L-JacobiNet and S-JacobiNet: An Analysis of Adaptive Generalization, Stabilization, and Spectral Domain Trade-offs in GNNs

• URL: http://arxiv.org/abs/2511.16081v1
• Date: Thu, 20 Nov 2025 06:17:02 GMT
• Title: L-JacobiNet and S-JacobiNet: An Analysis of Adaptive Generalization, Stabilization, and Spectral Domain Trade-offs in GNNs
• Authors: Huseyin Goksu,
• Abstract summary: Spectral GNNs, like ChebyNet, are limited by heterophily and over-smoothing due to their static, low-pass filter design.<n>This work investigates the "Adaptive Orthogonal Polynomial Filter" (AOPF) class as a solution.<n>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
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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>20). 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.

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