Graphs for deep learning representations

TL;DR

This paper introduces a graph-based formalism using Graph Signal Processing to analyze deep learning architectures, aiming to improve interpretability, robustness, and efficiency of neural networks.

Contribution

It proposes a novel graph formalism for representing neural network latent spaces, enabling better understanding and optimization of deep learning models.

Findings

Graph formalism helps analyze generalization abilities.

Reduces arbitrary design choices in training.

Improves robustness to input perturbations.

Abstract

In recent years, Deep Learning methods have achieved state of the art performance in a vast range of machine learning tasks, including image classification and multilingual automatic text translation. These architectures are trained to solve machine learning tasks in an end-to-end fashion. In order to reach top-tier performance, these architectures often require a very large number of trainable parameters. There are multiple undesirable consequences, and in order to tackle these issues, it is desired to be able to open the black boxes of deep learning architectures. Problematically, doing so is difficult due to the high dimensionality of representations and the stochasticity of the training process. In this thesis, we investigate these architectures by introducing a graph formalism based on the recent advances in Graph Signal Processing (GSP). Namely, we use graphs to represent the latent spaces of deep neural networks. We showcase that this graph formalism allows us to answer various questions including: ensuring generalization abilities, reducing the amount of arbitrary choices in the design of the learning process, improving robustness to small perturbations added to the inputs, and reducing computational complexity