---
title: "A Unified Spectral-Spatial Framework for GNNs: Balancing Over-Smoothing and Over-Squashing"
authors:
  - "Xinya Qin"
  - "Lu Bai"
  - "Lixin Cui"
  - "Ming Li"
  - "Hangyuan Du"
  - "Jing Li"
doi: "10.24963/ijcai.2026/330"
url: "https://ijcai.org/proceedings/2026/330"
pdf: "https://ijcai.org/proceedings/2026/0330.pdf"
venue: "Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence"
year: 2026
pages: "2969-2978"
track: "Main Track"
keywords:
  - "Data Mining: Mining graphs"
---

# 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

*Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence*, pages 2969-2978. DOI: [10.24963/ijcai.2026/330](https://doi.org/10.24963/ijcai.2026/330)

## 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.