HoloNets: Spectral Convolutions do extend to Directed Graphs
Authors: Christian Koke,Daniel Cremers
Presentation: ICLR 2024,Poster

Abstract: Within the graph learning community, conventional wisdom dictates that spectral convolutional networks may only be deployed on undirected graphs: Only there could the existence of a well-defined graph Fourier transform be guaranteed, so that information may be translated between spatial- and spectral domains. Here we show this traditional reliance on the graph Fourier transform to be superfluous and -- making use of certain advanced tools from  complex analysis and spectral theory -- extend spectral convolutions to directed graphs. 
We provide a frequency-response interpretation of newly developed filters, investigate the influence of the basis used to express filters and discuss the interplay with characteristic operators on which networks are based. In order to thoroughly test the developed  theory, we conduct experiments in real world settings, showcasing that  directed spectral convolutional networks provide new state of the art results for heterophilic node classification on many  datasets  and -- as opposed to baselines -- may be rendered stable to resolution-scale varying topological perturbations.