In classification, it is usual to observe that models trained on a given set of classes can generalize to previously unseen ones, suggesting the ability to learn beyond the initial task. This ability is often leveraged in the context of transfer learning where a pretrained model can be used to process new classes, with or without fine tuning. Surprisingly, there are a few papers looking at the theoretical roots beyond this phenomenon. In this work, we are interested in laying the foundations of such a theoretical framework for transferability between sets of classes. Namely, we establish a partially ordered set of subsets of classes. This tool allows to represent which subset of classes can generalize to others. In a more practical setting, we explore the ability of our framework to predict which subset of classes can lead to the best performance when testing on all of them. We also explore few-shot learning, where transfer is the golden standard. Our work contributes to better understanding of transfer mechanics and model generalization.

翻译：在分类任务中，通常观察到在给定类别集上训练的模型能够泛化到未见过的类别，这表明模型具备超越初始任务的学习能力。这种能力在迁移学习场景中常被利用，预训练模型可通过微调或免微调方式处理新类别。令人惊讶的是，鲜有文献探究此现象的理论根源。本研究致力于为类别集间的可迁移性建立理论框架基础。具体而言，我们构建了类别子集的偏序集结构，该工具可表征哪些类别子集能够泛化至其他子集。在实际应用层面，我们探索了该框架预测在全体类别上测试时最佳性能来源子集的能力。我们还探究了以迁移学习为黄金标准的少样本学习场景。本研究有助于深入理解迁移机制与模型泛化特性。