mlsanityData to 14 Oct 2026

Mathematical Foundation of Interpretable Equivariant Surrogate Models

arXiv 2503.01942 ↗First posted 3 Mar 2025stat.ML cs.AI cs.LGcited by 5

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Abstract (arXiv)

This paper introduces a rigorous mathematical framework for neural network explainability, and more broadly for the explainability of equivariant operators called Group Equivariant Operators (GEOs) based on Group Equivariant Non-Expansive Operators (GENEOs) transformations. The central concept involves quantifying the distance between GEOs by measuring the non-commutativity of specific diagrams. Additionally, the paper proposes a definition of interpretability of GEOs according to a complexity measure that can be defined according to each user preferences. Moreover, we explore the formal properties of this framework and show how it can be applied in classical machine learning scenarios, like image classification with convolutional neural networks.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 22 of its 42 references that are in the map. First posted on arXiv 3 Mar 2025.

Builds on

22 of 42 references.

References · 22

  1. 2016Group Equivariant Convolutional Networkscited by 1,165
  2. 2018A Survey Of Methods For Explaining Black Box Modelscited by 973
  3. 2021E(n) Equivariant Graph Neural Networkscited by 965
  4. 2022From Anecdotal Evidence to Quantitative Evaluation Methods: A Systematic Review on Evaluating Explainable AIcited by 302
  5. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 295
  6. 2021Benchmarking and Survey of Explanation Methods for Black Box Modelscited by 136
  7. 2021Geometric Deep Learning and Equivariant Neural Networkscited by 65
  8. 2023Clifford Group Equivariant Neural Networkscited by 55
  9. 2021Logic Explained Networkscited by 45
  10. 2017Disintegration and Bayesian Inversion via String Diagramscited by 32
  11. 2019Interpretable and Differentially Private Predictionscited by 28
  12. 2021Explain, Edit, and Understand: Rethinking User Study Design for Evaluating Model Explanationscited by 26
10 more
  1. 2018Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learningcited by 24
  2. 2023Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learningcited by 22
  3. 2015On Invariance and Selectivity in Representation Learningcited by 18
  4. 2021XAI Handbook: Towards a Unified Framework for Explainable AIcited by 14
  5. 2023Categorical Foundations of Explainable AI: A Unifying Theorycited by 7
  6. 2013Combining persistent homology and invariance groups for shape comparisoncited by 5
  7. 2022Generalized Permutants and Graph GENEOscited by 5
  8. 2024A novel approach to graph distinction through GENEOs and permutantscited by 4
  9. 2021On the geometric and Riemannian structure of the spaces of group equivariant non-expansive operatorscited by 3
  10. 2022Exploration-oriented sampling strategies for global surrogate modeling: A comparison between one-stage and adaptive methodscited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 3.

5 papers.

  1. 2026Actionable Interpretability Must Be Defined in Terms of Symmetriescited by 4
  2. 2026Mixture of Concept Bottleneck Expertscited by 2
  3. 2025Logic Explanation of AI Classifiers by Categorical Explaining Functorscited by 1
  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