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BaLeNAS: Differentiable Architecture Search via the Bayesian Learning RuleMiao Zhang Shirui Pan Xiaojun Chang Steven Su Jilin Hu Gholamreza (Reza) Haffari Bin YangIEEE Conference on Computer Vision and Pattern Recognition
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[(2.)-250(Pr)18(eliminaries)]TJ
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[(2.1.)-250(Differ)18.1(entiable)-250(Ar)18(chitectur)18(e)-250(Sear)18(ch)]TJ
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[(Dif)25(ferentiable)-313.8(architecture)-314.9(search)-313.8(\(D)39(AR)59(TS\))-315(is)-314(b)19(uilt)-314(on)]TJ
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[(weight-sharing)-284.7(N)35(A)0(S)-285([)]TJ
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[(for)-253.9(once)-254.1(per)-254(the)-254(architecture)-254.2(search)-254.1(c)15(ycle.)-316(Rather)-254(than)-254(using)]TJ
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[(,)-252(D)41(AR)60(TS)-252([)]TJ
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[(architecture)-228.1(space)-229.1(and)-228(enabling)-228.1(gradient)-228.1(descent)-229.1(for)-228.1(architec-)]TJ
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[(ture)-233(optimization.)-309.1(Therefore,)-238.2(architecture)-233.1(parameters)]TJ
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[(could)-300.9(be)-302(jointly)-301(optimized)-301(during)-301(the)]TJ
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[(supernet)-253.8(training,)-254(and)-254(the)-252.9(promising)-253.9(architecture)-253(parameters)]TJ
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[(are)-248(searched)-248(from)-248(the)-248(continuous)-248(search)-248(space)]TJ
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[(the)-256(supernet)-256(is)-256(trained.)-319(The)-256(bile)26(v)15(e)0(l)-256(optimization)-256(formulation)]TJ
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[(is)-250(usually)-250(adopted)-250(to)-250(alternati)25(v)15(ely)-250(learn)]TJ
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(\(1\))Tj
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[(and)-250.9(the)-251.9(best)-251(discrete)-251.9(architecture)]TJ
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[(is)-251(obtained)-252(after)-251(apply-)]TJ
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(ing)Tj
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[(ar)37(gmax)]TJ
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(on)Tj
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<02>Tj
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(.)Tj
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[(Despite)-216.1(notable)-215(bene\223ts)-216.1(on)-216(computational)-216(ef)26(\223cienc)16(y)-216(from)]TJ
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[(D)39(A)0(R)60(TS,)-247(more)-248(recent)-247(w)10(orks)-247<936e64>-247(it)-247(is)-248(still)-248(unreliable)-247([)]TJ
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(50)Tj
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[(that)-258.9(directly)-258.9(optimizes)-259.9(the)-258.9(architecture)-258.8(magnitudes,)-262.8(where)]TJ
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[(D)39(A)0(R)59(T)0(S)-459(usually)-459(observ)15(es)-459(a)-460(performance)-460(collapses)-459(with)]TJ
T*
[(search)-286.8(progresses.)-431.9(This)-286.9(phenomenon)-287.8(is)-287(also)-287(called)-288(the)-287(in-)]TJ
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[(stability)-252.9(of)-253(dif)25(ferentiable)-254(N)36(A)0(S)-254([)]TJ
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(8)Tj
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[(].)-315(Zela)]TJ
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[(et)-253(al)]TJ
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(.[)Tj
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(50)Tj
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[(])-253(observ)15(ed)]TJ
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[(that)-249.9(the)-251(there)-249.9(is)-250(a)-251(s)1(trong)-251(correlation)-250(between)-250(the)-251(dominant)]TJ
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[(eigen)41(v)25(alue)-229(of)-230(the)-230(Hessian)-229(of)-230(the)-230(v)26(alidation)-230(loss)-230(and)-229(the)-230(archi-)]TJ
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[(tecture\220)56(s)-244(generalization)-245(error)-244(in)-244(D)40(A)0(R)62(TS,)-245(and)-244(k)10(eeping)-244(the)-245(the)]TJ
T*
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[(tifying)-245.9(the)-246(performance)-245.9(of)-246(dif)25(ferentiable)-246(N)35(A)0(S)-246([)]TJ
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(8)Tj
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[(].)-306(In)-246(addi-)]TJ
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[(tion,)-253(as)-254(described)-254(abo)15(v)16(e)0(,)-254(the)-253(dif)25(ferentiable)-253(N)35(A)0(S)-253<93727374>-253(relax)15(es)]TJ
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[(the)-361.9(discrete)-361(architectures)-361.7(into)-362(continuous)-361.9(representations)]TJ
0 -1.2001 TD
[(to)-346(enable)-346(the)-346(gradient)-346(descent)-346(optimization,)-371(and)-346(projects)]TJ
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[(the)-252.9(continuous)-251.9(architecture)-252.8(representation)]TJ
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<02>Tj
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<02>Tj
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[(into)-252.9(discrete)]TJ
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(architecture)Tj
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<02>Tj
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[(after)-250(the)-249.9(dif)25(ferentiable)-250.1(architecture)-251(optimiza-)]TJ
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[(tion.)-389.9(Ho)24(we)25(v)14(e)0(r)40(,)-281(more)-274(recent)-274(w)10(orks)-274([)]TJ
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(44)Tj
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[(])-274(cast)-274(doubts)-274(on)-274(the)]TJ
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[(rob)20.1(ustness)-248(of)-247(this)-247(discretization)-248(process)-247(in)-248(D)40(A)0(R)59(T)0(S)-247(that)-247(the)]TJ
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[(magnitude)-269.8(of)-270(architecture)-270(parameter)]TJ
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<02>Tj
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<02>Tj
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<02>Tj
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[(could)-269.9(hardly)-269.9(indi-)]TJ
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[(cate)-247(the)-246(importance)-247(of)-247(operations)-247(with)]TJ
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[(ar)36(gmax)]TJ
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[(.)-306(T)79(aking)-247(the)]TJ
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[(D)39(A)0(R)59(T)0(S)-295(a)0(s)-296(e)15(xample,)-308(the)-296(searched)-295(architecture)-296(parameters)]TJ
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<02>Tj
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[(are)-247(continuous,)-245.9(while)]TJ
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<02>Tj
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[(is)-247(represented)-246(with)]TJ
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({)Tj
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[(0,)-247(1)]TJ
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(after)Tj
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[(ar)36(gmax)]TJ
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[(.)-405(D)39(AR)59(TS)-279(assumes)-278(that)-279(the)]TJ
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(L)Tj
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[(va)35.7(l)]TJ
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0 Tc
(\()Tj
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<02>Tj
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<2c02>Tj
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0 Tc
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<02>Tj
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(\))Tj
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[(is)-279(a)-279(good)]TJ
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[(indicator)-247.9(to)-247(the)-248(v)25(alidation)-248(performance)-247(of)]TJ
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(L)Tj
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[(va)35.7(l)]TJ
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(.)Tj
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[(Ho)25(we)24(v)15(e)0(r)39(,)-382(when)-355(we)-355(conduct)-355(the)-355(T)78(aylor)-355(e)15(xpansion)-355(on)-355(the)]TJ
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[(local)-249.9(optimal)]TJ
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<02>Tj
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([)Tj
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(8)Tj
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(9)Tj
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[(],)-250(we)-250(ha)20(v)15(e)0(:)]TJ
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(L)Tj
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[(va)35.7(l)]TJ
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0 Tc
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(w)Tj
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<02>Tj
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(L)Tj
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[(va)35.7(l)]TJ
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0 Tc
(\()Tj
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<02>Tj
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[(va)35.7(l)]TJ
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<02>Tj
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(\))Tj
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(T)Tj
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(\(6\))Tj
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[(A)-298(straightforw)9(ard)-297(approach)-298(is)-297(using)-298(the)-297(stochastic)-298(gra-)]TJ
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[(dient)-298.9(descent)-297.9(to)-299(learn)]TJ
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Tj
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[(along)-298.9(with)-298(minimizing)]TJ
