# Identifiability, the KL property in metric spaces, and subgradient curves

arXiv: https://arxiv.org/abs/2205.02868 · HTML: https://mlsanity.com/paper/2205.02868/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2022.

## Built on by (most cited first, 1 of 1)

- [Stochastic Saddle Avoidance Beyond Unit Excitation and Smoothness: A Pathwise Lyapunov-Perron Framework](https://mlsanity.com/paper/2608.03001/) (2026)

## Abstract (arXiv)

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.