# Energy Guided smoothness to improve Robustness in Graph Classification

arXiv: https://arxiv.org/abs/2412.08419 · HTML: https://mlsanity.com/paper/2412.08419/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 41 of its 62 references that are in the map.
- First posted on arXiv 11 Dec 2024.

## Builds on (most cited first, 30 of 41)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Training Deep Neural Networks on Noisy Labels with Bootstrapping](https://mlsanity.com/paper/1412.6596/) (2014)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Identifying Mislabeled Data using the Area Under the Margin Ranking](https://mlsanity.com/paper/2001.10528/) (2020)
- [A Note on Over-Smoothing for Graph Neural Networks](https://mlsanity.com/paper/2006.13318/) (2020)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [Image Classification with Deep Learning in the Presence of Noisy Labels: A Survey](https://mlsanity.com/paper/1912.05170/) (2019)
- [Dirichlet Energy Constrained Learning for Deep Graph Neural Networks](https://mlsanity.com/paper/2107.02392/) (2021)
- [Robust Training under Label Noise by Over-parameterization](https://mlsanity.com/paper/2202.14026/) (2022)
- [Propagation Kernels](https://mlsanity.com/paper/1410.3314/) (2014)
- [Hierarchical Graph Pooling with Structure Learning](https://mlsanity.com/paper/1911.05954/) (2019)
- [NRGNN: Learning a Label Noise-Resistant Graph Neural Network on Sparsely and Noisily Labeled Graphs](https://mlsanity.com/paper/2106.04714/) (2021)
- [Towards Robust Graph Neural Networks for Noisy Graphs with Sparse Labels](https://mlsanity.com/paper/2201.00232/) (2022)
- [Understanding convolution on graphs via energies](https://mlsanity.com/paper/2206.10991/) (2022)
- [Detecting Corrupted Labels Without Training a Model to Predict](https://mlsanity.com/paper/2110.06283/) (2021)
- [Tree Mover's Distance: Bridging Graph Metrics and Stability of Graph Neural Networks](https://mlsanity.com/paper/2210.01906/) (2022)
- [Towards Understanding Deep Learning from Noisy Labels with Small-Loss Criterion](https://mlsanity.com/paper/2106.09291/) (2021)

## Abstract (arXiv)

Graph Neural Networks (GNNs) are powerful at solving graph classification tasks, yet applied problems often contain noisy labels. In this work, we study GNN robustness to label noise, demonstrate GNN failure modes when models struggle to generalise on low-order graphs, low label coverage, or when a model is over-parameterized. We establish both empirical and theoretical links between GNN robustness and the reduction of the total Dirichlet Energy of learned node representations, which encapsulates the hypothesized GNN smoothness inductive bias. Finally, we introduce two training strategies to enhance GNN robustness: (1) by incorporating a novel inductive bias in the weight matrices through the removal of negative eigenvalues, connected to Dirichlet Energy minimization; (2) by extending to GNNs a loss penalty that promotes learned smoothness. Importantly, neither approach negatively impacts performance in noise-free settings, supporting our hypothesis that the source of GNNs robustness is their smoothness inductive bias.