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Simplicial Neural Networks

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arxiv 2010.03633 v2 pith:PFDTQWPR submitted 2020-10-07 cs.LG math.ATstat.ML

Stefania Ebli , Michaël Defferrard , Gard Spreemann This is my paper · ORCID
classification cs.LGmath.ATstat.ML
keywords networksneuraldatasimplicialcomplexessnnsallowingappropriate
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abstract

We present simplicial neural networks (SNNs), a generalization of graph neural networks to data that live on a class of topological spaces called simplicial complexes. These are natural multi-dimensional extensions of graphs that encode not only pairwise relationships but also higher-order interactions between vertices - allowing us to consider richer data, including vector fields and $n$-fold collaboration networks. We define an appropriate notion of convolution that we leverage to construct the desired convolutional neural networks. We test the SNNs on the task of imputing missing data on coauthorship complexes.

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Forward citations

Cited by 4 Pith papers

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

  1. Geometry-Induced Hodge Stars on Rips and Dowker--Rips Complexes

    math.AT 2026-07 conditional novelty 6.0 of 10

    A weighted Hodge Laplacian on Rips-type complexes with volume- or witness-based diagonal weights preserves Betti numbers and yields geometry-sensitive spectra.

  2. Heat Kernel Goes Topological

    cs.LG 2025-07 reject novelty 5.0 of 10

    TopoHKS defines a weighted combinatorial-complex Laplacian and heat kernel descriptor, claiming maximal expressive power; the supporting uniqueness theorem is incorrect.

  3. 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.

  4. A Sheaf-Theoretic and Topological Perspective on Complex Network Modeling and Attention Mechanisms in Graph Neural Models

    cs.LG 2026-01 conditional novelty 3.0 of 10

    Any fixed GAT attention-weight matrix can be encoded as a cellular sheaf whose harmonic edges give a monotone filtration, but the framework is definitional and untested.

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