mlsanityData to 7 Oct 2026

A novel approach to graph distinction through GENEOs and permutants

arXiv 2406.08045 ↗First posted 12 Jun 2024cs.LG math.GRcited by 4

Not on the map. Why?

Abstract (arXiv)

The theory of Group Equivariant Non-Expansive Operators (GENEOs) was initially developed in Topological Data Analysis for the geometric approximation of data observers, including their invariances and symmetries. This paper departs from that line of research and explores the use of GENEOs for distinguishing r-regular graphs up to isomorphisms. In doing so, we aim to test the capabilities and flexibility of these operators. Our experiments show that GENEOs offer a good compromise between efficiency and computational cost in comparing r-regular graphs, while their actions on data are easily interpretable. This supports the idea that GENEOs could be a general-purpose approach to discriminative problems in Machine Learning when some structural information about data and observers is explicitly given.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 13 of its 31 references that are in the map. First posted on arXiv 12 Jun 2024.

Builds on

13 of 31 references.

References · 13

  1. 2018How Powerful are Graph Neural Networks?cited by 4,355
  2. 2016Group Equivariant Convolutional Networkscited by 1,154
  3. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
  4. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 293
  5. 2019On the equivalence between graph isomorphism testing and function approximation with GNNscited by 172
  6. 2020A Survey on The Expressive Power of Graph Neural Networkscited by 111
  7. 2016Understanding Deep Convolutional Networkscited by 76
  8. 2021Geometric Deep Learning and Equivariant Neural Networkscited by 64
  9. 2018Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learningcited by 24
  10. 2015On Invariance and Selectivity in Representation Learningcited by 18
  11. 2020On the finite representation of group equivariant operators via permutant measurescited by 7
  12. 2022Generalized Permutants and Graph GENEOscited by 5
1 more
  1. 2016Position paper: Towards an observer-oriented theory of shape comparisoncited by 3

Built on by

Cited by year (2026 to 7 Oct)

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

4 papers.

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