Aug 2026· Proceedings of the 32nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.2· pp. 5614-5625· 0 citations· 23 references
Abstract
Identifying influential nodes in graph-structured data is a fundamental challenge. Traditional metrics ignore non-linear GNN semantics, while deep influence maximization methods require computationally expensive, simulation-based supervision. To bridge the gap between topological analysis and deep representation learning, we propose Hyperspherical Representation Equilibrium Shift (HyRES), a theoretically grounded, unsupervised framework that redefines node influence as a geometric displacement within the latent space. We conceptualize a trained GNN on a hyperspherical manifold as a physical system in thermodynamic equilibrium, stabilized by competing attractive and repulsive forces. We leverage Linear Response Theory to derive a closed-form approximation of the global representation shift caused by a node's removal. This mathematically decouples influence into the node's residual force and local structural stiffness, explaining why lower-degree bridges often exert greater global impact than redundant dense hubs. Empirically, HyRES enables efficient, near-linear time inference via Hessian-Vector Products, scaling seamlessly to large graphs. Extensive experiments demonstrate that HyRES outperforms state-of-the-art supervised baselines, exhibiting exceptional robustness on heterophilic graphs and under unknown diffusion dynamics. Code is available at: https://github.com/xianyt/HyRES.
ELSS learns an explicit and nonlinear low-rank subspace within a graph-structured embedding space, effectively un-covering latent cluster structures and introduces a homophily-aware adaptive graph filter, which dynamically calibrates smoothing intensity to preserve discriminative ego-information.
Yaoming Cai, Song Liu, Zijia Zhang et al.· 0 citations
H4G, a framework that systematically reduces embedding radii using learnable block-diagonal scaling matrices and Möbius matrix multiplication, is proposed, demonstrating that faithful preservation of fine-grained structural details requires faithful preservation of fine-grained structural details in graph learning.
Heng Zhang, Jin Huang· Proceedings of the 32nd ACM...· 0 citations
The Stable Reaction-Diffusion encoder (SRD) provides a trajectory-stabilizing forward evolution mechanism that explicitly controls propagation drift and finite-depth sensitivity, rather than simply stacking additional message-passing layers.
Jiajun Lin, Yuxin Tian, Li Feng et al.· Neural Networks· 0 citations
Deep graph neural networks(GNNs) suffer from oversmoothing- a progressive collapse of node representation towards a low information subspace as network depth increases because the normalized graph propagation operator is repeatedly applied directly to the hidden representations. In this work we study Householder Graph Neural Network (HouseGNN). Rather than updating the hidden state like standard GCN, HouseGNN uses the aggregated neighbourhood message solely to estimate a reflection direction; the node embedding is then updated by a Householder reflector followed by GroupSort, yielding a piecewise orthogonal layer that preserves Euclidean norm at every node and at every depth. We prove three core properties: (i) every internal layer preserves the node-wise Euclidean norm; (ii) the Householder reflector is scale scale and sign-invariant in the message; and (iii) pairwise distance between nodes can change through mismatch between node-wise orthogonal operators.
DiffGCC is a generative graph contrastive clustering framework that couples global–local feature encoding with a latent-space diffusion denoising mechanism and substantially outperforms existing methods across ACC, NMI, ARI, and F1, with particularly strong gains on denser, noisier product graphs.
Lun Liu, Chengyun Song· Pattern Analysis and Applica...· 0 citations
This framework introduces a dual-encoder architecture that separately processes structural and attribute information, incorporates node positional encoding to approximate Neighborhood Identity Distribution (NID), and employs dual reconstruction tasks for both edges and node attributes.
