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arXiv 1807.02547cs.LGstat.ML

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

University of Amsterdam（阿姆斯特丹大学）；EPFL（洛桑联邦理工学院）；CIFAR（加拿大高等研究院）；Qualcomm AI Research（高通人工智能研究院）；University of Copenhagen（哥本哈根大学）

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

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英文摘要：

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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