From Alexnet to Transformers: Measuring the Non-linearity of Deep Neural Networks with Affine Optimal Transport
This provides a tool for researchers to analyze and compare DNN architectures, though it is incremental as it builds on existing optimal transport concepts.
The paper tackles the problem of explaining performance differences in deep neural network architectures by introducing a non-linearity signature, a theoretically sound method to measure non-linearity using affine optimal transport, which helps understand inner workings across various architectures in computer vision.
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