Group-invariant Coresets for Data-efficient Active Learning

2026-07-01

AI Summary

This work addresses the inefficiency of standard coreset-based active learning methods, which ignore group symmetries in data and consequently waste labeling budgets on transformationally redundant samples. The paper introduces group invariance into coreset construction for the first time, proposing GRINCO—a novel orbit-based active learning framework that samples entire orbits induced by group actions in the quotient space. GRINCO combines k-center coverage in the quotient space with orbit-averaged loss, defining distances via canonical representatives or learned orbit-separating invariant embeddings. Theoretical analysis establishes generalization error bounds tied to quotient-space coverage, label uncertainty, and intra-orbit variation. Experiments demonstrate that GRINCO significantly improves orbit coverage and label efficiency on synthetic scale-invariant data and image benchmarks with rotational redundancy, outperforming existing methods—especially when group-induced redundancy is pronounced.

Abstract

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.

Problem

• active learning
• coresets
• group invariance
• data symmetry
• label efficiency

Innovation

• group-invariant
• coreset
• active learning
• quotient space
• orbit-averaged loss