# Understanding and Tackling Over-Dilution in Graph Neural Networks

arXiv: https://arxiv.org/abs/2508.16829 · HTML: https://mlsanity.com/paper/2508.16829/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 42 references that are in the map.
- First posted on arXiv 22 Aug 2025.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Pure Transformers are Powerful Graph Learners](https://mlsanity.com/paper/2207.02505/) (2022)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [GRPE: Relative Positional Encoding for Graph Transformer](https://mlsanity.com/paper/2201.12787/) (2022)
- [Inductive Link Prediction for Nodes Having Only Attribute Information](https://mlsanity.com/paper/2007.08053/) (2020)
- [Spectral Graph Pruning Against Over-Squashing and Over-Smoothing](https://mlsanity.com/paper/2404.04612/) (2024)
- [Feature Overcorrelation in Deep Graph Neural Networks: A New Perspective](https://mlsanity.com/paper/2206.07743/) (2022)
- [Probabilistic Graph Rewiring via Virtual Nodes](https://mlsanity.com/paper/2405.17311/) (2024)
- [TSC: A Simple Two-Sided Constraint against Over-Smoothing](https://mlsanity.com/paper/2408.03152/) (2024)

## Built on by (most cited first, 1 of 1)

- [Relieving the Over-Aggregating Effect in Graph Transformers](https://mlsanity.com/paper/2510.21267/) (2025)

## Abstract (arXiv)

Message Passing Neural Networks (MPNNs) hold a key position in machine learning on graphs, but they struggle with unintended behaviors, such as over-smoothing and over-squashing, due to irregular data structures. The observation and formulation of these limitations have become foundational in constructing more informative graph representations. In this paper, we delve into the limitations of MPNNs, focusing on aspects that have previously been overlooked. Our observations reveal that even within a single layer, the information specific to an individual node can become significantly diluted. To delve into this phenomenon in depth, we present the concept of Over-dilution and formulate it with two dilution factors: intra-node dilution for attribute-level and inter-node dilution for node-level representations. We also introduce a transformer-based solution that alleviates over-dilution and complements existing node embedding methods like MPNNs. Our findings provide new insights and contribute to the development of informative representations. The implementation and supplementary materials are publicly available at https://github.com/LeeJunHyun/NATR.