## BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation

21 May 2021, 20:48 (modified: 08 Nov 2021, 03:49)NeurIPS 2021 PosterReaders: Everyone
Keywords: Graph Neural Networks, Bernstein Polynomial Approximation, Arbitrary Spectral Filters
TL;DR: We propose BernNet, a graph neural network that designs and learns an arbitrary spectral filter via Bernstein polynomial approximation.
Abstract: Many representative graph neural networks, $e.g.$, GPR-GNN and ChebNet, approximate graph convolutions with graph spectral filters. However, existing work either applies predefined filter weights or learns them without necessary constraints, which may lead to oversimplified or ill-posed filters. To overcome these issues, we propose $\textit{BernNet}$, a novel graph neural network with theoretical support that provides a simple but effective scheme for designing and learning arbitrary graph spectral filters. In particular, for any filter over the normalized Laplacian spectrum of a graph, our BernNet estimates it by an order-$K$ Bernstein polynomial approximation and designs its spectral property by setting the coefficients of the Bernstein basis. Moreover, we can learn the coefficients (and the corresponding filter weights) based on observed graphs and their associated signals and thus achieve the BernNet specialized for the data. Our experiments demonstrate that BernNet can learn arbitrary spectral filters, including complicated band-rejection and comb filters, and it achieves superior performance in real-world graph modeling tasks. Code is available at https://github.com/ivam-he/BernNet.
Supplementary Material: zip
Code Of Conduct: I certify that all co-authors of this work have read and commit to adhering to the NeurIPS Statement on Ethics, Fairness, Inclusivity, and Code of Conduct.
Code: https://github.com/ivam-he/BernNet
9 Replies