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Affine Invariance in Continuous-Domain Convolutional Neural Networks

arXiv 2311.09245 ↗First posted 13 Nov 2023cs.LG math.ST stat.MLcited by 0

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Abstract (arXiv)

The notion of group invariance helps neural networks in recognizing patterns and features under geometric transformations. Group convolutional neural networks enhance traditional convolutional neural networks by incorporating group-based geometric structures into their design. This research studies affine invariance on continuous-domain convolutional neural networks. Despite other research considering isometric invariance or similarity invariance, we focus on the full structure of affine transforms generated by the group of all invertible 2 × 2 real matrices (generalized linear group GL2(ℝ)). We introduce a new criterion to assess the invariance of two signals under affine transformations. The input image is embedded into the affine Lie group G2 = ℝ2 ltimes GL2(ℝ) to facilitate group convolution operations that respect affine invariance. Then, we analyze the convolution of embedded signals over G2. In sum, our research could eventually extend the scope of geometrical transformations that usual deep-learning pipelines can handle.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 18 of its 34 references that are in the map. First posted on arXiv 13 Nov 2023.

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18 of 34 references.

References · 18

  1. 2016Group Equivariant Convolutional Networkscited by 1,154
  2. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  3. 2015An Introduction to Convolutional Neural Networkscited by 510
  4. 2018Spherical CNNscited by 452
  5. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  6. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  7. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 293
  8. 2020The Computational Limits of Deep Learningcited by 188
  9. 2019B-Spline CNNs on Lie Groupscited by 97
  10. 2016Exploiting Cyclic Symmetry in Convolutional Neural Networkscited by 91
  11. 2021Equivariant Point Network for 3D Point Cloud Analysiscited by 81
  12. 2017Oriented Response Networkscited by 67
6 more
  1. 2018CubeNet: Equivariance to 3D Rotation and Translationcited by 59
  2. 2014Deep Roto-Translation Scattering for Object Classificationcited by 49
  3. 20183D G-CNNs for Pulmonary Nodule Detectioncited by 36
  4. 2020PDE-based Group Equivariant Convolutional Neural Networkscited by 28
  5. 2021Exploiting Redundancy: Separable Group Convolutional Networks on Lie Groupscited by 22
  6. 2018An optimized system to solve text-based CAPTCHAcited by 1

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