# Introducing Graph Smoothness Loss for Training Deep Learning Architectures

## TL;DR

This paper proposes a new graph-based loss function for training deep classifiers that enhances robustness and maintains performance comparable to traditional methods by focusing on inter-class distances in the output space.

## Contribution

The paper introduces a novel graph smoothness loss for deep learning that emphasizes inter-class separation and improves robustness without sacrificing accuracy.

## Key findings

- Achieves similar classification accuracy as cross-entropy loss.
- Increases robustness to input deviations.
- Provides additional degrees of freedom in training.

## Abstract

We introduce a novel loss function for training deep learning architectures to perform classification. It consists in minimizing the smoothness of label signals on similarity graphs built at the output of the architecture. Equivalently, it can be seen as maximizing the distances between the network function images of training inputs from distinct classes. As such, only distances between pairs of examples in distinct classes are taken into account in the process, and the training does not prevent inputs from the same class to be mapped to distant locations in the output domain. We show that this loss leads to similar performance in classification as architectures trained using the classical cross-entropy, while offering interesting degrees of freedom and properties. We also demonstrate the interest of the proposed loss to increase robustness of trained architectures to deviations of the inputs.