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Stability Analysis of Equivariant Convolutional Representations Through The Lens of Equivariant Multi-layered CKNs

arXiv 2408.04277 ↗First posted 8 Aug 2024cs.LGcited by 0

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Abstract (arXiv)

In this paper we construct and theoretically analyse group equivariant convolutional kernel networks (CKNs) which are useful in understanding the geometry of (equivariant) CNNs through the lens of reproducing kernel Hilbert spaces (RKHSs). We then proceed to study the stability analysis of such equiv-CKNs under the action of diffeomorphism and draw a connection with equiv-CNNs, where the goal is to analyse the geometry of inductive biases of equiv-CNNs through the lens of reproducing kernel Hilbert spaces (RKHSs). Traditional deep learning architectures, including CNNs, trained with sophisticated optimization algorithms is vulnerable to perturbations, including `adversarial examples'. Understanding the RKHS norm of such models through CKNs is useful in designing the appropriate architecture and can be useful in designing robust equivariant representation learning models.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 27 of its 41 references that are in the map. First posted on arXiv 8 Aug 2024.

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27 of 41 references.

References · 27

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15 more
  1. 2017Learning Steerable Filters for Rotation Equivariant CNNscited by 193
  2. 2020Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphscited by 90
  3. 2022The Lie Derivative for Measuring Learned Equivariancecited by 51
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  5. 2020A Wigner-Eckart Theorem for Group Equivariant Convolution Kernelscited by 46
  6. 2020Why Are Convolutional Nets More Sample-Efficient than Fully-Connected Nets?cited by 32
  7. 2021Approximation and Learning with Deep Convolutional Models: a Kernel Perspectivecited by 31
  8. 2016End-to-End Kernel Learning with Supervised Convolutional Kernel Networkscited by 28
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  14. 2021Deformation Robust Roto-Scale-Translation Equivariant CNNscited by 7
  15. 2023Provable Adversarial Robustness for Group Equivariant Tasks: Graphs, Point Clouds, Molecules, and Morecited by 3

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