# Introducing Graph Smoothness Loss for Training Deep Learning Architectures

arXiv: https://arxiv.org/abs/1905.00301 · HTML: https://mlsanity.com/paper/1905.00301/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2019.

## Built on by (most cited first, 6 of 6)

- [The Geometry of Self-supervised Learning Models and its Impact on Transfer Learning](https://mlsanity.com/paper/2209.08622/) (2022)
- [Spatiotemporal Imputation with Graph-Informed Flow Matching](https://mlsanity.com/paper/2606.06682/) (2026)
- [Ensemble Learning with Manifold-Based Data Splitting for Noisy Label Correction](https://mlsanity.com/paper/2103.07641/) (2021)
- [Graphs as Tools to Improve Deep Learning Methods](https://mlsanity.com/paper/2110.03999/) (2021)
- [Spatiotemporal Air Quality Mapping in Urban Areas Using Sparse Sensor Data, Satellite Imagery, Meteorological Factors, and Spatial Features](https://mlsanity.com/paper/2501.11270/) (2025)
- [Improving Fine-Tuning with Latent Cluster Correction](https://mlsanity.com/paper/2501.11919/) (2025)

## Abstract (arXiv)

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.