Identifiability, and the closely related idea of partial smoothness, unify classical active set methods and more general notions of solution structure. Diverse optimization algorithms generate iterates in discrete time that are eventually confined to identifiable sets. We present two fresh perspectives on identifiability. The first distills the notion to a simple metric property, applicable not just in Euclidean settings but to optimization over manifolds and beyond; the second reveals analogous continuous-time behavior for subgradient descent curves. The Kurdya-Lojasiewicz property typically governs convergence in both discrete and continuous time: we explore its interplay with identifiability.

翻译：可辨识性及其密切相关的部分光滑性概念，统一了经典有效集方法与更一般的解结构描述。各类优化算法在离散时间下生成的迭代点最终会被限制在可辨识集合中。本文提出关于可辨识性的两个新视角：首先将其提炼为一种适用于流形乃至更一般空间的简单度量性质，突破欧几里得空间的限制；其次揭示次梯度下降曲线在连续时间中的类似行为。Kurdya-Łojasiewicz性质通常主导着离散与连续时间下的收敛性，本文深入探讨其与可辨识性的相互作用关系。