mlsanityData to 7 Oct 2026

Simplicial Attention Neural Networks

arXiv 2203.07485 ↗First posted 14 Mar 2022cs.LG cs.NEcited by 21

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Abstract (arXiv)

The aim of this work is to introduce simplicial attention networks (SANs), i.e., novel neural architectures that operate on data defined on simplicial complexes leveraging masked self-attentional layers. Hinging on formal arguments from topological signal processing, we introduce a proper self-attention mechanism able to process data components at different layers (e.g., nodes, edges, triangles, and so on), while learning how to weight both upper and lower neighborhoods of the given topological domain in a totally task-oriented fashion. The proposed SANs generalize most of the current architectures available for processing data defined on simplicial complexes. The proposed approach compares favorably with other methods when applied to different (inductive and transductive) tasks such as trajectory prediction and missing data imputations in citation complexes.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). Builds on 27 of its 39 references that are in the map. First posted on arXiv 14 Mar 2022.

Builds on

27 of 39 references.

References · 27

  1. 2017Attention Is All You Needcited by 59,932
  2. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  3. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  4. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  5. 2017Graph Attention Networkscited by 8,854
  6. 2017Inductive Representation Learning on Large Graphscited by 6,284
  7. 2014Neural Machine Translation by Jointly Learning to Align and Translatecited by 4,530
  8. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  9. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,097
  10. 2018Link Prediction Based on Graph Neural Networkscited by 829
  11. 2015Convolutional Networks on Graphs for Learning Molecular Fingerprintscited by 751
  12. 2019Graph Transformer Networkscited by 520
15 more
  1. 2019Multi-Label Image Recognition with Graph Convolutional Networkscited by 320
  2. 2017A Structured Self-attentive Sentence Embeddingcited by 318
  3. 2015Diffusion-Convolutional Neural Networkscited by 268
  4. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 219
  5. 2016Long Short-Term Memory-Networks for Machine Readingcited by 161
  6. 2020Simplicial Neural Networkscited by 105
  7. 2019Topological Signal Processing over Simplicial Complexescited by 94
  8. 2018Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplaciancited by 84
  9. 2021Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyondcited by 81
  10. 2021Principled Simplicial Neural Networks for Trajectory Predictioncited by 77
  11. 2016A Convolutional Encoder Model for Neural Machine Translationcited by 54
  12. 2019Missing Data Imputation with Adversarially-trained Graph Convolutional Networkscited by 54
  13. 2021Simplicial Convolutional Neural Networkscited by 40
  14. 2019HodgeNet: Graph Neural Networks for Edge Datacited by 39
  15. 2021Finite Impulse Response Filters for Simplicial Complexescited by 15

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 5; 2023: 4; 2024: 8; 2025: 3; 2026: 1.

21 papers.

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  1. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  2. 2022Simplicial Attention Networkscited by 40
  3. 2022Cell Attention Networkscited by 34
  4. 2023Generalized Simplicial Attention Neural Networkscited by 27
  5. 2024TopoBench: A Framework for Benchmarking Topological Deep Learningcited by 24
  6. 2024E(n) Equivariant Topological Neural Networkscited by 22
  7. 2023Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Backcited by 21
  8. 2023From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Modulecited by 19
  9. 2022Tangent Bundle Filters and Neural Networks: from Manifolds to Cellular Sheaves and Backcited by 9
  10. 2024On the Theoretical Expressive Power and the Design Space of Higher-Order Graph Transformerscited by 8
  11. 2023Topo-MLP : A Simplicial Network Without Message Passingcited by 7
  12. 2022Pooling Strategies for Simplicial Convolutional Networkscited by 5
9 more
  1. 2022Representation Power of Graph Neural Networks: Improved Expressivity via Algebraic Analysiscited by 3
  2. 2024Binarized Simplicial Convolutional Neural Networkscited by 3
  3. 2024Graph Neural Networks for Edge Signals: Orientation Equivariance and Invariancecited by 2
  4. 2025Continuous Simplicial Neural Networkscited by 2
  5. 2024Topological Neural Networks: Mitigating the Bottlenecks of Graph Neural Networks via Higher-Order Interactionscited by 0
  6. 2024Learning From Simplicial Data Based on Random Walks and 1D Convolutionscited by 0
  7. 2025Topological Neural Networks over the Aircited by 0
  8. 2025Directed Semi-Simplicial Learning with Applications to Brain Activity Decodingcited by 0
  9. 2026TopoU-Net: a U-Net architecture for topological domainscited by 0