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General E(2)-Equivariant Steerable CNNs

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arxiv 1911.08251 v2 pith:5EXLJYHS submitted 2019-11-19 cs.CV cs.LGeess.IV

General E(2)-Equivariant Steerable CNNs

Maurice Weiler , Gabriele Cesa This is my paper
classification cs.CV cs.LGeess.IV
keywords equivariantcnnsgrouprepresentationssteerableconstraintsconvolutionsgeneral
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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The big empirical success of group equivariant networks has led in recent years to the sprouting of a great variety of equivariant network architectures. A particular focus has thereby been on rotation and reflection equivariant CNNs for planar images. Here we give a general description of $E(2)$-equivariant convolutions in the framework of Steerable CNNs. The theory of Steerable CNNs thereby yields constraints on the convolution kernels which depend on group representations describing the transformation laws of feature spaces. We show that these constraints for arbitrary group representations can be reduced to constraints under irreducible representations. A general solution of the kernel space constraint is given for arbitrary representations of the Euclidean group $E(2)$ and its subgroups. We implement a wide range of previously proposed and entirely new equivariant network architectures and extensively compare their performances. $E(2)$-steerable convolutions are further shown to yield remarkable gains on CIFAR-10, CIFAR-100 and STL-10 when used as a drop-in replacement for non-equivariant convolutions.

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