Deformation Robust Roto-Scale-Translation Equivariant CNNs
- URL: http://arxiv.org/abs/2111.10978v1
- Date: Mon, 22 Nov 2021 03:58:24 GMT
- Title: Deformation Robust Roto-Scale-Translation Equivariant CNNs
- Authors: Liyao Gao, Guang Lin, Wei Zhu
- Abstract summary: Group-equivariant convolutional neural networks (G-CNNs) achieve significantly improved generalization performance with intrinsic symmetry.
General theory and practical implementation of G-CNNs have been studied for planar images under either rotation or scaling transformation.
- Score: 10.44236628142169
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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