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Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters

Publication ,  Journal Article
Zhu, W; Qiu, Q; Calderbank, R; Sapiro, G; Cheng, X
Published in: Journal of Machine Learning Research
January 1, 2022

Encoding the scale information explicitly into the representation learned by a convolutional neural network (CNN) is beneficial for many computer vision tasks especially when dealing with multiscale inputs. We study, in this paper, a scaling-translation-equivariant (ST -equivariant) CNN with joint convolutions across the space and the scaling group, which is shown to be both sufficient and necessary to achieve equivariance for the regular representation of the scaling-translation group ST . To reduce the model complexity and computational burden, we decompose the convolutional filters under two pre-fixed separable bases and truncate the expansion to low-frequency components. A further benefit of the truncated filter expansion is the improved deformation robustness of the equivariant representation, a property which is theoretically analyzed and empirically verified. Numerical experiments demonstrate that the proposed scaling-translation-equivariant network with decomposed convolutional filters (ScDCFNet) achieves significantly improved performance in multiscale image classification and better interpretability than regular CNNs at a reduced model size.

Duke Scholars

Published In

Journal of Machine Learning Research

EISSN

1533-7928

ISSN

1532-4435

Publication Date

January 1, 2022

Volume

23

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4905 Statistics
  • 4611 Machine learning
  • 17 Psychology and Cognitive Sciences
  • 08 Information and Computing Sciences
 

Citation

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MLA
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Zhu, W., Qiu, Q., Calderbank, R., Sapiro, G., & Cheng, X. (2022). Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters. Journal of Machine Learning Research, 23.
Zhu, W., Q. Qiu, R. Calderbank, G. Sapiro, and X. Cheng. “Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters.” Journal of Machine Learning Research 23 (January 1, 2022).
Zhu W, Qiu Q, Calderbank R, Sapiro G, Cheng X. Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters. Journal of Machine Learning Research. 2022 Jan 1;23.
Zhu, W., et al. “Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters.” Journal of Machine Learning Research, vol. 23, Jan. 2022.
Zhu W, Qiu Q, Calderbank R, Sapiro G, Cheng X. Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters. Journal of Machine Learning Research. 2022 Jan 1;23.

Published In

Journal of Machine Learning Research

EISSN

1533-7928

ISSN

1532-4435

Publication Date

January 1, 2022

Volume

23

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4905 Statistics
  • 4611 Machine learning
  • 17 Psychology and Cognitive Sciences
  • 08 Information and Computing Sciences