Papers › HoloNets: Spectral Convolutions do extend to Directed Graphs
HoloNets: Spectral Convolutions do extend to Directed Graphs
Christian Koke, Daniel Cremers
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.
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Node Classification | Chameleon | FaberNet | Accuracy | 80.33±1.19 | #2 of 61 | Archive leaderboard | report |
| Node Classification | Squirrel | FaberNet | Accuracy | 76.71±1.92 | #1 of 59 | Archive leaderboard | report |
| Node Classification | arXiv-year | FaberNet | Accuracy | 64.62±1.01 | #2 of 12 | Archive leaderboard | report |
| Node Classification | roman-empire | FaberNet | Accuracy (% ) | 92.24±0.43 | #3 of 7 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
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