Research map / Graph learning / GNN architectures
Theory of graph convolutional networks
Analyze convergence and transferability of graph convolutional networks on random graphs.
83 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in GNN architectures, keyword cluster “convolutional · gcns · spectral”
State History Benchmarks Tried Baselines Checklist Preprints Who Export
Where it stands
Quiet None of the tracked benchmarks has a report from 2025–26.
23 papers in 2023–24 and 15 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 4.9% to 3.0%.
No longer reported by papers here: NCI1 (accuracy (%), last in 2022).
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering (NeurIPS 2016 · 1,699 citations)
- 2017 · Deep Learning with Dynamic Computation Graphs (ICLR 2017 · 88 citations)
- 2018 · SplineCNN: Fast Geometric Deep Learning With Continuous B-Spline Kernels (CVPR 2018 · 460 citations)
- 2019 · LanczosNet: Multi-Scale Deep Graph Convolutional Networks (ICLR 2019 · 183 citations)
- 2020 · Learning-Based Efficient Graph Similarity Computation via Multi-Scale Convolutional Set Matching (AAAI 2020 · 86 citations)
- 2021 · MagNet: A Neural Network for Directed Graphs (NeurIPS 2021 · 47 citations)
- 2022 · Early-Bird GCNs: Graph-Network Co-optimization towards More Efficient GCN Training and Inference via Drawing Early-Bird Lottery Tickets (AAAI 2022 · 20 citations)
- 2023 · SigMaNet: One Laplacian to Rule Them All (AAAI 2023 · 23 citations)
- 2024 · Generating Diagnostic and Actionable Explanations for Fair Graph Neural Networks (AAAI 2024 · 21 citations)
- 2025 · DeepSN: A Sheaf Neural Framework for Influence Maximization (AAAI 2025 · 10 citations)
- 2026 · Neural Graph Navigation for Intelligent Subgraph Matching (AAAI 2026 · 1 citation)
Earliest papers here
- Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering (NeurIPS 2016 · 1,699 citations)
- Learning Convolutional Neural Networks for Graphs (ICML 2016 · 808 citations)
- Semiparametric Differential Graph Models (NeurIPS 2016 · 12 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.
NCI1 · accuracy (%) (higher is better)
4 papers, 2016–2022 · not reported since 2022
| Year | Best so far | Set by |
|---|---|---|
| 2016 | 78.59 | Learning Convolutional Neural Networks for Graphs (ICML 2016 · 808 citations) |
| 2022 | 81.9 | Capturing Graphs with Hypo-Elliptic Diffusions (NeurIPS 2022 · 0 citations) |
What has been tried
68 papers here report 683 measured changes (a component added, removed or swapped, compared with a baseline): helped 66%, no clear effect 11%, hurt 20%, mixed 3%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Remove the identified biased subgraphs without performing stage two | NBA, Pokec-z, and Pokec-n · ∆SP | Helped | Generating Diagnostic and Actionable Explanations for Fair Graph Neural Networks (AAAI 2024 · 21 citations) | |
| add pointwise and coupled reaction components | Cora-ML, 1% seeds · average total influence (%) | 9.7 -> 11.5 | Helped | DeepSN: A Sheaf Neural Framework for Influence Maximization (AAAI 2025 · 10 citations) |
| add stochastic path dropout decay | ImageNet-100 · Top-1 accuracy | 81.89 -> 84.36 | Helped | Hypergraph Vision Transformers: Images are More than Nodes, More than Edges (CVPR 2025 · 8 citations) |
| Replace linear similarity sampling with Gaussian similarity sampling | CiteSeer · accuracy | 67.23±0.23 -> 69.19±0.14 | Helped | Neural Gaussian Similarity Modeling for Differential Graph Structure Learning (AAAI 2024 · 5 citations) |
| Add information bottleneck (IB) optimization to multi-scale condensation | Citeseer, multiple target reduction scales · accuracy consistency across scales | Helped | Bi-Directional Multi-Scale Graph Dataset Condensation via Information Bottleneck (AAAI 2025 · 4 citations) | |
| use joint product-graph learning instead of sequential TTS | MetrLA H=12 · MAE | 3.67 -> 3.44 | Helped | Continuous Product Graph Neural Networks (NeurIPS 2024 · 4 citations) |
| add the label network | MIRFlickr · mAP (32 bits) | 0.859 -> 0.871 | Helped | Deep Graph Online Hashing for Multi-Label Image Retrieval (AAAI 2025 · 2 citations) |
| Multiply the learned threshold parameter by 0.1 | synthetic sparse precision matrix recovery · convergence | 0.1 | Helped | Schur's Positive-Definite Network: Deep Learning in the SPD cone with structure (ICLR 2025 · 1 citation) |
| Add BAM | Undirected graph estimation, Chebyshev dependencies · loss | 0.202 ± 0.005 -> 0.173 ± 0.007 | Helped | Graph Structure Inference with BAM: Neural Dependency Processing via Bilinear Attention (NeurIPS 2024 · 1 citation) |
| Add L1 regularization to the WILT edge-weight objective | Mutagenicity · RMSE | Hurt | WILTing Trees: Interpreting the Distance Between MPNN Embeddings (ICML 2025 · 0 citations) | |
| add shortcut connections to the unsupervised embeddings | NCI1 · accuracy | 76.5 -> 76.6 | Helped | Tractable Probabilistic Graph Representation Learning with Graph-Induced Sum-Product Networks (ICLR 2024 · 0 citations) |
| use random layer-wise asynchronous updates instead of synchronous forward/backward sweeps | MNIST · accuracy (%) | 98.16±0.03% -> 98.11±0.04% | No clear effect | Learning in Deep Factor Graphs with Gaussian Belief Propagation (ICML 2024 · 0 citations) |
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.
| Baseline | Benchmark | Metric | Reported | Papers |
|---|---|---|---|---|
| GCN | Cora | accuracy | 81.5 – 87.17 | 2 papers, e.g. ICLR 2019 and CVPR 2018 |
What reviewers will expect
Datasets and baselines named in the 9 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Baselines
- GCN · 2 of 9 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 38 papers; from OpenAlex and the papers' affiliations).
- University of Bergamo · 2 papers
- University of Milano-Bicocca · 2 papers
- National University of Singapore · 2 papers
- Huawei · 2 papers
- University of Oxford · 2 papers
- Harvard University · 2 papers
- Inria · 2 papers
Use it
Download BibTeX of 39 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)
- Spectral GNN design (37 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).