mlsanityData to 7 Oct 2026

Sign and Basis Invariant Networks for Spectral Graph Representation Learning

arXiv 2202.13013 ↗First posted 25 Feb 2022cs.LG stat.MLcited by 176

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Abstract (arXiv)

We introduce SignNet and BasisNet -- new neural architectures that are invariant to two key symmetries displayed by eigenvectors: (i) sign flips, since if v is an eigenvector then so is -v; and (ii) more general basis symmetries, which occur in higher dimensional eigenspaces with infinitely many choices of basis eigenvectors. We prove that under certain conditions our networks are universal, i.e., they can approximate any continuous function of eigenvectors with the desired invariances. When used with Laplacian eigenvectors, our networks are provably more expressive than existing spectral methods on graphs; for instance, they subsume all spectral graph convolutions, certain spectral graph invariants, and previously proposed graph positional encodings as special cases. Experiments show that our networks significantly outperform existing baselines on molecular graph regression, learning expressive graph representations, and learning neural fields on triangle meshes. Our code is available at https://github.com/cptq/SignNet-BasisNet .

Key facts. Cited by 176 papers in the map (data through 7 Oct 2026). Builds on 67 of its 142 references that are in the map. First posted on arXiv 25 Feb 2022.

Builds on

67 of 142 references.

References · 67

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50 most cited of 67 All 67 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 16; 2023: 38; 2024: 51; 2025: 43; 2026: 28.

176 papers.

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  1. 2022Recipe for a General, Powerful, Scalable Graph Transformercited by 702
  2. 2022Long Range Graph Benchmarkcited by 258
  3. 2022Pure Transformers are Powerful Graph Learnerscited by 188
  4. 2023Graph Inductive Biases in Transformers without Message Passingcited by 150
  5. 2023Rethinking the Expressive Power of GNNs via Graph Biconnectivitycited by 119
  6. 2022Understanding and Extending Subgraph GNNs by Rethinking Their Symmetriescited by 112
  7. 2024Let Your Graph Do the Talking: Encoding Structured Data for LLMscited by 112
  8. 2023Equivariant Architectures for Learning in Deep Weight Spacescited by 106
  9. 2022Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networkscited by 94
  10. 2022A Generalization of ViT/MLP-Mixer to Graphscited by 93
  11. 2024Position: Graph Foundation Models are Already Herecited by 84
  12. 2024Graph Mamba: Towards Learning on Graphs with State Space Modelscited by 84
38 more
  1. 2023Attending to Graph Transformerscited by 81
  2. 2022DiffWire: Inductive Graph Rewiring via the Lov'asz Boundcited by 79
  3. 2023A Complete Expressiveness Hierarchy for Subgraph GNNs via Subgraph Weisfeiler-Lehman Testscited by 64
  4. 2022Theory of Graph Neural Networks: Representation and Learningcited by 60
  5. 2023On the Connection Between MPNN and Graph Transformercited by 60
  6. 2023Swallowing the Bitter Pill: Simplified Scalable Conformer Generationcited by 55
  7. 2023Graph Metanetworks for Processing Diverse Neural Architecturescited by 55
  8. 2022Tree Mover's Distance: Bridging Graph Metrics and Stability of Graph Neural Networkscited by 39
  9. 2023Transformers Meet Directed Graphscited by 39
  10. 2022OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphscited by 38
  11. 2023Equivariant Polynomials for Graph Neural Networkscited by 38
  12. 2024Beyond Weisfeiler-Lehman: A Quantitative Framework for GNN Expressivenesscited by 38
  13. 2023Efficient and Scalable Graph Generation through Iterative Local Expansioncited by 35
  14. 2023Equivariant Deep Weight Space Alignmentcited by 34
  15. 2025Relational Transformer: Toward Zero-Shot Foundation Models for Relational Datacited by 32
  16. 2022Generalised Implicit Neural Representationscited by 31
  17. 2023Graph Positional and Structural Encodercited by 31
  18. 2023On the Stability of Expressive Positional Encodings for Graphscited by 31
  19. 2023Graph Positional Encoding via Random Feature Propagationcited by 30
  20. 2025Relational Graph Transformercited by 30
  21. 2024Cometh: A continuous-time discrete-state graph diffusion modelcited by 29
  22. 2023The Exact Sample Complexity Gain from Invariances for Kernel Regressioncited by 27
  23. 2023A Survey on Spectral Graph Neural Networkscited by 26
  24. 2024A Canonicalization Perspective on Invariant and Equivariant Learningcited by 25
  25. 2024Unifying Generation and Prediction on Graphs with Latent Graph Diffusioncited by 24
  26. 2024Scale Equivariant Graph Metanetworkscited by 23
  27. 2023Data-centric Graph Learning: A Surveycited by 22
  28. 2022Generalized Laplacian Positional Encoding for Graph Representation Learningcited by 21
  29. 2023Laplacian Canonization: A Minimalist Approach to Sign and Basis Invariant Spectral Embeddingcited by 21
  30. 2024Learning on LoRAs: GL-Equivariant Processing of Low-Rank Weight Spaces for Large Finetuned Modelscited by 21
  31. 2025Learning Efficient Positional Encodings with Graph Neural Networkscited by 21
  32. 2024Comparing Graph Transformers via Positional Encodingscited by 20
  33. 2024Spatio-Spectral Graph Neural Networkscited by 17
  34. 2023Expressive Sign Equivariant Networks for Spectral Geometric Learningcited by 15
  35. 2024On the Expressive Power of Spectral Invariant Graph Neural Networkscited by 15
  36. 2025Improving Equivariant Networks with Probabilistic Symmetry Breakingcited by 15
  37. 2023Facilitating Graph Neural Networks with Random Walk on Simplicial Complexescited by 14
  38. 2024A Universal Class of Sharpness-Aware Minimization Algorithmscited by 14

50 most cited of 176 All 176 (JSON)