mlsanityData to 7 Oct 2026

Generalized Permutants and Graph GENEOs

arXiv 2206.14798 ↗First posted 29 Jun 2022math.CO cs.LGcited by 5

Not on the map. Why?

Abstract (arXiv)

In this paper we establish a bridge between Topological Data Analysis and Geometric Deep Learning, adapting the topological theory of group equivariant non-expansive operators (GENEOs) to act on the space of all graphs weighted on vertices or edges. This is done by showing how the general concept of GENEO can be used to transform graphs and to give information about their structure. This requires the introduction of the new concepts of generalized permutant and generalized permutant measure and the mathematical proof that these concepts allow us to build GENEOs between graphs. An experimental section concludes the paper, illustrating the possible use of our operators to extract information from graphs. This paper is part of a line of research devoted to developing a compositional and geometric theory of GENEOs for Geometric Deep Learning.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 18 of its 46 references that are in the map. First posted on arXiv 29 Jun 2022.

Builds on

18 of 46 references.

References · 18

  1. 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,148
  2. 2016Group Equivariant Convolutional Networkscited by 1,154
  3. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  4. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  5. 2018Deep Learning on Graphs: A Surveycited by 393
  6. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  7. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 293
  8. 2019Explainable Machine Learning for Scientific Insights and Discoveriescited by 165
  9. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  10. 2016Understanding Deep Convolutional Networkscited by 76
  11. 2021Geometric Deep Learning and Equivariant Neural Networkscited by 64
  12. 2021Universal Approximation Theorems for Differentiable Geometric Deep Learningcited by 41
6 more
  1. 2018Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learningcited by 24
  2. 2015On Invariance and Selectivity in Representation Learningcited by 18
  3. 2020On the finite representation of group equivariant operators via permutant measurescited by 7
  4. 2015Graphs in machine learning: an introductioncited by 4
  5. 2020Steady and ranging sets in graph persistencecited by 3
  6. 2022Machines of finite depth: towards a formalization of neural networkscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 3; 2026: 1.

5 papers.

  1. 2025Mathematical Foundation of Interpretable Equivariant Surrogate Modelscited by 5
  2. 2024A novel approach to graph distinction through GENEOs and permutantscited by 4
  3. 2025GENEOnet: Statistical analysis supporting explainability and trustworthinesscited by 0
  4. 2025Reconstruction of SINR Maps from Sparse Measurements using Group Equivariant Non-Expansive Operatorscited by 0
  5. 2026An Algebraic Representation Theorem for Linear GENEOs in Geometric Machine Learningcited by 0