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

Soutrik Roy Chowdhury
Proceedings of the Geometry-grounded Representation Learning and Generative Modeling Workshop (GRaM), PMLR 251:50-64, 2024.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v251-chowdhury24a, title = {Stability Analysis of Equivariant Convolutional Representations Through The Lens of Equivariant Multi-layered {CKN}s}, author = {Chowdhury, Soutrik Roy}, booktitle = {Proceedings of the Geometry-grounded Representation Learning and Generative Modeling Workshop (GRaM)}, pages = {50--64}, year = {2024}, editor = {Vadgama, Sharvaree and Bekkers, Erik and Pouplin, Alison and Kaba, Sekou-Oumar and Walters, Robin and Lawrence, Hannah and Emerson, Tegan and Kvinge, Henry and Tomczak, Jakub and Jegelka, Stephanie}, volume = {251}, series = {Proceedings of Machine Learning Research}, month = {29 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v251/main/assets/chowdhury24a/chowdhury24a.pdf}, url = {https://proceedings.mlr.press/v251/chowdhury24a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Stability Analysis of Equivariant Convolutional Representations Through The Lens of Equivariant Multi-layered CKNs %A Soutrik Roy Chowdhury %B Proceedings of the Geometry-grounded Representation Learning and Generative Modeling Workshop (GRaM) %C Proceedings of Machine Learning Research %D 2024 %E Sharvaree Vadgama %E Erik Bekkers %E Alison Pouplin %E Sekou-Oumar Kaba %E Robin Walters %E Hannah Lawrence %E Tegan Emerson %E Henry Kvinge %E Jakub Tomczak %E Stephanie Jegelka %F pmlr-v251-chowdhury24a %I PMLR %P 50--64 %U https://proceedings.mlr.press/v251/chowdhury24a.html %V 251 %X 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.
APA
Chowdhury, S.R.. (2024). Stability Analysis of Equivariant Convolutional Representations Through The Lens of Equivariant Multi-layered CKNs. Proceedings of the Geometry-grounded Representation Learning and Generative Modeling Workshop (GRaM), in Proceedings of Machine Learning Research 251:50-64 Available from https://proceedings.mlr.press/v251/chowdhury24a.html.

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