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• W3217687076 abstract "Incorporating group symmetry directly into the learning process has proved to be an effective guideline for model design. By producing features that are guaranteed to transform covariantly to the group actions on the inputs, group-equivariant convolutional neural networks (G-CNNs) achieve significantly improved generalization performance in learning tasks with intrinsic symmetry. General theory and practical implementation of G-CNNs have been studied for planar images under either rotation or scaling transformation, but only individually. We present, in this paper, a roto-scale-translation equivariant CNN (RST-CNN), that is guaranteed to achieve equivariance jointly over these three groups via coupled group convolutions. Moreover, as symmetry transformations in reality are rarely perfect and typically subject to input deformation, we provide a stability analysis of the equivariance of representation to input distortion, which motivates the truncated expansion of the convolutional filters under (pre-fixed) low-frequency spatial modes. The resulting model provably achieves deformation-robust RST equivariance, i.e., the RST symmetry is still approximately preserved when the transformation is contaminated by a nuisance data deformation, a property that is especially important for out-of-distribution generalization. Numerical experiments on MNIST, Fashion-MNIST, and STL-10 demonstrate that the proposed model yields remarkable gains over prior arts, especially in the small data regime where both rotation and scaling variations are present within the data." @default.
• W3217687076 created "2021-12-06" @default.
• W3217687076 creator A5011441236 @default.
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• W3217687076 date "2021-11-21" @default.
• W3217687076 modified "2023-09-23" @default.
• W3217687076 title "Deformation Robust Roto-Scale-Translation Equivariant CNNs" @default.
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• W3217687076 doi "https://doi.org/10.48550/arxiv.2111.10978" @default.
• W3217687076 hasPublicationYear "2021" @default.
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