# Group-invariant Coresets for Data-efficient Active Learning

arXiv: https://arxiv.org/abs/2607.01089 · HTML: https://mlsanity.com/paper/2607.01089/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 66 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 30 of 31)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds](https://mlsanity.com/paper/1906.03671/) (2019)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [A Survey on Self-supervised Learning: Algorithms, Applications, and Future Trends](https://mlsanity.com/paper/2301.05712/) (2023)
- [Active Learning Through a Covering Lens](https://mlsanity.com/paper/2205.11320/) (2022)
- [A Survey on Deep Active Learning: Recent Advances and New Frontiers](https://mlsanity.com/paper/2405.00334/) (2024)
- [Reducing Label Effort: Self-Supervised meets Active Learning](https://mlsanity.com/paper/2108.11458/) (2021)
- [Unsupervised Learning of Group Invariant and Equivariant Representations](https://mlsanity.com/paper/2202.07559/) (2022)
- [Low Dimensional Invariant Embeddings for Universal Geometric Learning](https://mlsanity.com/paper/2205.02956/) (2022)
- [A Coreset Selection of Coreset Selection Literature: Introduction and Recent Advances](https://mlsanity.com/paper/2505.17799/) (2025)
- [In Defense of Core-set: A Density-aware Core-set Selection for Active Learning](https://mlsanity.com/paper/2206.04838/) (2022)
- [Equivariant Representation Learning via Class-Pose Decomposition](https://mlsanity.com/paper/2207.03116/) (2022)
- [Label-Efficient Learning in Agriculture: A Comprehensive Review](https://mlsanity.com/paper/2305.14691/) (2023)
- [Generalized Coverage for More Robust Low-Budget Active Learning](https://mlsanity.com/paper/2407.12212/) (2024)
- [Estimation under group actions: recovering orbits from invariants](https://mlsanity.com/paper/1712.10163/) (2017)
- [Group invariant machine learning by fundamental domain projections](https://mlsanity.com/paper/2202.02164/) (2022)
- [Learning (Approximately) Equivariant Networks via Constrained Optimization](https://mlsanity.com/paper/2505.13631/) (2025)
- [Fair Wasserstein Coresets](https://mlsanity.com/paper/2311.05436/) (2023)
- [Integrating Deep Metric Learning with Coreset for Active Learning in 3D Segmentation](https://mlsanity.com/paper/2411.15763/) (2024)
- [Bridging Diversity and Uncertainty in Active learning with Self-Supervised Pre-Training](https://mlsanity.com/paper/2403.03728/) (2024)
- [Diffusion Maps for Group-Invariant Manifolds](https://mlsanity.com/paper/2303.16169/) (2023)
- [Learning Symmetrization for Equivariance with Orbit Distance Minimization](https://mlsanity.com/paper/2311.07143/) (2023)
- [Small coresets via negative dependence: DPPs, linear statistics, and concentration](https://mlsanity.com/paper/2411.00611/) (2024)

## Abstract (arXiv)

Active learning reduces labeling cost by querying the most informative unlabeled samples, but standard coreset methods ignore known data symmetries and can waste budget on transformed versions of the same instance. We propose GRINCO, a group-invariant coreset framework that performs acquisition in the quotient space induced by a transformation group, so that selection operates on orbits rather than raw samples. The method uses either canonical representatives or learned orbit-separating invariant embeddings to define practical quotient metrics, and combines quotient-space k-center selection with invariant training through an orbit-averaged loss. We further derive a generalization bound that relates excess orbit-averaged risk to quotient-space coverage, label uncertainty, and intra-orbit variability. Experiments on synthetic scale-invariant data and image benchmarks with rotation-induced redundancy show that GRINCO improves orbit coverage and achieves stronger label efficiency than conventional coreset baselines, especially when group-induced redundancy is substantial.