{"ID":2839505,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.15327","arxiv_id":"2511.15327","title":"KrawtchoukNet: A Unified GNN Solution for Heterophily and Over-smoothing with Adaptive Bounded Polynomials","abstract":"Spectral Graph Neural Networks (GNNs) based on polynomial filters, such as ChebyNet, suffer from two critical limitations: 1) performance collapse on \"heterophilic\" graphs and 2) performance collapse at high polynomial degrees (K), known as over-smoothing. Both issues stem from the static, low-pass nature of standard filters. In this work, we propose `KrawtchoukNet`, a GNN filter based on the discrete Krawtchouk polynomials. We demonstrate that `KrawtchoukNet` provides a unified solution to both problems through two key design choices. First, by fixing the polynomial's domain N to a small constant (e.g., N=20), we create the first GNN filter whose recurrence coefficients are \\textit{inherently bounded}, making it exceptionally robust to over-smoothing (achieving SOTA results at K=10). Second, by making the filter's shape parameter p learnable, the filter adapts its spectral response to the graph data. We show this adaptive nature allows `KrawtchoukNet` to achieve SOTA performance on challenging heterophilic benchmarks (Texas, Cornell), decisively outperforming standard GNNs like GAT and APPNP.","short_abstract":"Spectral Graph Neural Networks (GNNs) based on polynomial filters, such as ChebyNet, suffer from two critical limitations: 1) performance collapse on \"heterophilic\" graphs and 2) performance collapse at high polynomial degrees (K), known as over-smoothing. Both issues stem from the static, low-pass nature of standard f...","url_abs":"https://arxiv.org/abs/2511.15327","url_pdf":"https://arxiv.org/pdf/2511.15327v1","authors":"[\"Huseyin Goksu\"]","published":"2025-11-19T10:47:15Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"eess.SP\"]","methods":"[\"Graph Neural Network\"]","has_code":false}