GRINCO解决了主动学习里重复标注变换样本的浪费问题，用商空间选轨道来省钱，比普通核心集方法更聪明。
GRINCO是一种基于群不变性的核心集主动学习框架，通过在变换群诱导的商空间中选择轨道而非原始样本，避免重复标注同一实例的变换版本。框架使用规范代表或轨道分离不变嵌入定义实用的商空间度量，结合商空间k-center选择与轨道平均损失进行不变训练。推导的泛化界将轨道平均风险上界表示为商空间覆盖度、标签不确定性和轨道内变异性的函数。在合成尺度不变数据和旋转冗余图像基准上，GRINCO比传统核心集基线显著提升轨道覆盖度和标签效率。
Group-invariant Coresets for Data-efficient Active Learning
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.