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[(called)-250(as)-250(the)-250(Bayes)-250(by)-250(Backprob)-250(\(BBB\))-250([)]TJ
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Tj
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0 Tc
(t)Tj
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(=)Tj
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(t)Tj
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<8a>Tj
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1 0 TD
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(t)Tj
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(\(7\))Tj
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(t)Tj
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[(are)-253(the)-252(learning)-253(rates,)-253(and)]TJ
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<1a>Tj
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<03>Tj
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Tj
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<1a>Tj
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<04>Tj
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[(are)-349(the)-349(unbiased)-348.9(stochastic)-348.8(gradient)-348.9(estimates)-348.8(of)]TJ
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Tj
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<07>Tj
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[(.)-311(H)0(o)25(w)0(e)25(v)15(er)39(,)-250(V)0(I)-250(remains)-250(to)-250(be)-250(impractical)-250(for)-250(learning)]TJ
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[(lar)18(ge)-251(deep)-252(netw)10(orks.)-315(The)-252(ob)16(vious)-252(issue)-252(is)-251(that)-252(VI)-252(introduces)]TJ
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[(more)-293.8(parameters)-292.8(to)-294(learn,)-306(as)-294(it)-294(needs)-293(to)-294(replace)-294(all)-294(neural)]TJ
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[(netw)10(orks)-254(weights)-254(with)-254(random)-254(v)25(ariables)-254(and)-254(simultaneously)]TJ
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[(optimize)-313.9(tw)9(o)-314(v)15(ectors)]TJ
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Tj
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<07>Tj
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9.8799 0 0 9.6862 422.6078 703.1471 Tm
[(to)-314(estimate)-315(the)-314(distrib)19(ution)]TJ
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(of)Tj
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<03>Tj
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[(,)-247(s)0(o)-246(the)-247(memory)-247(requirement)-246(is)-247(also)-247(doubled,)-247(leading)-246(a)]TJ
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[(lot)-254(of)-255(modi\223cations)-254(when)-254(\223tting)-255(e)16(xisting)-255(dif)26(ferentiable)-254(N)36(A)0(S)]TJ
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[(codebases)-249.9(with)-250(the)-250(v)25(ariational)-250(inference.)]TJ
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[(2.3.)-250(T)74(raining)-250(Fr)18(ee)-250(Pr)18(oxies)-250(f)25(o)0(r)-250(N)20(AS)]TJ
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[(T)34(raining)-274(Free)-274(N)35(A)0(S)-274(tries)-274(to)-274(identify)-274(promising)-274(architec-)]TJ
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[(tures)-269.9(at)-270(initialization)-270(without)-270(incurring)-271(training.)-380(Mellor)]TJ
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(et)Tj
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(al)Tj
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(.[)Tj
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0 Tc
(32)Tj
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[(])-251(empirically)-251<936e64>-252(that)-252(the)-251(correlation)-251(between)-251(sample-)]TJ
9.8799 0 0 9.6862 299.9446 596.5308 Tm
[(wise)-306.9(input-output)-306.8(Jacobian)-306.9(can)-307.9(indicate)-306.9(the)-306.9(architecture\220)54.2(s)]TJ
9.6572 0 0 9.6862 300.2936 584.9078 Tm
[(test)-250.9(performance,)-252(and)-251(propose)-252(using)-251(the)-252.1(Jacobian)-251(t)0(o)-252(score)-251(a)]TJ
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[(set)-247(of)-247(randomly)-248(sampled)-247(models)-247(with)-247(randomly)-247(initialized)]TJ
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[(weights,)-305.8(which)-294.9(greedily)-293.9(chooses)-293.9(the)-294(model)-294(with)-295(the)-294(high-)]TJ
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[(est)-274.9(score.)-393(TE-N)34.1(AS)-275([)]TJ
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(7)Tj
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[(])-275(utilizes)-275(the)-275(spectrum)-275(of)-275(NTKs)-275(and)]TJ
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[(the)-335.9(number)-335.9(of)-337(linear)-336(re)15(gions)-336(to)-337(analyzing)-336(the)-336(trainability)]TJ
T*
[(and)-342.9(e)15(xpressi)24(vity)-343(of)-343(architectures.)-598(Rather)-344(than)-343(e)25(v)24(aluating)]TJ
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[(the)-253.9(whole)-255.1(architecture,)-254(TE-N)35(AS)-254(uses)-254(the)-255(perturbation-based)]TJ
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[(architecture)-250.1(selection)-250.2(as)-251([)]TJ
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(44)Tj
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[(],)-250(to)-250(measure)-250(the)-251(importance)-250(of)]TJ
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[(each)-249.9(operation)-249.9(for)-250(the)-250(supernet)-249.9(prune.)]TJ
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[(Zero-cost)-329.8(N)34(A)0(S)-330([)]TJ
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(1)Tj
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[(])-330(e)15(xtends)-330(the)-330(salienc)15(y)-330(metrics)-330(in)-330(the)]TJ
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[(netw)10.1(ork)-345(pruning)-344.9(at)-344(initialization)-345(to)-345(score)-345(an)-344(architecture,)]TJ
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[(through)-249(summing)-248.1(scores)-249(of)-249(all)-248(parameters)]TJ
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<03>Tj
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(\))Tj
/F9 1 Tf
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<2c02>Tj
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0 Tc
<02>Tj
/F16 1 Tf
9.6862 0 0 9.6862 238.3635 489.6936 Tm
(\))Tj
/F9 1 Tf
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(,)Tj
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2.5803 .7469 TD
(\(9\))Tj
9.7831 0 0 9.6862 48.3727 463.4566 Tm
(where)Tj
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Tj
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(and)Tj
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<07>Tj
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9.7831 0 0 9.6862 107.7992 463.4566 Tm
[(are)-246.9(the)-248(tw)10(o)-247(learnable)-247(parameters)-248(for)-247(the)-248(dis-)]TJ
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[(trib)20(ution)]TJ
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(q)Tj
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<02>Tj
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[-167.2<07>]TJ
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[(\):)278.1(=)]TJ
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(N)Tj
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<02>Tj
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<02>Tj
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(|)Tj
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Tj
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(diag)Tj
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<07>Tj
/F18 1 Tf
6.7803 0 0 6.7803 214.5494 455.3485 Tm
(2)Tj
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.0009 Tc
(\)\))Tj
/F2 1 Tf
9.5312 0 0 9.6862 226.4284 451.8326 Tm
0 Tc
[(.)-316(Considering)]TJ
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[(the)-249(v)25(ariational)-248(inference)-249(and)-249(Bayesian)-249(deep)-248(learning,)-249(based)]TJ
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[(on)-254(Eq.)]TJ
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(\()Tj
0 .99399 1 0 k
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(4)Tj
/Cs8 cs 1 scn
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(-)Tj
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(6)Tj
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(\))Tj
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[(,)-257(the)-254(loss)-255(function)-254(for)-255(the)-254(outer)20(-loop)-255(architec-)]TJ
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[(ture)-246(distrib)20(ution)-246(optimization)-245.1(problem)-246.1(could)-246(be)-245(de\223ned)-246(as:)]TJ
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(E)Tj
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(q)Tj
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([)Tj
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[(]:)278(=)]TJ
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<8a>Tj
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(E)Tj
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(q)Tj
1.3947 2.0001 TD
(N)Tj
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<04>Tj
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(i)Tj
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(i)Tj
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(|)Tj
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<02>Tj
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<02>Tj
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(E)Tj
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(q)Tj
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<06>Tj
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(log)Tj
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1.6584 .6766 TD
(q)Tj
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(\()Tj
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<02>Tj
/F10 1 Tf
6.3087 0 0 6.3087 249.4125 382.9084 Tm
<02>Tj
/F16 1 Tf
9.0124 0 0 9.0124 253.4905 384.2604 Tm
(\))Tj
ET
/Cs8 CS 1 SCN
0 J 0 j .36 w 10 M [] 0 d
/GS2 gs
1 i
q 1 0 0 1 235.701 380.416 cm 0 0 m
21.388 0 l
S
Q
BT
/F9 1 Tf
9.0124 0 0 9.0124 235.7015 371.9804 Tm
(p)Tj
/F16 1 Tf
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(\()Tj
/F9 1 Tf
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<02>Tj
/F10 1 Tf
6.3087 0 0 6.3087 249.5065 370.6294 Tm
<02>Tj
/F16 1 Tf
9.0124 0 0 9.0124 253.5845 371.9804 Tm
(\))Tj
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<07>Tj
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(.)Tj
