# On Invariance and Selectivity in Representation Learning

arXiv: https://arxiv.org/abs/1503.05938 · HTML: https://mlsanity.com/paper/1503.05938/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2015.

## Built on by (most cited first, 18 of 18)

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- [Understanding the Generalization Benefit of Model Invariance from a Data Perspective](https://mlsanity.com/paper/2111.05529/) (2021)
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- [Mathematical Foundation of Interpretable Equivariant Surrogate Models](https://mlsanity.com/paper/2503.01942/) (2025)
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- [A novel approach to graph distinction through GENEOs and permutants](https://mlsanity.com/paper/2406.08045/) (2024)
- [On the geometric and Riemannian structure of the spaces of group equivariant non-expansive operators](https://mlsanity.com/paper/2103.02543/) (2021)
- [Three approaches to facilitate DNN generalization to objects in out-of-distribution orientations and illuminations](https://mlsanity.com/paper/2111.00131/) (2021)
- [LiDAR dataset distillation within bayesian active learning framework: Understanding the effect of data augmentation](https://mlsanity.com/paper/2202.02661/) (2022)
- [Deephys: Deep Electrophysiology, Debugging Neural Networks under Distribution Shifts](https://mlsanity.com/paper/2303.11912/) (2023)
- [Evaluating the effect of data augmentation and BALD heuristics on distillation of Semantic-KITTI dataset](https://mlsanity.com/paper/2302.10679/) (2023)
- [Symplectic Representation of Legendre Dynamics](https://mlsanity.com/paper/2512.19409/) (2025)
- [Improving Robustness of Tabular Retrieval via Representational Stability](https://mlsanity.com/paper/2604.24040/) (2026)

## 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.