Thisworkdiscusses howtoachieveworst-case Out-Of-Distribution(OOD) generalization for avariety of distributions based on arelatively small labeling cost.

We then propose a novel algorithm based on minimum-distance functionals in the setting where the transition model is given and the expert is deterministic.Thealgorithmissuboptimalby .|S|H3/2/N,matchingourlower

Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure anduniform error bounds havebeen derived,which allowsafe control based on thesemodels.

In order to perform a wide search over the space of the trees, it is critical to solve this projection problem fast.

The sufficiency result can be extendedtodeepernetworks;weshowthatan L-layernetworkwith W parameters in the hidden layers can memorizeN data points ifW = Ω(N).

Moreo randominitializationH( 0)conv deterministic H asthewidthNeur ker ( , ) (Equation (2)) evaluatedH(t)= H forallt, then (3) becomes du(t) dt = H (u(t) y). Suppose (z)= max ( 0,z), 1/ = poly ( 1/ ,log (n / )) and d1 = d2 = = dL = m with m poly ( 1/ , L,1/ 0,n,log ( 1/ )).

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Intuitively,theseconcentration arguments ensure that, for anygiven function, most sample sets are good "representatives" of the distribution.

The theory enables a systematicclassification of all existing G-CNNs in terms of their symmetry group, base space,andfieldtype.

As a result of this analysis, we are able to pinpoint possible future paths to improvement forscalability andcomputational speed.