Research map / Graph learning / GNN architectures

Spectral GNN design

Improve spectral GNN filters and understand their reliance on Fourier basis.

37 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2019–2026) · an approach in GNN architectures, keyword cluster “convolutional · gcns · spectral”

State History Benchmarks Tried Baselines Checklist Preprints Who Export

How it got here

Most cited paper of each year

• 2019 · Stability of Graph Scattering Transforms (NeurIPS 2019 · 38 citations)
• 2020 · On the equivalence of molecular graph convolution and molecular wave function with poor basis set (NeurIPS 2020 · 6 citations)
• 2021 · BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation (NeurIPS 2021 · 30 citations)
• 2022 · Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited (NeurIPS 2022 · 46 citations)
• 2023 · Sign and Basis Invariant Networks for Spectral Graph Representation Learning (ICLR 2023 · 24 citations)
• 2024 · Improving Expressive Power of Spectral Graph Neural Networks with Eigenvalue Correction (AAAI 2024 · 12 citations)
• 2025 · A General Graph Spectral Wavelet Convolution via Chebyshev Order Decomposition (ICML 2025 · 2 citations)
• 2026 · L2G-NET: Local to Global Spectral Graph Neural Networks via Cauchy Factorizations (ICML 2026 · 0 citations)

Earliest papers here

• Stability of Graph Scattering Transforms (NeurIPS 2019 · 38 citations)
• DFNets: Spectral CNNs for Graphs with Feedback-Looped Filters (NeurIPS 2019 · 13 citations)
• On the equivalence of molecular graph convolution and molecular wave function with poor basis set (NeurIPS 2020 · 6 citations)

Benchmark records

The best number each year that beat every earlier one, among papers of this approach reporting their own method. Numbers are extracted by AI from each paper's text; check the paper before citing.

What has been tried

28 papers here report 300 measured changes (a component added, removed or swapped, compared with a baseline): helped 67%, no clear effect 9%, hurt 19%, mixed 5%. Papers mostly publish changes that helped, so "helped" is over-represented.

Ablations in recent papers

Baseline numbers that disagree

The same baseline on the same benchmark and metric, reported more than 5% apart by different papers here. Training budgets, data splits and reimplementations differ, so state which number you compare with.

What reviewers will expect

Datasets and baselines named in the 12 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.

Recent preprints

Who publishes on it

Institutions on the most papers of this approach since 2023 (of 29 papers; from OpenAlex and the papers' affiliations).

• National University of Singapore · 4 papers
• Renmin University of China · 2 papers
• Massachusetts Institute of Technology · 2 papers
• Dalian University of Technology · 2 papers
• University of Illinois, Urbana Champaign · 2 papers
• IBM · 2 papers

Use it

Download BibTeX of 32 key papersOpen the topic in the interactive map

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Related approaches

Same keyword cluster

• Deep graph convolution and simplification (82 papers)
• Oversmoothing and heterophily (60 papers)
• Theory of graph convolutional networks (83 papers)

Elsewhere in the topic

• Graph structure learning (201 papers)
• GNN generalization theory (187 papers)
• Simple and scalable GNNs (131 papers)
• Expressive equivariant message passing (109 papers)
• Robustness, privacy, and fairness of GNNs (94 papers)
• Physics-inspired GNNs (81 papers)
• Graph rewiring and scalable message passing (72 papers)
• Weisfeiler-Leman expressivity hierarchies (66 papers)

Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).