{"ID":2838927,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.16081","arxiv_id":"2511.16081","title":"L-JacobiNet and S-JacobiNet: An Analysis of Adaptive Generalization, Stabilization, and Spectral Domain Trade-offs in GNNs","abstract":"Spectral GNNs, like ChebyNet, are limited by heterophily and over-smoothing due to their static, low-pass filter design. This work investigates the \"Adaptive Orthogonal Polynomial Filter\" (AOPF) class as a solution. We introduce two models operating in the [-1, 1] domain: 1) `L-JacobiNet`, the adaptive generalization of `ChebyNet` with learnable alpha, beta shape parameters, and 2) `S-JacobiNet`, a novel baseline representing a LayerNorm-stabilized static `ChebyNet`. Our analysis, comparing these models against AOPFs in the [0, infty) domain (e.g., `LaguerreNet`), reveals critical, previously unknown trade-offs. We find that the [0, infty) domain is superior for modeling heterophily, while the [-1, 1] domain (Jacobi) provides superior numerical stability at high K (K\u003e20). Most significantly, we discover that `ChebyNet`'s main flaw is stabilization, not its static nature. Our static `S-JacobiNet` (ChebyNet+LayerNorm) outperforms the adaptive `L-JacobiNet` on 4 out of 5 benchmark datasets, identifying `S-JacobiNet` as a powerful, overlooked baseline and suggesting that adaptation in the [-1, 1] domain can lead to overfitting.","short_abstract":"Spectral GNNs, like ChebyNet, are limited by heterophily and over-smoothing due to their static, low-pass filter design. This work investigates the \"Adaptive Orthogonal Polynomial Filter\" (AOPF) class as a solution. We introduce two models operating in the [-1, 1] domain: 1) `L-JacobiNet`, the adaptive generalization o...","url_abs":"https://arxiv.org/abs/2511.16081","url_pdf":"https://arxiv.org/pdf/2511.16081v1","authors":"[\"Huseyin Goksu\"]","published":"2025-11-20T06:17:02Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"eess.SP\"]","methods":"[\"Graph Neural Network\"]","has_code":false}