{"ID":2848302,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.00113","arxiv_id":"2511.00113","title":"MeixnerNet: Adaptive and Robust Spectral Graph Neural Networks with Discrete Orthogonal Polynomials","abstract":"Spectral Graph Neural Networks (GNNs) have achieved state-of-the-art results by defining graph convolutions in the spectral domain. A common approach, popularized by ChebyNet, is to use polynomial filters based on continuous orthogonal polynomials (e.g., Chebyshev). This creates a theoretical disconnect, as these continuous-domain filters are applied to inherently discrete graph structures. We hypothesize this mismatch can lead to suboptimal performance and fragility to hyperparameter settings. In this paper, we introduce MeixnerNet, a novel spectral GNN architecture that employs discrete orthogonal polynomials -- specifically, the Meixner polynomials $M_k(x; β, c)$. Our model makes the two key shape parameters of the polynomial, beta and c, learnable, allowing the filter to adapt its polynomial basis to the specific spectral properties of a given graph. We overcome the significant numerical instability of these polynomials by introducing a novel stabilization technique that combines Laplacian scaling with per-basis LayerNorm. We demonstrate experimentally that MeixnerNet achieves competitive-to-superior performance against the strong ChebyNet baseline at the optimal K = 2 setting (winning on 2 out of 3 benchmarks). More critically, we show that MeixnerNet is exceptionally robust to variations in the polynomial degree K, a hyperparameter to which ChebyNet proves to be highly fragile, collapsing in performance where MeixnerNet remains stable.","short_abstract":"Spectral Graph Neural Networks (GNNs) have achieved state-of-the-art results by defining graph convolutions in the spectral domain. A common approach, popularized by ChebyNet, is to use polynomial filters based on continuous orthogonal polynomials (e.g., Chebyshev). This creates a theoretical disconnect, as these conti...","url_abs":"https://arxiv.org/abs/2511.00113","url_pdf":"https://arxiv.org/pdf/2511.00113v1","authors":"[\"Huseyin Goksu\"]","published":"2025-10-30T23:50:21Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"eess.SP\"]","methods":"[\"Graph Neural Network\"]","has_code":false}