Research map / Graph learning / GNN architectures
Substructure-aware GNN expressivity
Analyze GNN capability to count motifs and substructures, including topological and geometric variants.
50 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2018–2026) · an approach in GNN architectures, keyword cluster “wl · expressive · power”
State History Benchmarks Tried Baselines Checklist Preprints Who Export
Where it stands
Few recent reports The tracked benchmarks have at most one report from 2025–26 that could beat the old record, too few to say whether they are still moving.
16 papers in 2023–24 and 17 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic held steady, from 3.4% to 3.3%.
No longer reported by papers here: PROTEINS (accuracy, last in 2024); IMDB-B (accuracy, last in 2024); CSL (accuracy (%), last in 2024).
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
- 2018 · Towards a Unified Framework for Syntactic Inconsistency Measures (AAAI 2018 · 17 citations)
- 2019 · GeniePath: Graph Neural Networks with Adaptive Receptive Paths (AAAI 2019 · 324 citations)
- 2020 · Weisfeiler and Leman go sparse: Towards scalable higher-order graph embeddings (NeurIPS 2020 · 41 citations)
- 2021 · Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks (ICML 2021 · 45 citations)
- 2022 · Graph Filtration Kernels (AAAI 2022 · 13 citations)
- 2023 · Substructure Aware Graph Neural Networks (AAAI 2023 · 56 citations)
- 2024 · Non-convolutional graph neural networks. (NeurIPS 2024 · 5 citations)
- 2025 · The Generalized Skew Spectrum of Graphs (ICML 2025 · 0 citations)
- 2026 · Expressive Power of Deep Homomorphism Networks over Relational Databases (NeurIPS 2026 · 0 citations)
Earliest papers here
- Towards a Unified Framework for Syntactic Inconsistency Measures (AAAI 2018 · 17 citations)
- GeniePath: Graph Neural Networks with Adaptive Receptive Paths (AAAI 2019 · 324 citations)
- Relational Pooling for Graph Representations (ICML 2019 · 37 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)
9 papers, 2020–2025 · one report since 2024, not better
| Year | Best so far | Set by |
|---|---|---|
| 2020 | 91.4 | Weisfeiler and Leman go sparse: Towards scalable higher-order graph embeddings (NeurIPS 2020 · 41 citations) |
PROTEINS · accuracy (higher is better)
8 papers, 2019–2024 · not reported since 2024
| Year | Best so far | Set by |
|---|---|---|
| 2019 | 75.7 | On the equivalence between graph isomorphism testing and function approximation with GNNs (NeurIPS 2019 · 37 citations) |
| 2020 | 79.3 | Weisfeiler and Leman go sparse: Towards scalable higher-order graph embeddings (NeurIPS 2020 · 41 citations) |
| 2023 | 79.8 | Substructure Aware Graph Neural Networks (AAAI 2023 · 56 citations) |
MUTAG · accuracy (higher is better)
7 papers, 2019–2025 · one report since 2024, not better
| Year | Best so far | Set by |
|---|---|---|
| 2019 | 86.8 | On the equivalence between graph isomorphism testing and function approximation with GNNs (NeurIPS 2019 · 37 citations) |
| 2020 | 89.28 | Graph Homomorphism Convolution (ICML 2020 · 5 citations) |
| 2022 | 91.1 | Equivariant Subgraph Aggregation Networks (ICLR 2022 · 12 citations) |
| 2023 | 95.2 | Substructure Aware Graph Neural Networks (AAAI 2023 · 56 citations) |
IMDB-B · accuracy (higher is better)
6 papers, 2021–2024 · not reported since 2024
| Year | Best so far | Set by |
|---|---|---|
| 2021 | 75.6 | Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks (ICML 2021 · 45 citations) |
| 2022 | 77.1 | Equivariant Subgraph Aggregation Networks (ICLR 2022 · 12 citations) |
| 2024 | 81.1 | Non-convolutional graph neural networks. (NeurIPS 2024 · 5 citations) |
NCI109 · accuracy (higher is better)
5 papers, 2020–2025 · one report since 2024, not better
| Year | Best so far | Set by |
