KrawtchoukNet: A Unified GNN Solution for Heterophily and Over-smoothing with Adaptive Bounded Polynomials
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| Format: | Preprint |
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2025
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| _version_ | 1866915626778361856 |
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| author | Goksu, Huseyin |
| author_facet | Goksu, Huseyin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_15327 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | KrawtchoukNet: A Unified GNN Solution for Heterophily and Over-smoothing with Adaptive Bounded Polynomials Goksu, Huseyin Machine Learning Signal Processing 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. |
| title | KrawtchoukNet: A Unified GNN Solution for Heterophily and Over-smoothing with Adaptive Bounded Polynomials |
| topic | Machine Learning Signal Processing |
| url | https://arxiv.org/abs/2511.15327 |