We consider both exact andapproximate recoveryofthelabels. Our results hold for anyconstant-factor approximation tothek-means problem.

Weintroduce thenotions of proxy convexity and proxy Polyak-Lojasiewicz (PL) inequalities, which are satisfied iftheoriginal objectivefunction induces aproxy objectivefunction that is implicitly minimized when using gradient methods.

We tackle the problem ofnovel class discovery and localization (NCDL). In this setting, we assume a source dataset with supervision for only some object classes.

Typicalness-A ware Learning (T AL) to address this issue and improve failure detection performance.

Our understanding of learning input-output relationships with neural nets has improved rapidly in recent years, but little is known about the convergence of the underlying representations, even in the simple case of linear autoencoders (LAEs).

However, in many cases, potential participants in such collaborative schemes are competitors on a downstream task, such as firms that each aim to attract customers by providing the best recommendations.