What is learning? 20 century formalizations of learning theory -- which precipitated revolutions in artificial intelligence -- focus primarily on \textit{in-distribution} learning, that is, learning under the assumption that the training data are sampled from the same distribution as the evaluation distribution. This assumption renders these theories inadequate for characterizing 21$^{st}$ century real world data problems, which are typically characterized by evaluation distributions that differ from the training data distributions (referred to as out-of-distribution learning). We therefore make a small change to existing formal definitions of learnability by relaxing that assumption. We then introduce \textbf{learning efficiency} (LE) to quantify the amount a learner is able to leverage data for a given problem, regardless of whether it is an in- or out-of-distribution problem. We then define and prove the relationship between generalized notions of learnability, and show how this framework is sufficiently general to characterize transfer, multitask, meta, continual, and lifelong learning. We hope this unification helps bridge the gap between empirical practice and theoretical guidance in real world problems. Finally, because biological learning continues to outperform machine learning algorithms on certain OOD challenges, we discuss the limitations of this framework vis-\'a-vis its ability to formalize biological learning, suggesting multiple avenues for future research.

翻译：学习是什么? 20世纪的学习理论正规化,它催生了人工智能的革命 -- -- 主要是以学习效率的学习为主,也就是说,学习的假设是,培训数据是从与评价分布相同的分布中抽样的。这种假设使这些理论不足以说明21美元/日/日/日/日/日/月/月/月/日)这个世纪真实的世界数据问题,其典型特征是评价分布不同于培训数据分布(称为分配以外的学习),因此,我们通过放松这一假设,对现有的正式学习能力定义做了小的改变。我们希望这种统一有助于弥合实际世界问题的经验实践与理论指导之间的差距。最后,由于生物学习继续超越了生物研究的正规化框架,因此我们不断在生物学上学习多种途径,以学习某些生物学的正规化框架。