{"ID":2846373,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.13729","arxiv_id":"2511.13729","title":"DualLaguerreNet: A Decoupled Spectral Filter GNN and the Uncovering of the Flexibility-Stability Trade-off","abstract":"Graph Neural Networks (GNNs) based on spectral filters, such as the Adaptive Orthogonal Polynomial Filter (AOPF) class (e.g., LaguerreNet), have shown promise in unifying the solutions for heterophily and over-smoothing. However, these single-filter models suffer from a \"compromise\" problem, as their single adaptive parameter (e.g., alpha) must learn a suboptimal, averaged response across the entire graph spectrum. In this paper, we propose DualLaguerreNet, a novel GNN architecture that solves this by introducing \"Decoupled Spectral Flexibility.\" DualLaguerreNet splits the graph Laplacian into two operators, L_low (low-frequency) and L_high (high-frequency), and learns two independent, adaptive Laguerre polynomial filters, parameterized by alpha_1 and alpha_2, respectively. This work, however, uncovers a deeper finding. While our experiments show DualLaguerreNet's flexibility allows it to achieve state-of-the-art results on complex heterophilic tasks (outperforming LaguerreNet), it simultaneously underperforms on simpler, homophilic tasks. We identify this as a fundamental \"Flexibility-Stability Trade-off\". The increased parameterization (2x filter parameters and 2x model parameters) leads to overfitting on simple tasks, demonstrating that the \"compromise\" of simpler models acts as a crucial regularizer. This paper presents a new SOTA architecture for heterophily while providing a critical analysis of the bias-variance trade-off inherent in adaptive GNN filter design.","short_abstract":"Graph Neural Networks (GNNs) based on spectral filters, such as the Adaptive Orthogonal Polynomial Filter (AOPF) class (e.g., LaguerreNet), have shown promise in unifying the solutions for heterophily and over-smoothing. However, these single-filter models suffer from a \"compromise\" problem, as their single adaptive pa...","url_abs":"https://arxiv.org/abs/2511.13729","url_pdf":"https://arxiv.org/pdf/2511.13729v1","authors":"[\"Huseyin Goksu\"]","published":"2025-11-04T19:33:29Z","proceeding":"eess.SP","tasks":"[\"eess.SP\",\"cs.AI\",\"cs.LG\"]","methods":"[\"Graph Neural Network\"]","has_code":false}