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Simplicial Attention Neural Networks

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arxiv 2203.07485 v2 pith:3GV5CBAT submitted 2022-03-14 cs.LG cs.NE

L. Giusti , C. Battiloro , P. Di Lorenzo , S. Sardellitti , S. Barbarossa This is my paper · ORCID
classification cs.LGcs.NE
keywords datasimplicialcomplexesarchitecturesattentiondefineddifferentintroduce
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. HiPoNet: A Multi-View Simplicial Complex Network for High Dimensional Point-Cloud and Single-Cell Data

    cs.LG 2025-02 conditional novelty 6.0 of 10

    HiPoNet combines learned feature reweighting, Vietoris-Rips complexes, and simplicial scattering transforms to classify high-dimensional point clouds, reporting top accuracy on several single-cell and spatial transcri...

  2. CellCLAT: Preserving Topology and Trimming Redundancy in Self-Supervised Cellular Contrastive Learning

    cs.LG 2025-05 conditional novelty 5.0 of 10

    CellCLAT applies parameter-perturbation contrastive learning to cellular complexes and adaptively trims 2-cells to improve downstream graph classification.

  3. Topological Neural Networks over the Air

    cs.IT 2025-02 conditional novelty 4.0 of 10

    AirTNN treats wireless channel fading and noise as part of the topological convolutional filter, improving robustness over graph-based and communication-agnostic baselines in synthetic source localization.

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