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(\(10\))Tj
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[(Since)-251.9(the)-252(architecture)-252.8(parameters)]TJ
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<02>Tj
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<02>Tj
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[(are)-252(random)-251.8(v)24(ariables)]TJ
-14.8829 -1.2001 TD
[(sampled)-325.9(from)-326(the)-326(Gaussian)-326(distrib)19(ution)]TJ
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(q)Tj
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<02>Tj
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(|)Tj
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[-167.2<07>]TJ
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(\))Tj
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[(,)-346(the)]TJ
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[(distrib)20(ution)-251(learning-based)-250.9(method)-250(naturally)-250.9(encourages)-251(e)15(x)0(-)]TJ
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[(ploration)-250(during)-250(the)-250(architecture)-249.9(search.)]TJ
/F1 1 Tf
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[(3.2.)-250(Natural-Gradient)-249.9(VI)-250(f)25(o)0(r)-250(N)20(AS)]TJ
/F2 1 Tf
9.8799 0 0 9.6862 60.345 275.6652 Tm
[(As)-289(describe)-289(in)-289(Sec.)]TJ
0 .99399 1 0 k
7.782 0 TD
(2.2)Tj
/Cs8 cs 1 scn
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[(,)-300(t)1(he)-289(traditional)-289(v)24(ariational)-289(infer)20(-)]TJ
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[(ence)-241(has)-240(double)-241(memory)-241.1(requirement)-241.2(and)-240(needs)-241.1(to)-241(re-design)]TJ
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[(the)-246(object)-245.9(function,)-245.9(making)-244.9(it)-246(dif)24(\223cult)-246(to)-246<9374>-246(with)-246(the)-245(dif)24(fer)19(-)]TJ
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[(entiable)-295.9(N)35(AS.)-296(Thus,)-309(this)-295(paper)-296(considers)-296(natural-gradient)]TJ
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[(v)25(ariational)-246(inference)-245(\(NGVI\))-245(methods)-245([)]TJ
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15.84 0 TD
(22)Tj
/Cs8 cs 1 scn
1.0001 0 TD
(,)Tj
.62765 0 1 0 k
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(35)Tj
/Cs8 cs 1 scn
1 0 TD
[(])-246(t)0(o)-245(optimize)]TJ
9.4925 0 0 9.6862 48.7217 217.5481 Tm
[(the)-228(architecture)-228.1(distrib)19.9(ution)]TJ
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9.6862 0 0 9.6862 155.2083 217.5481 Tm
(p)Tj
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(\()Tj
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<02>Tj
/F10 1 Tf
6.7803 0 0 6.7803 170.0443 216.0951 Tm
<02>Tj
/F8 1 Tf
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(|D)Tj
/F16 1 Tf
1.3547 0 TD
0 Tc
(\))Tj
/F2 1 Tf
9.4925 0 0 9.6862 196.1734 217.5481 Tm
-.0001 Tc
[(in)-228.1(a)-228.1(natural)-229.1(parameter)]TJ
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0 Tc
[(space,)-360.9(which)-338(requires)-337.8(the)-338(same)-338.9(number)-337.9(of)-338(parameters)-338(as)]TJ
0 -1.2001 TD
[(the)-278(traditional)-277.8(learning)-276.9(method.)-401.9(By)-278(le)24(v)15(eraging)-278(NGVI,)-278(the)]TJ
9.599 0 0 9.6862 48.7217 182.677 Tm
[(architecture)-251.9(parameter)-252.9(distrib)20.1(ution)-252(could)-252.9(be)-252(learned)-253(by)-252(only)]TJ
9.6862 0 0 9.6862 48.7217 171.054 Tm
[(updating)-250(a)-250(natural)-250(parameter)]TJ
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11.7189 0 TD
<0b>Tj
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[(during)-250(the)-250(search.)]TJ
9.4925 0 0 9.6862 60.345 159.4089 Tm
[(NGVI)-244.1(parameterizes)-244.1(the)-244(distrib)19.9(ution)]TJ
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(q)Tj
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(\()Tj
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<02>Tj
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6.7803 0 0 6.7803 215.8654 157.955 Tm
<02>Tj
/F16 1 Tf
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(\))Tj
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9.4925 0 0 9.6862 226.3304 159.4089 Tm
[(with)-244.1(a)-244(natural)]TJ
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(parameter)Tj
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<0b>Tj
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9.8799 0 0 9.6862 96.933 147.7859 Tm
[(,)-326(considering)]TJ
/F9 1 Tf
9.6862 0 0 9.6862 151.7863 147.7859 Tm
(q)Tj
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(\()Tj
/F9 1 Tf
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<02>Tj
/F10 1 Tf
6.7803 0 0 6.7803 166.4203 146.332 Tm
<02>Tj
/F8 1 Tf
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(|)Tj
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<0b>Tj
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(\))Tj
/F2 1 Tf
9.8799 0 0 9.6862 193.7234 147.7859 Tm
[(in)-310(a)-310(class)-310(of)-309(minimal)]TJ
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[(e)15(xponential)-250(f)10(amily)-250(with)-250(natural)-250(parameter)]TJ
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<0b>Tj
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([)Tj
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(21)Tj
/Cs8 cs 1 scn
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(]:)Tj
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-17.0533 -2.2044 TD
(q)Tj
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(\()Tj
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<02>Tj
/F10 1 Tf
6.7803 0 0 6.7803 84.355 113.3559 Tm
<02>Tj
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(|)Tj
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<0b>Tj
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.2789 Tc
[(\):)278.1(=)]TJ
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(h)Tj
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(\()Tj
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<02>Tj
/F10 1 Tf
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<02>Tj
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9.6862 0 0 9.6862 141.7583 114.8089 Tm
(\))Tj
/F2 1 Tf
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-.015 Tc
[(ex)-15(p)]TJ
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1.5957 .81 TD
0 Tc
(\n)Tj
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<0b>Tj
/F10 1 Tf
6.7803 0 0 6.7803 170.6673 118.8079 Tm
(T)Tj
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(\f)Tj
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(\()Tj
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<02>Tj
/F10 1 Tf
6.7803 0 0 6.7803 192.5044 113.3559 Tm
<02>Tj
/F16 1 Tf
9.6862 0 0 9.6862 196.8854 114.8089 Tm
(\))Tj
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<8a>Tj
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(A)Tj
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(\()Tj
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<0b>Tj
/F16 1 Tf
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(\))Tj
/F15 1 Tf
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<0b>Tj
/F9 1 Tf
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(,)Tj
/F2 1 Tf
2.4456 0 TD
(\(11\))Tj
9.8799 0 0 9.6862 299.9446 726.394 Tm
(where)Tj
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(h)Tj
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(\()Tj
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<02>Tj
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6.7803 0 0 6.7803 343.1227 724.941 Tm
<02>Tj
/F16 1 Tf
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(\))Tj
/F2 1 Tf
9.8799 0 0 9.6862 354.7707 726.394 Tm
[(is)-354(the)-354(base)-354(measure,)]TJ
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(\f)Tj
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(\()Tj
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<02>Tj
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6.7803 0 0 6.7803 456.3759 724.941 Tm
<02>Tj
/F16 1 Tf
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(\))Tj
/F2 1 Tf
9.8799 0 0 9.6862 468.0239 726.394 Tm
[(is)-354(a)-354(v)15(ector)-355(con-)]TJ
-16.9769 -1.2 TD
[(taining)-377.9(suf)25.1(\223cient)-376.9(statistics,)-410.9(and)]TJ
/F9 1 Tf
9.6862 0 0 9.6862 430.2869 714.7711 Tm
(A)Tj
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(\()Tj
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<0b>Tj
/F16 1 Tf
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(\))Tj
/F2 1 Tf
9.8799 0 0 9.6862 454.4659 714.7711 Tm
[(is)-378(the)-377(log-partition)]TJ
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(function.)Tj
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(When)Tj
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(h)Tj
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<02>Tj
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<02>Tj
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(\))Tj
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<05>Tj
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(1)Tj
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9.8799 0 0 9.6862 383.1007 691.524 Tm
[(,)-345(the)-325(distrib)19(ution)]TJ
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(q)Tj
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(\()Tj
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<02>Tj
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<02>Tj
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(|)Tj
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<0b>Tj
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(\))Tj
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[(could)-324.9(be)]TJ
9.6765 0 0 9.6862 300.2936 679.901 Tm
[(learned)-250.1(by)-250(only)-250(updating)]TJ
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<0b>Tj
/F2 1 Tf
9.6765 0 0 9.6862 407.2608 679.901 Tm
[(during)-250(the)-250(training)-250.1([)]TJ
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(22)Tj
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(,)Tj
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(23)Tj
/Cs8 cs 1 scn
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[(],)-250(and)]TJ
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<0b>Tj
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[(could)-250.1(be)-250(learned)-250(in)-250(the)-250(natural-parameter)-250(space)-250(by:)]TJ
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<0b>Tj
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(t)Tj
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(+1)Tj
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[(=\()277.9(1)]TJ
