Communication Dans Un Congrès Année : 2025

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

Résumé

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 at https: //github.com/qbouniot/AffScoreDeep.

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hal-05013443 , version 1 (18-05-2025)

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Quentin Bouniot, Ievgen Redko, Anton Mallasto, Charlotte Laclau, Oliver Struckmeier, et al.. From Alexnet to Transformers: Measuring the Non-linearity of Deep Neural Networks with Affine Optimal Transport. The IEEE/CVF Conference on Computer Vision and Pattern Recognition 2025, Jun 2025, Nashville TN, United States. ⟨hal-05013443⟩
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