# Residual connections provably mitigate oversmoothing in graph neural networks

arXiv: https://arxiv.org/abs/2501.00762 · HTML: https://mlsanity.com/paper/2501.00762/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 33 references that are in the map.
- First posted on arXiv 1 Jan 2025.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [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)
- [Not too little, not too much: a theoretical analysis of graph (over)smoothing](https://mlsanity.com/paper/2205.12156/) (2022)
- [A Review on Graph Neural Network Methods in Financial Applications](https://mlsanity.com/paper/2111.15367/) (2021)
- [A Review of Graph Neural Networks and Their Applications in Power Systems](https://mlsanity.com/paper/2101.10025/) (2021)
- [A Non-Asymptotic Analysis of Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2212.10701/) (2022)
- [Demystifying Oversmoothing in Attention-Based Graph Neural Networks](https://mlsanity.com/paper/2305.16102/) (2023)
- [Residual Connections and Normalization Can Provably Prevent Oversmoothing in GNNs](https://mlsanity.com/paper/2406.02997/) (2024)
- [Graph Neural Networks Meet Wireless Communications: Motivation, Applications, and Future Directions](https://mlsanity.com/paper/2212.04047/) (2022)
- [Principles for Initialization and Architecture Selection in Graph Neural Networks with ReLU Activations](https://mlsanity.com/paper/2306.11668/) (2023)

## Built on by (most cited first, 7 of 7)

- [Critical attention scaling in long-context transformers](https://mlsanity.com/paper/2510.05554/) (2025)
- [Backward Oversmoothing: why is it hard to train deep Graph Neural Networks?](https://mlsanity.com/paper/2505.16736/) (2025)
- [On the Diverse Dynamical Behaviors Arising in Deep Linear Transformers](https://mlsanity.com/paper/2607.18584/) (2026)
- [Adaptive Initial Residual Connections for GNNs with Theoretical Guarantees](https://mlsanity.com/paper/2511.06598/) (2025)
- [GOMA: Toward Structure-Driven Multimodal Alignment from a Graph Signal Smoothing Perspective](https://mlsanity.com/paper/2605.15723/) (2026)
- [Exploding and vanishing gradients in deep neural networks: the effect of residual connections](https://mlsanity.com/paper/2606.17013/) (2026)
- [Unifying Graph Neural Networks Through a Common Layer Equation](https://mlsanity.com/paper/2608.16097/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) have achieved remarkable empirical success in processing and representing graph-structured data across various domains. However, a significant challenge known as "oversmoothing" persists, where vertex features become nearly indistinguishable in deep GNNs, severely restricting their expressive power and practical utility. In this work, we analyze the asymptotic oversmoothing rates of deep GNNs with and without residual connections by deriving explicit convergence rates for a normalized vertex similarity measure. Our analytical framework is grounded in the multiplicative ergodic theorem. Furthermore, we demonstrate that adding residual connections effectively mitigates or prevents oversmoothing across several broad families of parameter distributions. The theoretical findings are strongly supported by numerical experiments.