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(t)Tj
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(t)Tj
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<8a>Tj
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(t)Tj
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<03>Tj
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Tj
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(E)Tj
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(t)Tj
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(\n)Tj
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Tj
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<02>Tj
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6.7803 0 0 6.7803 477.0739 649.9589 Tm
<02>Tj
/F16 1 Tf
9.6862 0 0 9.6862 481.4569 651.413 Tm
(\))Tj
/F15 1 Tf
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<0b>Tj
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(,)Tj
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(\(12\))Tj
9.7927 0 0 9.6862 299.9446 634.5479 Tm
(where)Tj
/F9 1 Tf
9.6862 0 0 9.6862 326.2856 634.5479 Tm
(\r)Tj
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6.7803 0 0 6.7803 331.2936 633.0949 Tm
(t)Tj
/F2 1 Tf
9.7927 0 0 9.6862 337.1216 634.5479 Tm
-.0001 Tc
[(is)-247.1(the)-247.1(learning)-247.1(rate,)]TJ
/F16 1 Tf
9.6862 0 0 9.6862 415.1808 637.1039 Tm
0 Tc
Tj
/F9 1 Tf
-.0695 -.2639 TD
<04>Tj
/F2 1 Tf
9.7927 0 0 9.6862 420.9608 634.5479 Tm
[(is)-247(in)-247(the)-247(form)-246(of)-247(Eq.)]TJ
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(\()Tj
0 .99399 1 0 k
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(3)Tj
/Cs8 cs 1 scn
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(\))Tj
9.7927 0 0 9.6862 510.981 634.5479 Tm
[(,)-247(and)]TJ
9.4925 0 0 9.6862 300.2936 622.9249 Tm
[(the)-210.9(deri)26(v)25(ati)26(v)15(e)]TJ
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<03>Tj
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Tj
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Tj
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(\()Tj
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<02>Tj
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<02>Tj
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(\))Tj
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.3889 .8099 TD
<0b>Tj
/F2 1 Tf
9.4925 0 0 9.6862 428.8098 622.9249 Tm
[(is)-211(tak)11(en)-211(at)]TJ
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Tj
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(=)Tj
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Tj
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(t)Tj
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9.4925 0 0 9.6862 498.458 622.9249 Tm
[(which)-211(is)]TJ
9.6862 0 0 9.6862 300.2936 611.2999 Tm
[(the)-250.9(e)15(xpectation)-251(parameter)-251(with)-251(Mark)10(o)15(v)-252(Chain)-252(Monte)-251(Carlo)]TJ
9.8799 0 0 9.6862 299.9736 599.6768 Tm
[(\(MCMC\))-249.8(sampling.)-316.9(And)]TJ
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[(is)-250(the)]TJ
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<02>Tj
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(,)Tj
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Tj
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Tj
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[(is)-258(the)-259(e)15(xpectation)-259(parameter)-258(of)]TJ
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<02>Tj
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[(This)-250(is)-250(also)-250(called)-250(as)-250(the)-250(Bayesian)-250(learning)-250(rule)-250([)]TJ
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(23)Tj
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(].)Tj
9.5312 0 0 9.6862 311.9166 564.8068 Tm
[(When)-253.9(we)-253(consider)-254(Gaussin)-253(mean-\223eld)-254(VI)-253(that)]TJ
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<02>Tj
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(and)Tj
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(q)Tj
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6.7803 0 0 6.7803 314.9276 551.7297 Tm
<02>Tj
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(\))Tj
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9.8799 0 0 9.6862 327.0797 553.1837 Tm
[(are)-405(in)-405(the)-405(form)-405(of)-406(Eq.)]TJ
9.6862 0 0 9.6862 419.7988 553.1837 Tm
(\()Tj
0 .99399 1 0 k
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(5)Tj
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(\))Tj
9.8799 0 0 9.6862 431.0928 553.1837 Tm
[(,)-445(the)-405(V)109(ariational)-406(Online-)]TJ
9.4925 0 0 9.6862 300.2936 541.5598 Tm
[(Ne)26(wton)-255(\(V)41(ON\))-254(method)-254(proposed)-254(by)-255(Khan)-254(et.)-316(al.)-254([)]TJ
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[(])-254(sho)25(ws)]TJ
9.6862 0 0 9.6862 300.2936 529.9357 Tm
[(that)-249.9(the)-250(NGVI)-250.1(update)-250(could)-250(be)-250(written)-250(as)-250(follo)25(wing:)]TJ
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Tj
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(t)Tj
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Tj
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<8a>Tj
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(t)Tj
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9.6862 0 0 9.6862 395.0178 513.0717 Tm
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<06b5>Tj
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1.0466 .2639 TD
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Tj
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(\(14\))Tj
9.8799 0 0 9.6862 299.9446 469.8156 Tm
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9.8799 0 0 9.6862 339.7197 469.8156 Tm
[(is)-342(the)-341(learning)-342(rate,)]TJ
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<03>Tj
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Tj
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9.6862 0 0 9.6862 363.4607 458.1915 Tm
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1.1449 .2639 TD
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9.8799 0 0 9.6862 388.9338 458.1915 Tm
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<1f>Tj
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(=)Tj
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.0384 Tc
[<062f>94.4(N)]TJ
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9.8799 0 0 9.6862 447.0688 458.1915 Tm
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(.)Tj
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9.6862 0 0 9.6862 456.3969 458.6025 Tm
<1a>Tj
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0 -.0424 TD
(g)Tj
/F2 1 Tf
9.8799 0 0 9.6862 464.9469 458.1915 Tm
[(is)-375(the)-375(stochastic)]TJ
-16.6654 -1.2001 TD
-.0001 Tc
[(estimate)-316.9(with)-317.1(respect)-317.9(to)]TJ
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(q)Tj
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9.8799 0 0 9.6862 406.7958 446.5675 Tm
[(through)-317(MCMC)-316.9(sampling)-317.9(that,)]TJ
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9.6862 0 0 9.6862 300.7336 435.0785 Tm
<1a>Tj
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-.0454 -.0138 TD
(g)Tj
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<03>Tj
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(t)Tj
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9.6862 0 0 9.6862 317.7426 434.9445 Tm
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(\)=)Tj
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6.7803 0 0 6.7803 339.0407 438.7585 Tm
0 Tc
(1)Tj
ET
.387 w
q 1 0 0 1 336.915 437.367 cm 0 0 m
8.113 0 l
S
Q
BT
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6.7803 0 0 6.7803 336.9147 431.6045 Tm
(M)Tj
/F15 1 Tf
9.6862 0 0 9.6862 347.8047 442.2095 Tm
(\f)Tj
/F10 1 Tf
6.7803 0 0 6.7803 358.0287 432.0385 Tm
(i)Tj
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.0008 Tc
<034d>Tj
/F8 1 Tf
9.6862 0 0 9.6862 377.1917 434.9445 Tm
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<03>Tj
/F10 1 Tf
6.7803 0 0 6.7803 385.2637 433.4925 Tm
<03>Tj
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4.8431 0 0 4.8431 390.2988 432.4645 Tm
<02>Tj
/F16 1 Tf
9.6862 0 0 9.6862 395.3878 437.5005 Tm
Tj
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-.0695 -.2639 TD
<04>Tj
/F10 1 Tf
6.7803 0 0 6.7803 398.7508 433.4925 Tm
(i)Tj
/F16 1 Tf
9.6862 0 0 9.6862 401.9758 434.9445 Tm
(\()Tj
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.3889 0 TD
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/F10 1 Tf
6.7803 0 0 6.7803 411.9398 433.4925 Tm
<02>Tj
/F16 1 Tf
9.6862 0 0 9.6862 416.3208 434.9445 Tm
(\))Tj
/F2 1 Tf
9.8799 0 0 9.6862 420.0878 434.9445 Tm
[(,)-291(and)-281(the)-281(minibatch)]TJ
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9.6862 0 0 9.6862 499.628 434.9445 Tm
(M)Tj
/F2 1 Tf
9.8799 0 0 9.6862 514.04 434.9445 Tm
(con-)Tj
-21.6344 -1.2 TD
(tains)Tj
/F9 1 Tf
9.6862 0 0 9.6862 322.7526 423.3215 Tm
(M)Tj
/F2 1 Tf
9.8799 0 0 9.6862 337.0006 423.3215 Tm
[(samples.)-720.9(More)-383.8(details)-385(are)-383.9(in)-384([)]TJ
.62765 0 1 0 k
12.839 0 TD
(22)Tj
/Cs8 cs 1 scn
1 0 TD
[(].)-721(V)109(ariational)]TJ
-17.5543 -1.2001 TD
[(RMSprop)-411.8(\(Vprop\))-412.9([)]TJ
.62765 0 1 0 k
8.324 0 TD
(22)Tj
/Cs8 cs 1 scn
1 0 TD
[(])-412(further)-413(uses)-412(gradient)-413(magnitude)]TJ
9.6862 0 0 9.6862 299.9736 400.0745 Tm
[(\(GM\))-250([)]TJ
.62765 0 1 0 k
2.8599 0 TD
(5)Tj
/Cs8 cs 1 scn
.5 0 TD
[(])-250(approximation)-250(to)-250(reformulate)-250(Eq.\()]TJ
0 .99399 1 0 k
14.3029 0 TD
(14)Tj
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1 0 TD
[(\))-250(as:)]TJ
/F1 1 Tf
-14.4541 -1.7411 TD
(s)Tj
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6.7803 0 0 6.7803 344.5087 381.7564 Tm
(t)Tj
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.4315 0 TD
(+1)Tj
/F16 1 Tf
9.6862 0 0 9.6862 360.4177 383.2094 Tm
.2788 Tc
[(=\()277.9(1)]TJ
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2.1666 0 TD
0 Tc
<8a>Tj
/F9 1 Tf
1.0001 0 TD
<0e>Tj
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6.7803 0 0 6.7803 396.5688 381.7564 Tm
(t)Tj
/F16 1 Tf
9.6862 0 0 9.6862 399.9798 383.2094 Tm
(\))Tj
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.3888 0 TD
(s)Tj
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6.7803 0 0 6.7803 407.5138 381.7564 Tm
(t)Tj
/F16 1 Tf
9.6862 0 0 9.6862 413.0768 383.2094 Tm
(+)Tj
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1.0001 0 TD
<0e>Tj
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(2)Tj
/F16 1 Tf
9.6862 0 0 9.6862 212.5654 607.3069 Tm
(\))Tj
/F2 1 Tf
9.8799 0 0 9.6862 216.3324 607.3069 Tm
[(,)-296(and)-286(utilize)-286(the)]TJ
