Scale-Equivariant Steerable Networks

By Ivan Sosnovik, Michal Szmaja, Arnold M. W. Smeulders. 2019

175 citations recorded by the source corpus.

The effectiveness of Convolutional Neural Networks (CNNs) has been substantially attributed to their built-in property of translation equivariance. However, CNNs do not have embedded mechanisms to handle other types of transformations. In this work, we pay attention to scale changes, which regularly appear in various tasks due to the changing distances between the objects and the camera. First, we introduce the general theory for building scale-equivariant convolutional networks with steerable filters. We develop scale-convolution and generalize other common blocks to be scale-equivariant. We demonstrate the computational efficiency and numerical stability of the proposed method. We compare the proposed models to the previously developed methods for scale equivariance and local scale invariance. We demonstrate state-of-the-art results on MNIST-scale dataset and on STL-10 dataset in the supervised learning setting.

Subfields: Computational Theory and Mathematics, Computer Graphics and Computer-Aided Design, Geometry and Topology

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Citations in the corpus

Group Equivariant Stand-Alone Self-Attention For Vision (2020, background): “, 2019b), scaling (Marcos et al., 2018; Worrall & Welling, 2019; Sosnovik et al., 2020; Romero et al., 2020b) and more general symmetry groups (Cohen & Welling, 2016; Kondor & Trivedi, 2018; Weiler & Cesa, 2019; Cohen et al.”
SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks (2020, methodology): “Similar to [27, 39], we measure the exactness of equivariance by applying uniformly sampled SO(3)transformations to input and output.”
On Translation Invariance in CNNs: Convolutional Layers Can Exploit Absolute Spatial Location (2020, methodology): “Instead of adding transformed versions of the training data there are methods specifically designed to learn geometric transformations in an equivariant or invariant representation [7, 53, 60] where examples include rotation [19, 69, 102, 103, 110], scale [68, 92, 99, 104, 106] and other transformat”
Attentive Group Equivariant Convolutional Networks (2020, unknown): “…guarantee the validity of our theory for techniques deﬁned on continuous spaces, e.g., steerable and Lie group convolutions (Cohen & Welling, 2016b; Worrall et al., 2017; Bekkers et al., 2018; Weiler et al., 2018; Kondor & Trivedi, 2018; Thomas et al., 2018; Bekkers, 2020; Sosnovik et al., 2020).”
Wavelet Networks: Scale Equivariant Learning From Raw Waveforms (2020, methodology): “[62] Ivan Sosnovik, Michał Szmaja, and Arnold Smeulders.”