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

• URL: http://arxiv.org/abs/2310.11439v3
• Date: Mon, 1 Jul 2024 14:39:54 GMT
• Title: From Alexnet to Transformers: Measuring the Non-linearity of Deep Neural Networks with Affine Optimal Transport
• Authors: Quentin Bouniot, Ievgen Redko, Anton Mallasto, Charlotte Laclau, Karol Arndt, Oliver Struckmeier, Markus Heinonen, Ville Kyrki, Samuel Kaski,
• Abstract summary: We introduce the concept of the non-linearity signature of DNN, the first theoretically sound solution for measuring the non-linearity of deep neural networks. We provide extensive experimental results that highlight the practical usefulness of the proposed non-linearity signature.
• Score: 32.39176908225668
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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. The code for our work is available at https://github.com/qbouniot/AffScoreDeep

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