9.6862 0 0 9.6862 65.1878 595.6838 Tm
[(training)-250(free)-250(proxies)-249.9(for)-250(selection)]TJ
/Cs8 cs 1 scn
13.3299 0 TD
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ET
q 1 0 0 1 48.722 589.519 cm 0 0 m
229.696 0 l
S
Q
BT
/F1 1 Tf
9.6862 0 0 9.6862 89.1696 543.8817 Tm
(s)Tj
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6.7803 0 0 6.7803 92.9371 542.4297 Tm
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[(=\()277.9(1)]TJ
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2.1666 0 TD
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1.0001 0 TD
<0e>Tj
/F10 1 Tf
6.7803 0 0 6.7803 144.9973 542.4297 Tm
(t)Tj
/F16 1 Tf
9.6862 0 0 9.6862 148.4083 543.8817 Tm
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/F16 1 Tf
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1.0001 0 TD
<0e>Tj
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6.7803 0 0 6.7803 176.6703 542.4297 Tm
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/F16 1 Tf
9.6862 0 0 9.6862 180.0804 543.8817 Tm
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<1a>Tj
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0 -.0425 TD
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(\()Tj
/F9 1 Tf
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<03>Tj
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6.7803 0 0 6.7803 195.9284 542.4297 Tm
(t)Tj
/F16 1 Tf
9.6862 0 0 9.6862 199.3384 543.8817 Tm
(\))Tj
/F8 1 Tf
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<07>Tj
/F16 1 Tf
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<1a>Tj
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0 -.0425 TD
(g)Tj
/F16 1 Tf
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/F9 1 Tf
.3888 0 TD
<03>Tj
/F10 1 Tf
6.7803 0 0 6.7803 225.4104 542.4297 Tm
(t)Tj
/F16 1 Tf
9.6862 0 0 9.6862 228.8214 543.8817 Tm
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(\)])Tj
/F9 1 Tf
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(.)Tj
/F2 1 Tf
2.7875 0 TD
(\(18\))Tj
9.8799 0 0 9.6862 48.3727 523.5897 Tm
[(where)-298.9<8d>]TJ
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<07>Tj
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9.8799 0 0 9.6862 84.6893 523.5897 Tm
[<8e>-299(stands)-298(for)-299(element-wise)-298(product,)]TJ
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<03>Tj
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<064e>Tj
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2.1244 0 TD
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<02>Tj
/F10 1 Tf
6.7803 0 0 6.7803 267.6755 522.1377 Tm
<02>Tj
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9.6862 0 0 9.6862 275.7275 523.5897 Tm
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Tj
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6.7803 0 0 6.7803 54.5582 510.5147 Tm
(t)Tj
/F9 1 Tf
9.6862 0 0 9.6862 57.9688 511.9667 Tm
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/F18 1 Tf
6.7803 0 0 6.7803 68.1561 515.4827 Tm
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(2)Tj
/F10 1 Tf
-.0513 -.8718 TD
(t)Tj
/F16 1 Tf
9.6862 0 0 9.6862 72.5011 511.9667 Tm
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9.4925 0 0 9.6862 78.5195 511.9667 Tm
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<07>Tj
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6.7803 0 0 6.7803 103.5312 515.4827 Tm
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/F16 1 Tf
9.6862 0 0 9.6862 110.5672 511.9667 Tm
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1.5555 0 TD
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(N)Tj
/F16 1 Tf
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(s)Tj
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6.7803 0 0 6.7803 149.5423 510.5147 Tm
(t)Tj
/F16 1 Tf
9.6862 0 0 9.6862 154.4753 511.9667 Tm
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.9816 .2639 TD
<1f>Tj
/F9 1 Tf
-.0467 -.2639 TD
<06>Tj
/F16 1 Tf
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(\)])Tj
/F2 1 Tf
9.4925 0 0 9.6862 174.6603 511.9667 Tm
0 Tc
[(.)-310(A)0(s)-238(pointed)-237(out)-237(in)-237(Sec.)]TJ
0 .99399 1 0 k
9.68 0 TD
(2.2)Tj
9.6475 0 0 9.6862 48.7217 500.3436 Tm
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[(and)-251(sho)26(wn)-251(in)-250(Eq.)]TJ
9.6862 0 0 9.6862 115.4862 500.3436 Tm
(\()Tj
0 .99399 1 0 k
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(17)Tj
/Cs8 cs 1 scn
1 0 TD
(\))Tj
9.6475 0 0 9.6862 134.0413 500.3436 Tm
[(and)-250.9(Eq.)]TJ
9.6862 0 0 9.6862 163.5193 500.3436 Tm
(\()Tj
0 .99399 1 0 k
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(18)Tj
/Cs8 cs 1 scn
1 0 TD
(\))Tj
9.6475 0 0 9.6862 179.6563 500.3436 Tm
[(,)-251(the)-250(distrib)20(ution)]TJ
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9.6862 0 0 9.6862 245.4095 500.3436 Tm
(q)Tj
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(\()Tj
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<02>Tj
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6.7803 0 0 6.7803 260.0435 498.8906 Tm
<02>Tj
/F16 1 Tf
9.6862 0 0 9.6862 264.4255 500.3436 Tm
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(\)=)Tj
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-22.2692 -1.2 TD
0 Tc
(N)Tj
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/F9 1 Tf
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<02>Tj
/F10 1 Tf
6.7803 0 0 6.7803 68.0599 487.2666 Tm
<02>Tj
/F8 1 Tf
9.6862 0 0 9.6862 76.0304 488.7206 Tm
(|)Tj
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[-167.2<07>]TJ
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6.7803 0 0 6.7803 98.334 492.2346 Tm
0 Tc
(2)Tj
/F16 1 Tf
9.6862 0 0 9.6862 102.6802 488.7206 Tm
(\))Tj
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9.8799 0 0 9.6862 109.3532 488.7196 Tm
[(is)-294(no)24(w)-294(optimized,)-306(needing)-294(to)-295(calculate)-294(the)]TJ
9.6862 0 0 9.6862 48.7217 477.0966 Tm
[(gradient)-250(of)-250(only)-250(one)-250(parameter)55(.)]TJ
/F1 1 Tf
0 -1.5828 TD
[(Implicit)-243(Regularization)-242.9(fr)18(om)-243(MCMC)-243(Sampling:)]TJ
/F2 1 Tf
9.4925 0 0 9.6862 250.3365 461.7656 Tm
[(Se)25(v)16(eral)]TJ
-21.2394 -1.2002 TD
[(recent)-209.1(w)11(orks)-209([)]TJ
.62765 0 1 0 k
5.627 0 TD
(8)Tj
/Cs8 cs 1 scn
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(,)Tj
.62765 0 1 0 k
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(9)Tj
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(,)Tj
.62765 0 1 0 k
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(50)Tj
/Cs8 cs 1 scn
1 0 TD
[(])-208(empirically)-209(and)-209(theoretically)-208(sho)25(w)-209(that)]TJ
-8.2379 -1.2 TD
[(the)-202(performance)-202.2(of)-202(dif)25(ferentiable)-203(N)36(A)0(S)-202(i)0(s)-202(highly)-202(related)-202(to)-203(the)]TJ
9.8799 0 0 9.6862 48.7217 426.8945 Tm
[(norm)-262.9(of)]TJ
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(H)Tj
/F2 1 Tf
9.8799 0 0 9.6862 91.2784 426.8945 Tm
[(,)-267(the)-263(Hessian)-263(matrix)-263(of)]TJ
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9.6862 0 0 9.6862 184.1634 426.8945 Tm
(L)Tj
/F10 1 Tf
6.7803 0 0 6.7803 190.8434 425.4415 Tm
.0364 Tc
[(va)35.7(l)]TJ
/F16 1 Tf
9.6862 0 0 9.6862 202.1364 426.8945 Tm
0 Tc
(\()Tj
/F9 1 Tf
.3888 0 TD
(w)Tj
/F11 1 Tf
6.7803 0 0 6.7803 213.0984 430.4095 Tm
<02>Tj
/F9 1 Tf
9.6862 0 0 9.6862 217.5514 426.8945 Tm
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<2c02>Tj
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6.7803 0 0 6.7803 228.0524 425.4415 Tm
0 Tc
<02>Tj
/F16 1 Tf
9.6862 0 0 9.6862 232.4344 426.8945 Tm
(\))Tj
/F2 1 Tf
9.8799 0 0 9.6862 236.2025 426.8945 Tm
[(,)-267(and)-263(k)9(eep-)]TJ
9.7346 0 0 9.6862 48.7217 415.2715 Tm
[(ing)-249(this)-248(norm)-249(in)-249(a)-248(l)0(o)24(w)-248(le)25(v)15(e)0(l)-249(plays)-249(a)-248(k)10(e)14(y)-248(role)-249(in)-249(rob)20(ustifying)]TJ
9.8024 0 0 9.6862 48.7217 403.6475 Tm
[(dif)25(ferentiable)-245.9(N)35(AS.)-246(As)-246(described)-246(before,)-246(we)-246(kno)25(w)-246(the)-245(loss)]TJ
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(E)Tj
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(q)Tj
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4.8431 0 0 4.8431 58.7291 389.3054 Tm
(t)Tj
/F18 1 Tf
6.7803 0 0 6.7803 61.9434 390.2755 Tm
(\()Tj
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<03>Tj
/F13 1 Tf
4.8431 0 0 4.8431 70.0063 389.2474 Tm
<02>Tj
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6.7803 0 0 6.7803 73.9381 390.2755 Tm
(\))Tj
/F15 1 Tf
9.6862 0 0 9.6862 79.0639 399.8694 Tm
(\n)Tj
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Tj
/F9 1 Tf
-.0695 -.2639 TD
<04>Tj
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(\()Tj
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<02>Tj
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6.7803 0 0 6.7803 97.0983 390.5705 Tm
<02>Tj
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9.6862 0 0 9.6862 101.4812 392.0244 Tm
(\))Tj
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.3889 .8099 TD
<0b>Tj
/F2 1 Tf
9.5506 0 0 9.6862 111.7112 392.0244 Tm
[(of)-254(architecture)-254(optimization)-254(in)-254(BaLeN)35(AS)-254(is)]TJ
9.7153 0 0 9.6862 48.7217 380.4004 Tm
[(calculated)-249.9(based)-250.9(on)-250(MCMC)-250(sampling,)-251(sho)25(wing)-250(the)-250(natural-)]TJ
9.7734 0 0 9.6862 48.7217 368.7764 Tm
[(ity)-247(of)-248(enhancing)-247(e)15(xploration.)-308(Besides,)]TJ
/F20 1 Tf
9.6862 0 0 9.6862 199.6914 368.7764 Tm
(E)Tj
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6.7803 0 0 6.7803 206.1494 367.0274 Tm
(q)Tj
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4.8431 0 0 4.8431 209.6994 366.0594 Tm
(t)Tj
/F18 1 Tf
6.7803 0 0 6.7803 212.9134 367.0274 Tm
(\()Tj
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<03>Tj
/F13 1 Tf
4.8431 0 0 4.8431 220.9764 366.0004 Tm
<02>Tj
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6.7803 0 0 6.7803 224.9084 367.0274 Tm
(\))Tj
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9.6862 0 0 9.6862 230.0344 376.6224 Tm
(\n)Tj
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Tj
/F9 1 Tf
-.0695 -.2639 TD
<04>Tj
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(\()Tj
/F9 1 Tf
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<02>Tj
/F10 1 Tf
6.7803 0 0 6.7803 248.0685 367.3244 Tm
<02>Tj
/F16 1 Tf
9.6862 0 0 9.6862 252.4515 368.7764 Tm
(\))Tj
/F15 1 Tf
.3888 .81 TD
<0b>Tj
/F2 1 Tf
9.7734 0 0 9.6862 262.6725 368.7764 Tm
(also)Tj
9.8799 0 0 9.6862 48.7217 357.1534 Tm
[(has)-278(the)-277(naturality)-277.8(to)-278(enhance)-278(the)-277(stability)-278(in)-278(dif)25(ferentiable)]TJ
0 -1.2 TD
.2547 Tc
[(N)288.7(A)254.7(Sa)254.7(sS)254.7(D)294.7(A)254.7(R)313.7(T)254.7(S[)]TJ
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7.631 0 TD
0 Tc
