We show that many definitions of stability found in the learning theory literature are equivalent to one another. We distinguish between two families of definitions of stability: distribution-dependent and distribution-independent Bayesian stability. Within each family, we establish equivalences between various definitions, encompassing approximate differential privacy, pure differential privacy, replicability, global stability, perfect generalization, TV stability, mutual information stability, KL-divergence stability, and R\'enyi-divergence stability. Along the way, we prove boosting results that enable the amplification of the stability of a learning rule. This work is a step towards a more systematic taxonomy of stability notions in learning theory, which can promote clarity and an improved understanding of an array of stability concepts that have emerged in recent years.

翻译：我们证明，学习理论文献中许多稳定性的定义彼此等价。我们区分了两类稳定性定义：分布依赖型和分布独立型贝叶斯稳定性。在每个类别内，我们建立了多种定义之间的等价关系，涵盖近似差分隐私、纯差分隐私、可复现性、全局稳定性、完美泛化、TV稳定性、互信息稳定性、KL散度稳定性以及Rényi散度稳定性。在此过程中，我们证明了若干提升结果，可用于放大学习规则的稳定性。这项工作旨在推动学习理论中稳定性概念的系统化分类，以增强对近年来涌现的各种稳定性概念的清晰认知与深入理解。