted 2018-07-06 · 💻 cs.LG · stat.ML

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

Maurice Weiler , Mario Geiger , Max Welling , Wouter Boomsma , Taco Cohen
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classification 💻 cs.LG stat.ML
keywords equivariantconvolutionssteerablecnnsdatafieldslinearacid
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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.

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