# Local Group Invariant Representations via Orbit Embeddings

arXiv: https://arxiv.org/abs/1612.01988 · HTML: https://mlsanity.com/paper/1612.01988/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2016.

## Built on by (most cited first, 12 of 12)

- [Provably Strict Generalisation Benefit for Invariance in Kernel Methods](https://mlsanity.com/paper/2106.02346/) (2021)
- [The good, the bad and the ugly sides of data augmentation: An implicit spectral regularization perspective](https://mlsanity.com/paper/2210.05021/) (2022)
- [Understanding Augmentation-based Self-Supervised Representation Learning via RKHS Approximation and Regression](https://mlsanity.com/paper/2306.00788/) (2023)
- [Emergent Equivariance in Deep Ensembles](https://mlsanity.com/paper/2403.03103/) (2024)
- [Learning Invariant Weights in Neural Networks](https://mlsanity.com/paper/2202.12439/) (2022)
- [VolterraNet: A higher order convolutional network with group equivariance for homogeneous manifolds](https://mlsanity.com/paper/2106.15301/) (2021)
- [Regularising for invariance to data augmentation improves supervised learning](https://mlsanity.com/paper/2203.03304/) (2022)
- [Non-parametric Hypothesis Tests for Distributional Group Symmetry](https://mlsanity.com/paper/2307.15834/) (2023)
- [A Stochastic Approach to Bi-Level Optimization for Hyperparameter Optimization and Meta Learning](https://mlsanity.com/paper/2410.10417/) (2024)
- [Global optimality under amenable symmetry constraints](https://mlsanity.com/paper/2402.07613/) (2024)
- [Stability Analysis of Equivariant Convolutional Representations Through The Lens of Equivariant Multi-layered CKNs](https://mlsanity.com/paper/2408.04277/) (2024)
- [Improving Robustness of Tabular Retrieval via Representational Stability](https://mlsanity.com/paper/2604.24040/) (2026)

## Abstract (arXiv)

Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a group and propose an approach based on kernel methods to derive local group invariant representations. Locality is achieved by defining a suitable probability distribution over the group which in turn induces distributions in the input feature space. We learn a decision function over these distributions by appealing to the powerful framework of kernel methods and generate local invariant random feature maps via kernel approximations. We show uniform convergence bounds for kernel approximation and provide excess risk bounds for learning with these features. We evaluate our method on three real datasets, including Rotated MNIST and CIFAR-10, and observe that it outperforms competing kernel based approaches. The proposed method also outperforms deep CNN on Rotated-MNIST and performs comparably to the recently proposed group-equivariant CNN.