Proceedings

A Unified Spectral-Spatial Framework for GNNs: Balancing Over-Smoothing and Over-Squashing

Xinya Qin, Lu Bai, Lixin Cui, Ming Li, Hangyuan Du, Jing Li

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Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence. Main Track. Pages 2969-2978.

https://doi.org/10.24963/ijcai.2026/330

Keywords

  • Data Mining: Mining graphs

Abstract

Over-smoothing (OSM) and over-squashing (OSQ) are two fundamental phenomena that limit the performance of Graph Neural Networks (GNNs), yet a unified spectral-spatial understanding of these phenomena remains underexplored. In this paper, we adopt polynomial spectral filters as an analytical tool to establish a unified spectral-spatial framework for graph convolution and systematically characterize the effect of the polynomial order k on information propagation in GNNs. Within this framework, we reveal an intrinsic trade-off induced by the polynomial order. Specifically, higher-order filters enhance spectral expressiveness and alleviate OSM caused by the dominant low-frequency components. However, they also expand the spatial receptive field, thereby intensifying information compression and increasing the risk of OSQ. Based on this analysis, we provide a principled guideline for selecting the polynomial order and propose a Quadratic Spectral Graph Convolution Network (QS-GCN) for graph classification. Experiments demonstrate the effectiveness and robustness of the proposed method.

Xinya Qin, Lu Bai, Lixin Cui, Ming Li, Hangyuan Du, and Jing Li. 2026. A Unified Spectral-Spatial Framework for GNNs: Balancing Over-Smoothing and Over-Squashing. In Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence, IJCAI-26. IJCAI, 2969–2978. https://doi.org/10.24963/ijcai.2026/330
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