Poly-WaveGC: A Generalized Spectral Wavelet Graph Convolution Network with Adaptive Orthogonal Polynomials

Wei Cao, Rachid Hedjam, Bessam Abdulrazak, Jun-Peng Zhu
Proceedings of the The 39th Canadian Conference on Artificial Intelligence, PMLR 318:342-353, 2026.

Abstract

Spectral Graph Neural Networks (GNNs) typically rely on fixed polynomial bases, such as Chebyshev polynomials, to approximate graph filters. While efficient, these bases enforce a rigid weight function that implicitly assumes a specific prior on the graph signal density, often leading to suboptimal fitting on graphs with diverse spectral distributions. In this paper, we propose Poly-WaveGC, a generalized spectral graph wavelet framework. We introduce a novel zero-point shift mechanism to adapt general Jacobi polynomials for wavelet construction. This approach allows the basis parameters ($\alpha$, $\beta$) to flexibly learn the graph’s specific spectral density while strictly enforcing the wavelet admissibility condition (g(0)=0) structurally. To address the loss of orthogonality inherent in adaptive bases, we introduce an explicit frame-bound regularization that constrains the filter bank to approximate a tight frame, thereby guaranteeing numerical stability. Extensive experiments on 10 benchmarks demonstrate that Poly-WaveGC significantly outperforms fixed-basis baselines on diverse graph structures and tasks, while maintaining robustness in deep networks. The code is available at https://github.com/weicaocw/Poly-WaveGC-public.

Cite this Paper

BibTeX
@InProceedings{pmlr-v318-cao26a, title = {Poly-WaveGC: A Generalized Spectral Wavelet Graph Convolution Network with Adaptive Orthogonal Polynomials}, author = {Cao, Wei and Hedjam, Rachid and Abdulrazak, Bessam and Zhu, Jun-Peng}, booktitle = {Proceedings of the The 39th Canadian Conference on Artificial Intelligence}, pages = {342--353}, year = {2026}, editor = {Bouzar-Benlabiod, Lydia and Leung, Carson}, volume = {318}, series = {Proceedings of Machine Learning Research}, month = {25--29 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v318/main/assets/cao26a/cao26a.pdf}, url = {https://proceedings.mlr.press/v318/cao26a.html}, abstract = {Spectral Graph Neural Networks (GNNs) typically rely on fixed polynomial bases, such as Chebyshev polynomials, to approximate graph filters. While efficient, these bases enforce a rigid weight function that implicitly assumes a specific prior on the graph signal density, often leading to suboptimal fitting on graphs with diverse spectral distributions. In this paper, we propose Poly-WaveGC, a generalized spectral graph wavelet framework. We introduce a novel zero-point shift mechanism to adapt general Jacobi polynomials for wavelet construction. This approach allows the basis parameters ($\alpha$, $\beta$) to flexibly learn the graph’s specific spectral density while strictly enforcing the wavelet admissibility condition (g(0)=0) structurally. To address the loss of orthogonality inherent in adaptive bases, we introduce an explicit frame-bound regularization that constrains the filter bank to approximate a tight frame, thereby guaranteeing numerical stability. Extensive experiments on 10 benchmarks demonstrate that Poly-WaveGC significantly outperforms fixed-basis baselines on diverse graph structures and tasks, while maintaining robustness in deep networks. The code is available at https://github.com/weicaocw/Poly-WaveGC-public.} }
Endnote
%0 Conference Paper %T Poly-WaveGC: A Generalized Spectral Wavelet Graph Convolution Network with Adaptive Orthogonal Polynomials %A Wei Cao %A Rachid Hedjam %A Bessam Abdulrazak %A Jun-Peng Zhu %B Proceedings of the The 39th Canadian Conference on Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Lydia Bouzar-Benlabiod %E Carson Leung %F pmlr-v318-cao26a %I PMLR %P 342--353 %U https://proceedings.mlr.press/v318/cao26a.html %V 318 %X Spectral Graph Neural Networks (GNNs) typically rely on fixed polynomial bases, such as Chebyshev polynomials, to approximate graph filters. While efficient, these bases enforce a rigid weight function that implicitly assumes a specific prior on the graph signal density, often leading to suboptimal fitting on graphs with diverse spectral distributions. In this paper, we propose Poly-WaveGC, a generalized spectral graph wavelet framework. We introduce a novel zero-point shift mechanism to adapt general Jacobi polynomials for wavelet construction. This approach allows the basis parameters ($\alpha$, $\beta$) to flexibly learn the graph’s specific spectral density while strictly enforcing the wavelet admissibility condition (g(0)=0) structurally. To address the loss of orthogonality inherent in adaptive bases, we introduce an explicit frame-bound regularization that constrains the filter bank to approximate a tight frame, thereby guaranteeing numerical stability. Extensive experiments on 10 benchmarks demonstrate that Poly-WaveGC significantly outperforms fixed-basis baselines on diverse graph structures and tasks, while maintaining robustness in deep networks. The code is available at https://github.com/weicaocw/Poly-WaveGC-public.
APA
Cao, W., Hedjam, R., Abdulrazak, B. & Zhu, J.. (2026). Poly-WaveGC: A Generalized Spectral Wavelet Graph Convolution Network with Adaptive Orthogonal Polynomials. Proceedings of the The 39th Canadian Conference on Artificial Intelligence, in Proceedings of Machine Learning Research 318:342-353 Available from https://proceedings.mlr.press/v318/cao26a.html.

Related Material