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. The code for our work is available atthis https URL
View on arXiv@article{bouniot2025_2310.11439,
title={ From Alexnet to Transformers: Measuring the Non-linearity of Deep Neural Networks with Affine Optimal Transport },
author={ Quentin Bouniot and Ievgen Redko and Anton Mallasto and Charlotte Laclau and Oliver Struckmeier and Karol Arndt and Markus Heinonen and Ville Kyrki and Samuel Kaski },
journal={arXiv preprint arXiv:2310.11439},
year={ 2025 }
}