On Invariance and Selectivity in Representation Learning
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Abstract (arXiv)
We discuss data representation which can be learned automatically from data, are invariant to transformations, and at the same time selective, in the sense that two points have the same representation only if they are one the transformation of the other. The mathematical results here sharpen some of the key claims of i-theory -- a recent theory of feedforward processing in sensory cortex.
Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Mar 2015.
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Citing papers per year: 2021: 5; 2022: 5; 2023: 3; 2024: 1; 2025: 3; 2026: 1.
18 papers.
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- 2021SE(3)-equivariant prediction of molecular wavefunctions and electronic densitiescited by 67
- 2023Approximation-Generalization Trade-offs under (Approximate) Group Equivariancecited by 45
- 2022On the Strong Correlation Between Model Invariance and Generalizationcited by 23
- 2021Understanding the Generalization Benefit of Model Invariance from a Data Perspectivecited by 22
- 2025Bridging Symmetry and Robustness: On the Role of Equivariance in Enhancing Adversarial Robustnesscited by 8
- 2021BIGDML: Towards Exact Machine Learning Force Fields for Materialscited by 5
- 2022Generalized Permutants and Graph GENEOscited by 5
- 2025Mathematical Foundation of Interpretable Equivariant Surrogate Modelscited by 5
- 2022GENEOnet: A new machine learning paradigm based on Group Equivariant Non-Expansive Operators. An application to protein pocket detectioncited by 4
- 2022Predicting Out-of-Domain Generalization with Neighborhood Invariancecited by 4
- 2024A novel approach to graph distinction through GENEOs and permutantscited by 4
- 2021On the geometric and Riemannian structure of the spaces of group equivariant non-expansive operatorscited by 3
6 more
- 2021Three approaches to facilitate DNN generalization to objects in out-of-distribution orientations and illuminationscited by 2
- 2022LiDAR dataset distillation within bayesian active learning framework: Understanding the effect of data augmentationcited by 2
- 2023Deephys: Deep Electrophysiology, Debugging Neural Networks under Distribution Shiftscited by 1
- 2023Evaluating the effect of data augmentation and BALD heuristics on distillation of Semantic-KITTI datasetcited by 0
- 2025Symplectic Representation of Legendre Dynamicscited by 0
- 2026Improving Robustness of Tabular Retrieval via Representational Stabilitycited by 0
- 2026Improving Robustness of Tabular Retrieval via Representational Stability27 Apr 2026
- 2025Symplectic Representation of Legendre Dynamics22 Dec 2025
- 2025Bridging Symmetry and Robustness: On the Role of Equivariance in Enhancing Adversarial Robustness17 Oct 2025
- 2025Mathematical Foundation of Interpretable Equivariant Surrogate Models3 Mar 2025
- 2024A novel approach to graph distinction through GENEOs and permutants12 Jun 2024
- 2023Approximation-Generalization Trade-offs under (Approximate) Group Equivariance27 May 2023
- 2023Deephys: Deep Electrophysiology, Debugging Neural Networks under Distribution Shifts17 Mar 2023
- 2023Evaluating the effect of data augmentation and BALD heuristics on distillation of Semantic-KITTI dataset21 Feb 2023
- 2022On the Strong Correlation Between Model Invariance and Generalization14 Jul 2022
- 2022Predicting Out-of-Domain Generalization with Neighborhood Invariance5 Jul 2022
- 2022Generalized Permutants and Graph GENEOs29 Jun 2022
- 2022LiDAR dataset distillation within bayesian active learning framework: Understanding the effect of data augmentation6 Feb 2022
6 more
- 2022GENEOnet: A new machine learning paradigm based on Group Equivariant Non-Expansive Operators. An application to protein pocket detection31 Jan 2022
- 2021Understanding the Generalization Benefit of Model Invariance from a Data Perspective10 Nov 2021
- 2021Three approaches to facilitate DNN generalization to objects in out-of-distribution orientations and illuminations30 Oct 2021
- 2021BIGDML: Towards Exact Machine Learning Force Fields for Materials8 Jun 2021
- 2021SE(3)-equivariant prediction of molecular wavefunctions and electronic densities4 Jun 2021
- 2021On the geometric and Riemannian structure of the spaces of group equivariant non-expansive operators3 Mar 2021
- 2021SE(3)-equivariant prediction of molecular wavefunctions and electronic densitiescited by 67
- 2023Approximation-Generalization Trade-offs under (Approximate) Group Equivariancecited by 45
- 2022On the Strong Correlation Between Model Invariance and Generalizationcited by 23
- 2021Understanding the Generalization Benefit of Model Invariance from a Data Perspectivecited by 22
- 2025Bridging Symmetry and Robustness: On the Role of Equivariance in Enhancing Adversarial Robustnesscited by 8
- 2021BIGDML: Towards Exact Machine Learning Force Fields for Materialscited by 5
- 2022Generalized Permutants and Graph GENEOscited by 5
- 2025Mathematical Foundation of Interpretable Equivariant Surrogate Modelscited by 5
- 2022GENEOnet: A new machine learning paradigm based on Group Equivariant Non-Expansive Operators. An application to protein pocket detectioncited by 4
- 2022Predicting Out-of-Domain Generalization with Neighborhood Invariancecited by 4
- 2024A novel approach to graph distinction through GENEOs and permutantscited by 4
- 2021On the geometric and Riemannian structure of the spaces of group equivariant non-expansive operatorscited by 3
12 most cited of 18 All 18 (JSON)
- 2026Improving Robustness of Tabular Retrieval via Representational Stability27 Apr 2026
- 2025Symplectic Representation of Legendre Dynamics22 Dec 2025
- 2025Bridging Symmetry and Robustness: On the Role of Equivariance in Enhancing Adversarial Robustness17 Oct 2025
- 2025Mathematical Foundation of Interpretable Equivariant Surrogate Models3 Mar 2025
- 2024A novel approach to graph distinction through GENEOs and permutants12 Jun 2024
- 2023Approximation-Generalization Trade-offs under (Approximate) Group Equivariance27 May 2023
- 2023Deephys: Deep Electrophysiology, Debugging Neural Networks under Distribution Shifts17 Mar 2023
- 2023Evaluating the effect of data augmentation and BALD heuristics on distillation of Semantic-KITTI dataset21 Feb 2023
- 2022On the Strong Correlation Between Model Invariance and Generalization14 Jul 2022
- 2022Predicting Out-of-Domain Generalization with Neighborhood Invariance5 Jul 2022
- 2022Generalized Permutants and Graph GENEOs29 Jun 2022
- 2022LiDAR dataset distillation within bayesian active learning framework: Understanding the effect of data augmentation6 Feb 2022
12 newest of 18 All 18 (JSON)