In this paper, we revisit the Empirical Risk Minimization problem in the noninteractive local model of differential privacy. In the case of constant or low dimensions (pn), we first show that if the loss function is(,T)-smooth, wecanavoidadependence ofthesample complexity,toachieveerrorα,onthe exponential of the dimensionalityp with base1/α (i.e.,α p), which answers a questionin[19].

Pre-training plays a vital role in various vision tasks, such as object recognition and detection.

Many high-dimensional statistical inference problems are believed to possess inherent computational hardness. Various frameworks have been proposed to give rigorous evidence for such hardness, including lower bounds against restricted models of computation (such as low-degree functions), as well as methods rooted in statistical physics that are based on free energy landscapes. This paper aims to make a rigorousconnectionbetween the seeminglydifferent low-degreeand free-energybased approaches. We define a free-energybasedcriterionfor hardnessand formallyconnectit to the well-establishednotionof low-degree hardness for a broad class of statistical problems, namely all Gaussian additive models and certain models with a sparse planted signal.

Many high-dimensional statistical inference problems are believed to possess inherentcomputationalhardness.

We characterize the limit points of two basic first order methods, namely Gradient Descent/Ascent (GDA) and Optimistic Gradient Descent Ascent (OGDA).

It also does not enjoy SNIS's inherent stability and boundedness.