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

MCML Authors

Quentin Bouniot

Dr.

→ Group Zeynep Akata
 Interpretable and Reliable Machine Learning

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.

inproceedings

---

CVPR 2025

IEEE/CVF Conference on Computer Vision and Pattern Recognition. Nashville, TN, USA, Jun 11-15, 2025.

---

Authors

Q. Bouniot • I. Redko • A. Mallasto • C. Laclau • O. Struckmeier • K. Arndt • M. Heinonen • V. Kyrki • S. Kaski

---

Links

DOI

---

Research Area

 B1 | Computer Vision