Graph Attention is Not Always Beneficial: A Theoretical Analysis of Graph Attention Mechanisms via Contextual Stochastic Block Models

Zhongtian Ma, Qiaosheng Zhang, Bocheng Zhou, Yexin Zhang, Shuyue Hu, Zhen Wang
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:42252-42292, 2025.

Abstract

Despite the growing popularity of graph attention mechanisms, their theoretical understanding remains limited. This paper aims to explore the conditions under which these mechanisms are effective in node classification tasks through the lens of Contextual Stochastic Block Models (CSBMs). Our theoretical analysis reveals that incorporating graph attention mechanisms is not universally beneficial. Specifically, by appropriately defining structure noise and feature noise in graphs, we show that graph attention mechanisms can enhance classification performance when structure noise exceeds feature noise. Conversely, when feature noise predominates, simpler graph convolution operations are more effective. Furthermore, we examine the over-smoothing phenomenon and show that, in the high signal-to-noise ratio (SNR) regime, graph convolutional networks suffer from over-smoothing, whereas graph attention mechanisms can effectively resolve this issue. Building on these insights, we propose a novel multi-layer Graph Attention Network (GAT) architecture that significantly outperforms single-layer GATs in achieving perfect node classification in CSBMs, relaxing the SNR requirement from $\omega(\sqrt{\log n})$ to $\omega(\sqrt{\log n} / \sqrt[3]{n})$. To our knowledge, this is the first study to delineate the conditions for perfect node classification using multi-layer GATs. Our theoretical contributions are corroborated by extensive experiments on both synthetic and real-world datasets, highlighting the practical implications of our findings.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-ma25w, title = {Graph Attention is Not Always Beneficial: A Theoretical Analysis of Graph Attention Mechanisms via Contextual Stochastic Block Models}, author = {Ma, Zhongtian and Zhang, Qiaosheng and Zhou, Bocheng and Zhang, Yexin and Hu, Shuyue and Wang, Zhen}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {42252--42292}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/ma25w/ma25w.pdf}, url = {https://proceedings.mlr.press/v267/ma25w.html}, abstract = {Despite the growing popularity of graph attention mechanisms, their theoretical understanding remains limited. This paper aims to explore the conditions under which these mechanisms are effective in node classification tasks through the lens of Contextual Stochastic Block Models (CSBMs). Our theoretical analysis reveals that incorporating graph attention mechanisms is not universally beneficial. Specifically, by appropriately defining structure noise and feature noise in graphs, we show that graph attention mechanisms can enhance classification performance when structure noise exceeds feature noise. Conversely, when feature noise predominates, simpler graph convolution operations are more effective. Furthermore, we examine the over-smoothing phenomenon and show that, in the high signal-to-noise ratio (SNR) regime, graph convolutional networks suffer from over-smoothing, whereas graph attention mechanisms can effectively resolve this issue. Building on these insights, we propose a novel multi-layer Graph Attention Network (GAT) architecture that significantly outperforms single-layer GATs in achieving perfect node classification in CSBMs, relaxing the SNR requirement from $\omega(\sqrt{\log n})$ to $\omega(\sqrt{\log n} / \sqrt[3]{n})$. To our knowledge, this is the first study to delineate the conditions for perfect node classification using multi-layer GATs. Our theoretical contributions are corroborated by extensive experiments on both synthetic and real-world datasets, highlighting the practical implications of our findings.} }
Endnote
%0 Conference Paper %T Graph Attention is Not Always Beneficial: A Theoretical Analysis of Graph Attention Mechanisms via Contextual Stochastic Block Models %A Zhongtian Ma %A Qiaosheng Zhang %A Bocheng Zhou %A Yexin Zhang %A Shuyue Hu %A Zhen Wang %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-ma25w %I PMLR %P 42252--42292 %U https://proceedings.mlr.press/v267/ma25w.html %V 267 %X Despite the growing popularity of graph attention mechanisms, their theoretical understanding remains limited. This paper aims to explore the conditions under which these mechanisms are effective in node classification tasks through the lens of Contextual Stochastic Block Models (CSBMs). Our theoretical analysis reveals that incorporating graph attention mechanisms is not universally beneficial. Specifically, by appropriately defining structure noise and feature noise in graphs, we show that graph attention mechanisms can enhance classification performance when structure noise exceeds feature noise. Conversely, when feature noise predominates, simpler graph convolution operations are more effective. Furthermore, we examine the over-smoothing phenomenon and show that, in the high signal-to-noise ratio (SNR) regime, graph convolutional networks suffer from over-smoothing, whereas graph attention mechanisms can effectively resolve this issue. Building on these insights, we propose a novel multi-layer Graph Attention Network (GAT) architecture that significantly outperforms single-layer GATs in achieving perfect node classification in CSBMs, relaxing the SNR requirement from $\omega(\sqrt{\log n})$ to $\omega(\sqrt{\log n} / \sqrt[3]{n})$. To our knowledge, this is the first study to delineate the conditions for perfect node classification using multi-layer GATs. Our theoretical contributions are corroborated by extensive experiments on both synthetic and real-world datasets, highlighting the practical implications of our findings.
APA
Ma, Z., Zhang, Q., Zhou, B., Zhang, Y., Hu, S. & Wang, Z.. (2025). Graph Attention is Not Always Beneficial: A Theoretical Analysis of Graph Attention Mechanisms via Contextual Stochastic Block Models. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:42252-42292 Available from https://proceedings.mlr.press/v267/ma25w.html.

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