(8)Tj
/Cs8 cs 1 scn
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[(].)-332(When)-254(conducting)-255(the)-254(T)78(aylor)-254(e)15(xpan-)]TJ
9.4925 0 0 9.6862 48.7217 333.9063 Tm
[(sion,)-252.1(the)-251(loss)-251(function)-251.1(for)-251(the)-251(architecture)-251.1(parameters)-251.1(update)]TJ
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9.6862 0 0 9.6862 48.7217 322.2833 Tm
(E)Tj
/F10 1 Tf
6.7803 0 0 6.7803 55.1794 320.5342 Tm
(q)Tj
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4.8431 0 0 4.8431 58.7291 319.5653 Tm
(t)Tj
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6.7803 0 0 6.7803 61.9434 320.5342 Tm
(\()Tj
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<03>Tj
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4.8431 0 0 4.8431 70.0063 319.5063 Tm
<02>Tj
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6.7803 0 0 6.7803 73.9381 320.5342 Tm
(\))Tj
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9.6862 0 0 9.6862 79.0639 330.1283 Tm
(\n)Tj
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Tj
/F9 1 Tf
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<04>Tj
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(\()Tj
/F9 1 Tf
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<02>Tj
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6.7803 0 0 6.7803 97.0983 320.8303 Tm
<02>Tj
/F16 1 Tf
9.6862 0 0 9.6862 101.4812 322.2833 Tm
(\))Tj
/F15 1 Tf
.3889 .8099 TD
<0b>Tj
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[(could)-250.1(be)-250(described)-250(as:)]TJ
/F20 1 Tf
8.6665 0 0 8.6665 64.6154 298.9133 Tm
(E)Tj
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6.0666 0 0 6.0666 70.3933 297.3482 Tm
(q)Tj
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4.3333 0 0 4.3333 73.5694 296.4812 Tm
(t)Tj
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6.0666 0 0 6.0666 76.4453 297.3482 Tm
(\()Tj
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<03>Tj
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4.3333 0 0 4.3333 83.6595 296.4283 Tm
<02>Tj
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6.0666 0 0 6.0666 87.1774 297.3482 Tm
(\))Tj
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8.6665 0 0 8.6665 91.7636 305.9333 Tm
(\n)Tj
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Tj
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<04>Tj
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(\()Tj
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<02>Tj
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6.0666 0 0 6.0666 107.8992 297.6133 Tm
<02>Tj
/F16 1 Tf
8.6665 0 0 8.6665 111.8212 298.9133 Tm
(\))Tj
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.3889 .81 TD
<0b>Tj
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-6.6136 -2.31 TD
(=)Tj
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(E)Tj
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6.0666 0 0 6.0666 70.3934 284.3482 Tm
(q)Tj
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(\()Tj
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<03>Tj
/F13 1 Tf
4.3333 0 0 4.3333 81.0011 283.4282 Tm
<02>Tj
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6.0666 0 0 6.0666 84.519 284.3482 Tm
(|)Tj
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Tj
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1.7318 0 TD
0 Tc
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8.6665 0 0 8.6665 100.2252 285.9133 Tm
(L)Tj
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6.0666 0 0 6.0666 106.2022 284.6132 Tm
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[(va)35.7(l)]TJ
/F16 1 Tf
8.6665 0 0 8.6665 116.3062 285.9133 Tm
0 Tc
(\()Tj
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.3889 0 TD
.0279 Tc
[(w,)-139.9<02>]TJ
/F10 1 Tf
6.0666 0 0 6.0666 135.5103 284.6132 Tm
0 Tc
<02>Tj
/F16 1 Tf
8.6665 0 0 8.6665 139.4313 285.9133 Tm
.2789 Tc
(\)=)Tj
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1.7223 0 TD
0 Tc
(E)Tj
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6.0666 0 0 6.0666 160.1343 284.3482 Tm
<06>Tj
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<044e>Tj
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1.9787 0 TD
.0004 Tc
(\(0)Tj
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1.0159 0 TD
<2c04>Tj
/F21 1 Tf
4.3333 0 0 4.3333 187.4824 286.0822 Tm
0 Tc
(2)Tj
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6.0666 0 0 6.0666 190.8654 284.3482 Tm
(\))Tj
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8.6665 0 0 8.6665 194.0064 285.9133 Tm
(L)Tj
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6.0666 0 0 6.0666 199.9844 284.6132 Tm
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[(va)35.7(l)]TJ
/F16 1 Tf
8.6665 0 0 8.6665 210.0874 285.9133 Tm
0 Tc
(\()Tj
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.389 0 TD
.0279 Tc
[(w,)-139.9]TJ
/F16 1 Tf
2.012 0 TD
0 Tc
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1.0001 0 TD
<10>Tj
/F16 1 Tf
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(\))Tj
-21.3701 -2.081 TD
(=)Tj
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(E)Tj
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6.0666 0 0 6.0666 70.3934 266.3142 Tm
<06>Tj
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<044e>Tj
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1.9788 0 TD
.0004 Tc
(\(0)Tj
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1.016 0 TD
<2c04>Tj
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4.3333 0 0 4.3333 97.7416 268.0471 Tm
0 Tc
(2)Tj
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6.0666 0 0 6.0666 101.1242 266.3142 Tm
(\))Tj
/F16 1 Tf
8.6665 0 0 8.6665 104.2652 267.8782 Tm
([)Tj
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(L)Tj
/F10 1 Tf
6.0666 0 0 6.0666 112.6502 266.5782 Tm
.0364 Tc
[(va)35.7(l)]TJ
/F16 1 Tf
8.6665 0 0 8.6665 122.7542 267.8782 Tm
0 Tc
(\()Tj
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.3889 0 TD
.0279 Tc
[(w,)-139.9]TJ
/F16 1 Tf
1.7899 0 TD
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(\)+)Tj
/F17 1 Tf
1.611 0 TD
0 Tc
<02>Tj
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6.0666 0 0 6.0666 161.8583 266.5782 Tm
Tj
/F8 1 Tf
8.6665 0 0 8.6665 166.5053 267.8782 Tm
(L)Tj
/F10 1 Tf
6.0666 0 0 6.0666 172.4823 266.5782 Tm
.0364 Tc
[(va)35.7(l)]TJ
/F16 1 Tf
8.6665 0 0 8.6665 182.5863 267.8782 Tm
0 Tc
(\()Tj
/F9 1 Tf
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.0279 Tc
[(w,)-139.9]TJ
/F16 1 Tf
1.7899 0 TD
0 Tc
(\))Tj
/F10 1 Tf
6.0666 0 0 6.0666 204.8384 271.4572 Tm
(T)Tj
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8.6665 0 0 8.6665 210.2984 267.8782 Tm
<10>Tj
/F16 1 Tf
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1.1201 .6765 TD
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ET
.346 w
q 1 0 0 1 225.448 270.045 cm 0 0 m
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S
Q
BT
8.6665 0 0 8.6665 225.4484 261.9342 Tm
(2)Tj
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.62 .686 TD
<10>Tj
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6.0666 0 0 6.0666 234.3394 271.4572 Tm
(T)Tj
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8.6665 0 0 8.6665 239.7995 267.8792 Tm
(H)Tj
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(])Tj
-22.2517 -2.536 TD
(=)Tj
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<2c04>Tj
/F21 1 Tf
4.3333 0 0 4.3333 97.7416 246.0692 Tm
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6.0666 0 0 6.0666 101.1242 244.3361 Tm
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/F15 1 Tf
8.6665 0 0 8.6665 105.7102 258.1201 Tm
<06>Tj
/F8 1 Tf
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(L)Tj
/F10 1 Tf
6.0666 0 0 6.0666 116.2612 244.6001 Tm
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[(va)35.7(l)]TJ
/F16 1 Tf
8.6665 0 0 8.6665 126.3652 245.9011 Tm
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[(w,)-139.9]TJ
/F16 1 Tf
1.7899 0 TD
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1.731 .6764 TD
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(1)Tj
ET
q 1 0 0 1 160.249 248.067 cm 0 0 m
4.333 0 l
S
Q
BT
8.6665 0 0 8.6665 160.2493 239.9561 Tm
(2)Tj
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(T)Tj
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8.6665 0 0 8.6665 174.6003 245.9011 Tm
(H)Tj
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(=)Tj
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(L)Tj
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6.0666 0 0 6.0666 70.5934 219.9831 Tm
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[(va)35.7(l)]TJ
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[(w,)-139.9]TJ
/F16 1 Tf
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(\)+)Tj
/F9 1 Tf
1.7311 .6765 TD
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6.0666 0 0 6.0666 119.8452 230.2911 Tm
(2)Tj
ET
q 1 0 0 1 114.581 223.449 cm 0 0 m
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Q
BT
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8.6665 0 0 8.6665 116.9902 215.3381 Tm
(2)Tj
/F2 1 Tf
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(Tr)Tj
/F8 1 Tf
1.0757 0 TD
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[({H)-10.5(})]TJ
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(,)Tj
/F2 1 Tf
9.6862 0 0 9.6862 262.2795 258.6422 Tm
(\(19\))Tj
9.8799 0 0 9.6862 48.3727 196.173 Tm
[(where)-959.9(the)-960(line)-959.9(4)-960(i)0(n)-960(Eq.)]TJ
9.6862 0 0 9.6862 172.9043 196.173 Tm
(\()Tj
0 .99399 1 0 k
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(19)Tj
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9.8799 0 0 9.6862 198.5274 196.173 Tm
[(is)-960(obtained)-960(since)]TJ
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6.7803 0 0 6.7803 55.1794 182.801 Tm
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4.8431 0 0 4.8431 85.7443 184.738 Tm
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6.7803 0 0 6.7803 89.5254 182.801 Tm
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Tj
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9.6862 0 0 9.6862 107.9162 184.55 Tm
(L)Tj
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6.7803 0 0 6.7803 114.5982 183.097 Tm
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[(va)35.7(l)]TJ
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[(w,)-139.9<02>]TJ
/F10 1 Tf
6.7803 0 0 6.7803 147.3533 183.097 Tm
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6.7803 0 0 6.7803 155.5023 188.064 Tm
(T)Tj
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9.6862 0 0 9.6862 161.6043 184.55 Tm
<10>Tj
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(E)Tj
/F10 1 Tf
6.7803 0 0 6.7803 218.1434 182.801 Tm
<06>Tj
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<2c04>Tj