|---|---|---|
| 2020 | 89.3 | Weisfeiler and Leman go sparse: Towards scalable higher-order graph embeddings (NeurIPS 2020 · 41 citations) |
CSL · accuracy (%) (higher is better)
4 papers, 2020–2024 · not reported since 2024
| Year | Best so far | Set by |
|---|---|---|
| 2020 | 100 | Graph Homomorphism Convolution (ICML 2020 · 5 citations) |
What has been tried
40 papers here report 411 measured changes (a component added, removed or swapped, compared with a baseline): helped 67%, no clear effect 10%, hurt 17%, mixed 6%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| add topological walk representation ωu | Cora · accuracy | 82.2 ± 1.0 -> 84.1 (± 0.9) | Helped | Non-convolutional graph neural networks. (NeurIPS 2024 · 5 citations) |
| Encode Hom(spasm(P6)) counts with an MLP instead of positional encoding | COLLAB · Hits@50 | Hurt | Homomorphism Counts for Graph Neural Networks: All About That Basis (ICML 2024 · 1 citation) | |
| combine k=0 and k=D kernels rather than use either alone | Coreness · micro F1-score | 87.0 -> 91.3; 39.1 -> 91.3 | Helped | Generalizing Weisfeiler-Lehman Kernels to Subgraphs (ICLR 2025 · 0 citations) |
| Use SchNet on the 2-power graph rather than the original graph | Pair a · accuracy | 50.0 { { ± 0.0}} -> 100.0 { { ± 0.0}} | Helped | On the Expressive Power of Sparse Geometric MPNNs (ICLR 2025 · 0 citations) |
| fine-tune the Llama3-8b reader with QLoRA | ogbn-arxiv · accuracy | 73.17% -> 74.95% | Helped | Revisiting Random Walks for Learning on Graphs (ICLR 2025 · 0 citations) |
| Use cycles of lengths 2 to 10 rather than cycles of lengths 2 to 4 | EXP · accuracy (%) | 50 -> 98 | Helped | Deep Homomorphism Networks (NeurIPS 2024 · 0 citations) |
| remove singleton hyperedges when extracting induced sub-hypergraphs | IMDB-DIR-FORM · accuracy | 58.55±1.5 -> 68.11±2.4 | Helped | Improved Expressivity of Hypergraph Neural Networks through High-Dimensional Generalized Weisfeiler-Leman Algorithms (ICML 2025) |
| Increase r from 0 to 5 in ℓGIN | ZINC12K · test MAE | 0.209±0.007 -> 0.072±0.002 | Helped | Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning (NeurIPS 2024) |
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 |
|---|---|---|---|---|
| GIN | NCI1 | accuracy | 76.89 – 82.7 | 2 papers, e.g. NeurIPS 2023 and ICLR 2022 |
| GIN | NCI109 | accuracy | 76.9 – 82.2 | 2 papers, e.g. NeurIPS 2023 and ICLR 2022 |
| PersLay | NCI1 | accuracy | 68.86 – 73.5 | 2 papers, e.g. NeurIPS 2023 and ICLR 2022 |
What reviewers will expect
Datasets and baselines named in the 14 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- BREC · 4 of 14 papers
- ZINC · 3 of 14 papers
- minimal Cayley graphs · 2 of 14 papers
- NCI1 · 2 of 14 papers
- NCI109 · 2 of 14 papers
- ZINC12K · 2 of 14 papers
Baselines
- GCN · 5 of 14 papers
- GIN · 4 of 14 papers
- GraphSAGE · 3 of 14 papers
- GraphGPS · 2 of 14 papers
- GatedGCN · 2 of 14 papers
- GAT · 2 of 14 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 33 papers; from OpenAlex and the papers' affiliations).
- Federal Institute of Ceará · 4 papers
- Technische Universität Wien · 2 papers
- Genentech · 2 papers
- TU Wien · 2 papers
- University of Pennsylvania · 2 papers
Use it
Download BibTeX of 39 key papersOpen the topic in the interactive map
Get alerts. Describe your idea in scime atlas and save it (free scime account): you get a weekly email when new preprints land close to it.
Related approaches
Same keyword cluster
- Weisfeiler-Leman expressivity hierarchies (66 papers)
- Subgraph and distance-aware GNNs (46 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)
- Theory of graph convolutional networks (83 papers)
- Deep graph convolution and simplification (82 papers)
- Physics-inspired GNNs (81 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).