From AlexNet to Transformers: Measuring the Non-Linearity of Deep Neural Networks with Affine Optimal Transport

Quentin Bouniot, Ievgen Redko, Anton Mallasto, Charlotte Laclau, Oliver Struckmeier, Karol Arndt, Markus Heinonen, Ville Kyrki, Samuel Kaski

CVPR 2025 pp. 25250-25260

doi:10.1109/CVPR52734.2025.02351 /cvpr/2025/bouniot2025cvpr-alexnet/

Abstract

In the last decade, we have witnessed the introduction of several novel deep neural network (DNN) architectures exhibiting ever-increasing performance across diverse tasks. Explaining the upward trend of their performance, however, remains difficult as different DNN architectures of comparable depth and width -- common factors associated with their expressive power -- may exhibit a drastically different performance even when trained on the same dataset. In this paper, we introduce the concept of the non-linearity signature of DNN, the first theoretically sound solution for approximately measuring the non-linearity of deep neural networks. Built upon a score derived from closed-form optimal transport mappings, this signature provides a better understanding of the inner workings of a wide range of DNN architectures and learning paradigms, with a particular emphasis on the computer vision task. We provide extensive experimental results that highlight the practical usefulness of the proposed non-linearity signature and its potential for long-reaching implications.

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Cite

Text

Bouniot et al. "From AlexNet to Transformers: Measuring the Non-Linearity of Deep Neural Networks with Affine Optimal Transport." Conference on Computer Vision and Pattern Recognition, 2025. doi:10.1109/CVPR52734.2025.02351

Markdown

[Bouniot et al. "From AlexNet to Transformers: Measuring the Non-Linearity of Deep Neural Networks with Affine Optimal Transport." Conference on Computer Vision and Pattern Recognition, 2025.](https://mlanthology.org/cvpr/2025/bouniot2025cvpr-alexnet/) doi:10.1109/CVPR52734.2025.02351

BibTeX

@inproceedings{bouniot2025cvpr-alexnet,
  title     = {{From AlexNet to Transformers: Measuring the Non-Linearity of Deep Neural Networks with Affine Optimal Transport}},
  author    = {Bouniot, Quentin and Redko, Ievgen and Mallasto, Anton and Laclau, Charlotte and Struckmeier, Oliver and Arndt, Karol and Heinonen, Markus and Kyrki, Ville and Kaski, Samuel},
  booktitle = {Conference on Computer Vision and Pattern Recognition},
  year      = {2025},
  pages     = {25250-25260},
  doi       = {10.1109/CVPR52734.2025.02351},
  url       = {https://mlanthology.org/cvpr/2025/bouniot2025cvpr-alexnet/}
}