Exploiting Learned Symmetries in Group Equivariant Convolutions

Group Equivariant Convolutions (GConvs) enable convolutional neural networks to be equivariant to various transformation groups, but at an additional parameter and compute cost. We investigate the filter parameters learned by GConvs and find certain conditions under which they become highly redundant. We show that GConvs can be efficiently decomposed into depthwise separable convolutions while preserving equivariance properties and demonstrate improved performance and data efficiency on two datasets. All code is publicly available at this http URL.

[1]  J. V. Gemert,et al.  On Translation Invariance in CNNs: Convolutional Layers Can Exploit Absolute Spatial Location , 2020, 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[2]  Erik J. Bekkers,et al.  Attentive Group Equivariant Convolutional Networks , 2020, ICML.

[3]  Stephan J. Garbin,et al.  Harmonic Networks: Deep Translation and Rotation Equivariance , 2016, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[4]  Taco S. Cohen,et al.  A Data and Compute Efficient Design for Limited-Resources Deep Learning , 2020, ArXiv.

[5]  Mitko Veta,et al.  Roto-Translation Covariant Convolutional Networks for Medical Image Analysis , 2018, MICCAI.

[6]  Max Welling,et al.  Group Equivariant Convolutional Networks , 2016, ICML.

[7]  Deng Cai,et al.  Deep Rotation Equivariant Network , 2017, Neurocomputing.

[8]  Mark Hoogendoorn,et al.  Co-Attentive Equivariant Neural Networks: Focusing Equivariance On Transformations Co-Occurring In Data , 2019, ICLR.

[9]  Maurice Weiler,et al.  Learning Steerable Filters for Rotation Equivariant CNNs , 2017, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition.

[10]  Manuel Amthor,et al.  Rethinking Depthwise Separable Convolutions: How Intra-Kernel Correlations Lead to Improved MobileNets , 2020, 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[11]  Gabriel J. Brostow,et al.  CubeNet: Equivariance to 3D Rotation and Translation , 2018, ECCV.

[12]  Yoshua Bengio,et al.  An empirical evaluation of deep architectures on problems with many factors of variation , 2007, ICML '07.

[13]  Ivan Sosnovik,et al.  Scale-Equivariant Steerable Networks , 2020, ICLR.

[14]  Max Welling,et al.  3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data , 2018, NeurIPS.

[15]  Alexandru Paul Condurache,et al.  Boosting Deep Neural Networks with Geometrical Prior Knowledge: A Survey , 2020, ArXiv.

[16]  Quoc V. Le,et al.  Searching for MobileNetV3 , 2019, 2019 IEEE/CVF International Conference on Computer Vision (ICCV).

[17]  Quoc V. Le,et al.  EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks , 2019, ICML.

[18]  Taco S Cohen,et al.  Pulmonary nodule detection in CT scans with equivariant CNNs , 2019, Medical Image Anal..

[19]  Daniel E. Worrall,et al.  Deep Scale-spaces: Equivariance Over Scale , 2019, NeurIPS.