  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.