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4.8431 0 0 4.8431 248.7085 184.738 Tm
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6.7803 0 0 6.7803 252.4895 182.801 Tm
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9.6862 0 0 9.6862 256.0005 184.55 Tm
([)Tj
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(\t)Tj
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<02>Tj
/F10 1 Tf
6.7803 0 0 6.7803 55.7171 171.473 Tm
Tj
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9.6862 0 0 9.6862 60.9109 172.926 Tm
(L)Tj
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6.7803 0 0 6.7803 67.5923 171.473 Tm
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[(va)35.7(l)]TJ
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[(w,)-139.9<02>]TJ
/F10 1 Tf
6.7803 0 0 6.7803 100.3472 171.473 Tm
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9.6862 0 0 9.6862 104.7302 172.926 Tm
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(\)=0)Tj
/F2 1 Tf
9.8799 0 0 9.6862 134.7493 172.926 Tm
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[(,a)535(s)]TJ
/F9 1 Tf
9.6862 0 0 9.6862 155.4523 172.926 Tm
0 Tc
<10>Tj
/F8 1 Tf
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<064e>Tj
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/F9 1 Tf
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<2c07>Tj
/F18 1 Tf
6.7803 0 0 6.7803 208.9644 176.441 Tm
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9.6862 0 0 9.6862 213.3104 172.926 Tm
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/F2 1 Tf
9.8799 0 0 9.6862 221.7914 172.926 Tm
[(is)-477(a)-477(Gaussian)]TJ
-17.5173 -1.2 TD
[(distrib)20.1(ution)-384.9(with)-384.9(zero)-384.9(mean,)-420(and)]TJ
/F20 1 Tf
9.6862 0 0 9.6862 186.1624 161.303 Tm
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(2)Tj
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<07>Tj
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6.7803 0 0 6.7803 232.3474 164.818 Tm
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9.8799 0 0 9.6862 236.6925 161.303 Tm
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Tj
/F2 1 Tf
9.8799 0 0 9.6862 255.9505 161.303 Tm
[(is)-385(the)]TJ
-20.9747 -1.2 TD
[(e)15(xpectation)-474(parameter)-473(of)]TJ
/F9 1 Tf
9.6862 0 0 9.6862 155.8853 149.68 Tm
(q)Tj
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<02>Tj
/F10 1 Tf
6.7803 0 0 6.7803 170.5213 148.226 Tm
<02>Tj
/F8 1 Tf
9.6862 0 0 9.6862 181.7723 149.68 Tm
(|)Tj
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[-167.2<07>]TJ
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6.7803 0 0 6.7803 207.3564 153.1939 Tm
0 Tc
(2)Tj
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9.6862 0 0 9.6862 211.7014 149.68 Tm
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9.8799 0 0 9.6862 215.4674 149.68 Tm
[(,)-531(and)]TJ
/F8 1 Tf
9.6862 0 0 9.6862 242.1245 149.68 Tm
(H)Tj
/F2 1 Tf
9.8799 0 0 9.6862 255.0765 149.68 Tm
[(is)-473(the)]TJ
9.5506 0 0 9.6862 48.7217 138.055 Tm
[(Hessian)-253(matrix)-254(of)]TJ
/F8 1 Tf
9.6862 0 0 9.6862 119.1152 138.055 Tm
(L)Tj
/F10 1 Tf
6.7803 0 0 6.7803 125.7952 136.603 Tm
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[(va)35.7(l)]TJ
/F16 1 Tf
9.6862 0 0 9.6862 137.0883 138.055 Tm
0 Tc
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[(w,)-139.9]TJ
/F16 1 Tf
1.79 0 TD
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9.5506 0 0 9.6862 161.9583 138.055 Tm
[(.)-314(W)81(e)-254(can)-253<936e64>-254(the)-253(loss)-254(function)]TJ
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[(that)-343.9(could)-343.9(implicitly)-343.9(control)-343.8(the)-344(trace)-343.9(norm)-343.9(of)]TJ
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(H)Tj
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9.8799 0 0 9.6862 251.1355 126.4319 Tm
(similar)Tj
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[(as)-250([)]TJ
.62765 0 1 0 k
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(8)Tj
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(9)Tj
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(stabilizing)Tj
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[(dif)25(ferentiable)-249.9(N)35(AS.)]TJ
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10.6548 0 0 10.6548 300.2936 726.394 Tm
[(3.3.)-250(Ar)18(chitectur)18(e)-250(Selecting)-250(fr)18(om)-250(the)-250(Distrib)20(ution)]TJ
/F2 1 Tf
9.8799 0 0 9.6862 311.9166 708.2581 Tm
[(After)-280.9(the)-279.9(optimization)-280.8(of)-281(BaLeN)35(AS,)-281(we)-281(learns)-280(an)-281(opti-)]TJ
9.6959 0 0 9.6862 300.2936 696.634 Tm
[(mized)-249.1(Gaussian)-249.1(distrib)19.9(ution)-248(for)-249.1(the)-249(architecture)-249.2(parameters)]TJ
/F9 1 Tf
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(q)Tj
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<02>Tj
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-.0053 -.9231 TD
<02>Tj
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(|)Tj
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[-167.2<07>]TJ
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0 Tc
(2)Tj
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9.8799 0 0 9.6862 355.5587 685.011 Tm
[(,)-379(which)-353(is)-353(used)-352(to)-353(get)-353(the)-353(optimal)-353(architec-)]TJ
-5.5937 -1.2 TD
(ture)Tj
/F9 1 Tf
9.6862 0 0 9.6862 319.4566 673.388 Tm
<02>Tj
/F11 1 Tf
6.7803 0 0 6.7803 325.6886 676.902 Tm
<02>Tj
/F2 1 Tf
9.8799 0 0 9.6862 330.1416 673.388 Tm
[(.)-723(I)0(n)-384(this)-385(paper)39(,)-419(w)0(e)-385(consider)-384(tw)9(o)-384(methods)-385(to)-385(get)]TJ
-3.0211 -1.2002 TD
[(the)-293(discrete)-293.9(architecture)]TJ
/F9 1 Tf
9.6862 0 0 9.6862 398.4188 661.7629 Tm
<02>Tj
/F11 1 Tf
6.7803 0 0 6.7803 404.6518 665.279 Tm
<02>Tj
/F2 1 Tf
9.8799 0 0 9.6862 409.1038 661.7629 Tm
[(.)-449(The)-293<93727374>-293(one)-293(is)-294(a)-293(simple)-293(and)]TJ
-11.0133 -1.2 TD
[(direct)-316.9(method,)-335.8(which)-318(utilizes)-316.9(the)-318(e)15(xpectation)-317(of)]TJ
/F9 1 Tf
9.6862 0 0 9.6862 495.431 650.14 Tm
<02>Tj
/F11 1 Tf
6.7803 0 0 6.7803 501.663 653.6559 Tm
<02>Tj
/F10 1 Tf
-.0053 -.9231 TD
<02>Tj
/F2 1 Tf
9.8799 0 0 9.6862 509.253 650.14 Tm
[(to)-317(se-)]TJ
-21.1499 -1.2 TD
[(lect)-328.9(the)-328(best)-328.9(operation)-327.9(for)-328.9(each)-327.9(edge)-329(through)-327.9(the)]TJ
/F7 1 Tf
20.2299 0 TD
[(ar)36(gmax)]TJ
/F2 1 Tf
9.8412 0 0 9.6862 300.2936 626.8929 Tm
[(as)-245(D)39(A)0(R)59(TS,)-245(where)-245(the)-245(e)15(xpectation)-246(term)-245(is)-245(simply)-245(the)-245(mean)]TJ
/F9 1 Tf
9.6862 0 0 9.6862 300.2936 615.2699 Tm
Tj
/F2 1 Tf
9.8799 0 0 9.6862 308.9686 615.2699 Tm
([)Tj
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(9)Tj
/Cs8 cs 1 scn
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[(].)-431(Ho)25(we)24(v)15(e)0(r)39(,)-298(as)-287(we)-288(described)-287(in)-287(Sec.)]TJ
0 .99399 1 0 k
15.007 0 TD
(2.1)Tj
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1.2499 0 TD
[(,)-298(this)-288(method)]TJ
9.7153 0 0 9.6862 300.2936 603.6469 Tm
[(may)-249.9(result)-249.9(in)-250(instability)-250(and)-251(incongruence.)-311(The)-251(second)-250(one)]TJ
9.6765 0 0 9.6862 300.2936 592.0228 Tm
[(is)-250(more)-251(general,)-251(which)-250(samples)-251(a)-250(set)-251(of)]TJ
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<02>Tj
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9.6765 0 0 9.6862 463.5129 592.0228 Tm
[(from)-251(the)-249.9(distrib)19.9(u-)]TJ
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(tion)Tj
/F9 1 Tf
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(q)Tj
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<02>Tj
/F11 1 Tf
6.7803 0 0 6.7803 331.9826 583.9148 Tm
<02>Tj
/F10 1 Tf
-.0053 -.923 TD
<02>Tj
/F8 1 Tf
9.6862 0 0 9.6862 339.1257 580.3988 Tm
(|)Tj
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.0006 Tc
[-167.2<07>]TJ
/F18 1 Tf
6.7803 0 0 6.7803 360.5317 583.9148 Tm
0 Tc
(2)Tj
/F16 1 Tf
9.6862 0 0 9.6862 364.8767 580.3988 Tm
(\))Tj
/F2 1 Tf
9.4925 0 0 9.6862 370.8927 580.3988 Tm
[(for)-237(architecture)-237.1(selection.)-310.1(Ho)26(we)25(v)15(e)0(r)41(,)-240(in)-237(the)]TJ
9.8315 0 0 9.6862 300.2936 568.7758 Tm
[(neural)-246.9(architecture)-245.8(search,)-246.9(e)25(v)24(aluating)-246(a)-247(set)-247(of)-246(architectures)]TJ
9.8799 0 0 9.6862 299.9446 557.1528 Tm
[(will)-272.9(incur)-273.9(unaf)25(fordable)-272.9(computational)-273.7(costs.)-389(In)-273(this)-274(paper)39(,)]TJ
.0353 -1.2001 TD
[(instead)-303.9(of)-304(utilizing)-303(training-free)-304(proxies)-304(to)-304(assist)-304(N)35(A)0(S)-304(b)0(y)]TJ
/F7 1 Tf
9.7443 0 0 9.6862 300.2936 533.9057 Tm
(warmup)Tj
/F2 1 Tf
3.5255 0 TD
[(before)-248.1(search)-247(as)-248([)]TJ
.62765 0 1 0 k
7.017 0 TD
(1)Tj
/Cs8 cs 1 scn
.5 0 TD
[(],)-248(we)-247(le)25(v)14(erage)-247(these)-248(proxies,)-248(in-)]TJ
9.8218 0 0 9.6862 300.2936 522.2817 Tm
[(cluding)-247(SNIP)-246([)]TJ
.62765 0 1 0 k
5.9929 0 TD
(24)Tj
/Cs8 cs 1 scn
1 0 TD
[(],)-247(GraSP)-246([)]TJ
.62765 0 1 0 k
4.02 0 TD
(43)Tj
/Cs8 cs 1 scn
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[(],)-247(and)-246(Syn\224o)24(w)-246([)]TJ
.62765 0 1 0 k
6.409 0 TD
(42)Tj
/Cs8 cs 1 scn
1 0 TD
[(],)-247(to)-246(score)]TJ
9.6862 0 0 9.6862 300.2936 510.6577 Tm
[(the)-250(sampled)-249.9(architectures)-250(for)-249.9(selection)-250(after)-250(search.)]TJ
9.4925 0 0 9.6862 311.9166 498.3336 Tm
(Algorithm)Tj
0 .99399 1 0 k
4.419 0 TD
(1)Tj
/Cs8 cs 1 scn
.751 0 TD
[(gi)25(v)16(e)0(s)-252(a)-252(simple)-251(implementation)-252(of)-251(BaLeN)35(AS,)]TJ
9.5506 0 0 9.6862 299.9446 486.7106 Tm
[(where)-253.9(only)-253.1(the)-253.9(red)-254(part)-252.9(is)-254(dif)25(ferent)-254(from)-253(D)40(A)0(R)61(TS.)-253(As)-254(sho)25(wn,)]TJ
9.7637 0 0 9.6862 300.2936 475.0866 Tm
[(in)-247(our)-247(BaLeN)35(AS,)-247(only)-247(architecture)-247(parameter)-247(optimization)]TJ
0 -1.2001 TD
[(is)-247(dif)25(ferent)-248(from)-247(D)40(A)0(R)59(T)0(S)-247(which)-247(uses)-248(the)-247(V)134(Adam)-247(optimizer)40(,)]TJ
9.4925 0 0 9.6862 300.2936 451.8395 Tm
[(making)-205(it)-205(easy)-205(to)-206(be)-205(implemented)-205(and)-205(also)-205(easy)-205(to)-205(be)-206(adapted)]TJ
9.754 0 0 9.6862 300.2936 440.2165 Tm
[(to)-248(other)-248(e)15(xisting)-248(dif)25(ferentiable)-248(N)35(A)0(S)-248(methods)-248(with)-248(minimal)]TJ
9.6862 0 0 9.6862 300.2936 428.5925 Tm
(modi\223cations.)Tj
/F1 1 Tf
11.6235 0 0 11.6235 300.2936 403.2415 Tm
[(4.)-250(Experiments)-250(and)-250(Results)]TJ
/F2 1 Tf
9.6959 0 0 9.6862 311.9166 384.1364 Tm
[(In)-249(this)-250(section,)-249(we)-250(consider)-249(three)-249(dif)25(ferent)-250(search)-249(spaces)]TJ
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f
Q
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0 0 l
