{"type":"ScholarlyArticle","title":"A Unified Spectral-Spatial Framework for GNNs: Balancing Over-Smoothing and Over-Squashing","authors":[{"name":"Xinya Qin","slug":"xinya-qin","given":"Xinya","family":"Qin","affiliation":""},{"name":"Lu Bai","slug":"lu-bai","given":"Lu","family":"Bai","affiliation":""},{"name":"Lixin Cui","slug":"lixin-cui","given":"Lixin","family":"Cui","affiliation":""},{"name":"Ming Li","slug":"ming-li","given":"Ming","family":"Li","affiliation":""},{"name":"Hangyuan Du","slug":"hangyuan-du","given":"Hangyuan","family":"Du","affiliation":""},{"name":"Jing Li","slug":"jing-li","given":"Jing","family":"Li","affiliation":""}],"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.","doi":"10.24963/ijcai.2026/330","url":"https://ijcai.org/proceedings/2026/330","pdf":"https://ijcai.org/proceedings/2026/0330.pdf","markdown":"https://ijcai.org/proceedings/2026/330.md","bibtex":"https://ijcai.org/proceedings/2026/bibtex/330","volume":{"slug":"2026","title":"Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2026","url":"https://ijcai.org/proceedings/2026/","year":2026,"location":"Bremen, Germany","dates":"15-21 August 2026","editors":"Diego Calvanese","isbn":"978-1-956792-09-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2026"},"section":"Data Mining","track":"Main Track","number":330,"pages":{"first":2969,"last":2978},"keywords":["Data Mining: Mining graphs"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}