BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation

Many representative graph neural networks, e. g. , GPR-GNN and ChebNet, graph convolutions with graph spectral filters. However, existing either applies predefined filter weights or learns them without necessary, which may lead to oversimplified or ill-posed filters. To overcome issues, we propose BernNet, a novel graph neural network with theoretical that provides a simple but effective scheme for designing and learning graph spectral filters. In particular, for any filter over the Laplacian spectrum of a graph, our BernNet estimates it by an-K Bernstein polynomial approximation and designs its spectral property setting the coefficients of the Bernstein basis. Moreover, we can learn the (and the corresponding filter weights) based on observed graphs their associated signals and thus achieve the BernNet specialized for the. Our experiments demonstrate that BernNet can learn arbitrary spectral, including complicated band-rejection and comb filters, and it achieves performance in real-world graph modeling tasks. Code is available at: //github. com/ivam-he/BernNet.