Linear CNNs Discover the Statistical Structure of the Dataset Using Only the Most Dominant Frequencies

Hannah Pinson, Joeri Lenaerts, Vincent Ginis
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:27876-27906, 2023.

Abstract

We here present a stepping stone towards a deeper understanding of convolutional neural networks (CNNs) in the form of a theory of learning in linear CNNs. Through analyzing the gradient descent equations, we discover that the evolution of the network during training is determined by the interplay between the dataset structure and the convolutional network structure. We show that linear CNNs discover the statistical structure of the dataset with non-linear, ordered, stage-like transitions, and that the speed of discovery changes depending on the relationship between the dataset and the convolutional network structure. Moreover, we find that this interplay lies at the heart of what we call the "dominant frequency bias", where linear CNNs arrive at these discoveries using only the dominant frequencies of the different structural parts present in the dataset. We furthermore provide experiments that show how our theory relates to deep, non-linear CNNs used in practice. Our findings shed new light on the inner working of CNNs, and can help explain their shortcut learning and their tendency to rely on texture instead of shape.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-pinson23a, title = {Linear {CNN}s Discover the Statistical Structure of the Dataset Using Only the Most Dominant Frequencies}, author = {Pinson, Hannah and Lenaerts, Joeri and Ginis, Vincent}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {27876--27906}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/pinson23a/pinson23a.pdf}, url = {https://proceedings.mlr.press/v202/pinson23a.html}, abstract = {We here present a stepping stone towards a deeper understanding of convolutional neural networks (CNNs) in the form of a theory of learning in linear CNNs. Through analyzing the gradient descent equations, we discover that the evolution of the network during training is determined by the interplay between the dataset structure and the convolutional network structure. We show that linear CNNs discover the statistical structure of the dataset with non-linear, ordered, stage-like transitions, and that the speed of discovery changes depending on the relationship between the dataset and the convolutional network structure. Moreover, we find that this interplay lies at the heart of what we call the "dominant frequency bias", where linear CNNs arrive at these discoveries using only the dominant frequencies of the different structural parts present in the dataset. We furthermore provide experiments that show how our theory relates to deep, non-linear CNNs used in practice. Our findings shed new light on the inner working of CNNs, and can help explain their shortcut learning and their tendency to rely on texture instead of shape.} }
Endnote
%0 Conference Paper %T Linear CNNs Discover the Statistical Structure of the Dataset Using Only the Most Dominant Frequencies %A Hannah Pinson %A Joeri Lenaerts %A Vincent Ginis %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-pinson23a %I PMLR %P 27876--27906 %U https://proceedings.mlr.press/v202/pinson23a.html %V 202 %X We here present a stepping stone towards a deeper understanding of convolutional neural networks (CNNs) in the form of a theory of learning in linear CNNs. Through analyzing the gradient descent equations, we discover that the evolution of the network during training is determined by the interplay between the dataset structure and the convolutional network structure. We show that linear CNNs discover the statistical structure of the dataset with non-linear, ordered, stage-like transitions, and that the speed of discovery changes depending on the relationship between the dataset and the convolutional network structure. Moreover, we find that this interplay lies at the heart of what we call the "dominant frequency bias", where linear CNNs arrive at these discoveries using only the dominant frequencies of the different structural parts present in the dataset. We furthermore provide experiments that show how our theory relates to deep, non-linear CNNs used in practice. Our findings shed new light on the inner working of CNNs, and can help explain their shortcut learning and their tendency to rely on texture instead of shape.
APA
Pinson, H., Lenaerts, J. & Ginis, V.. (2023). Linear CNNs Discover the Statistical Structure of the Dataset Using Only the Most Dominant Frequencies. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:27876-27906 Available from https://proceedings.mlr.press/v202/pinson23a.html.

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