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f
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f
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f
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f
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f
Q
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f
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f
Q
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0 0 l
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S
Q
BT
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ET
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Q
BT
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ET
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S
Q
BT
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S
Q
BT
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BT
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ET
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Q
BT
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ET
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S
Q
BT
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ET
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S
Q
BT
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ET
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Q
BT
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BT
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(28)Tj
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ET
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Q
BT
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Tj
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(0.08)Tj
ET
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Q
BT
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ET
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S
Q
BT
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ET
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S
Q
BT
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ET
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S
Q
BT
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ET
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S
Q
BT
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ET
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Q
BT
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ET
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Q
BT
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(46)Tj
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S
Q
BT
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Tj
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ET
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Q
BT
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ET
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S
Q
BT
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ET
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S
Q
BT
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ET
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S
Q
BT
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ET
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S
Q
BT
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ET
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Q
BT
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BT
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Q
BT
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Tj
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ET
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BT
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ET
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S
Q
BT
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ET
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S
Q
BT
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ET
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Q
BT
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S
Q
BT
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ET
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Q
BT
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Q
BT
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ET
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Q
BT
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ET
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Q
BT
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ET
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Q
BT
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ET
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Q
BT
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ET
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Q
BT
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ET
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Q
BT
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ET
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Q
BT
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Q
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Q
BT
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ET
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Q
BT
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ET
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S
Q
BT
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ET
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Q
BT
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ET
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Q
BT
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ET
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Q
BT
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ET
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Tj
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(0.07)Tj
ET
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ET
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Q
BT
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ET
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ET
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Tj
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ET
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BT
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ET
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ET
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ET
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Tj
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ET
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ET
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ET
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Tj
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Tj
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(0.07)Tj
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ET
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Q
BT
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[(25.0)-250(/)-250(7.7)]TJ
ET
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S
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BT
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ET
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BT
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ET
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Q
BT
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ET
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BT
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ET
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[(mad)-253(Emtiyaz)-253.1(Khan.)-378.1(T)34(raining)-253(binary)-253(neural)-253(netw)10(orks)-253(using)]TJ
8.6479 0 0 8.7176 68.0881 576.0908 Tm
[(the)-253(bayesian)-253(learning)-252(rule.)]TJ
/F7 1 Tf
10.9249 0 TD
[(arXiv)-252(pr)37(eprint)-253(arXiv:2002.10778)]TJ
/F2 1 Tf
13.2725 0 TD
(,)Tj
8.7176 0 0 8.7176 68.0881 565.4358 Tm
(2020.)Tj
0 .99399 1 0 k
2.61 0 TD
(2)Tj
/Cs8 cs 1 scn
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([34])Tj
8.7787 0 0 8.7176 68.0881 554.4968 Tm
[(Ni)25(v)-247(Nayman,)-247(Asaf)-246(No)10(y)64(,)-247(T)80(a)0(l)-247(Ridnik,)-247(Itamar)-246(Friedman,)-247(Rong)]TJ
8.892 0 0 8.7176 67.9228 543.8417 Tm
[(Jin,)-251.1(and)-249(Lihi)-249.1(Zelnik.)-367.1(Xnas:)-313.1(Neural)-250.1(architecture)-250(search)-249.2(with)]TJ
8.5433 0 0 8.7176 68.0881 533.1877 Tm
[(e)15(xpert)-254(advice.)-367(In)]TJ
/F7 1 Tf
7.0522 0 TD
[(Advances)-254.8(in)-254(Neur)15(al)-254(Information)-255(Pr)46(ocessing)]TJ
8.7176 0 0 8.7176 67.8703 522.5327 Tm
(Systems)Tj
/F2 1 Tf
3.1659 0 TD
[(,)-250(pages)-250(1975\2051985,)-250(2019.)]TJ
0 .99399 1 0 k
10.637 0 TD
(12)Tj
/Cs8 cs 1 scn
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([35])Tj
8.8484 0 0 8.7176 68.0881 511.5937 Tm
[(Kazuki)-245.9(Osa)15.1(w)10(a)0(,)-246(Siddharth)-246(Sw)10(aroop,)-246(Mohammad)-246(Emtiyaz)-245(E)]TJ
8.892 0 0 8.7176 68.0881 500.9387 Tm
[(Khan,)-269.1(Anirudh)-264.1(Jain,)-270.1(Runa)-264.1(Eschenhagen,)-269.2(Richard)-264.1(E)-265(T)44(urner)40(,)]TJ
8.5694 0 0 8.7176 68.0881 490.2846 Tm
[(and)-254(Rio)-254(Y)112(o)0(k)10(ota.)-366(Practical)-254(deep)-255(learning)-254(with)-254(bayesian)-254(princi-)]TJ
8.7874 0 0 8.7176 68.0881 479.6296 Tm
[(ples.)-357(In)]TJ
/F7 1 Tf
3.2984 0 TD
[(Advances)-248(in)-247(neur)14(al)-247(information)-248(pr)45(ocessing)-248(systems)]TJ
/F2 1 Tf
20.5109 0 TD
(,)Tj
8.7176 0 0 8.7176 68.0881 468.9746 Tm
[(pages)-250(4287\2054299,)-250(2019.)]TJ
0 .99399 1 0 k
10.137 0 TD
(2)Tj
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(,)Tj
0 .99399 1 0 k
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(4)Tj
/Cs8 cs 1 scn
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([36])Tj
8.892 0 0 8.7176 68.0881 458.0356 Tm
[(Hieu)-265.1(Pham,)-270.1(Melody)-265.2(Guan,)-270(Barret)-265.2(Zoph,)-271(Quoc)-265.1(Le,)-270.1(and)-265(Jef)24.9(f)]TJ
8.5956 0 0 8.7176 68.0881 447.3806 Tm
[(Dean.)-364.9(Ef)25(\223cient)-254(neural)-254(architecture)-253(search)-254(via)-254(parameter)-254(shar)20(-)]TJ
8.5433 0 0 8.7176 68.0881 436.7256 Tm
[(ing.)-321.9(In)]TJ
/F7 1 Tf
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[(International)-233.7(Confer)38.1(ence)-233.9(on)-234(Mac)15(hine)-234(Learning)]TJ
/F2 1 Tf
18.937 0 TD
[(,)-238(pages)]TJ
8.7176 0 0 8.7176 67.7828 426.0705 Tm
[(4092\2054101,)-250(2018.)]TJ
0 .99399 1 0 k
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(,)Tj
0 .99399 1 0 k
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(2)Tj
/Cs8 cs 1 scn
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([37])Tj
8.7787 0 0 8.7176 68.0881 415.1315 Tm
-.0001 Tc
[(Esteban)-247(Real,)-247.1(Alok)-247(Aggarw)9.9(al,)-247.1(Y)99.9(anping)-247.1(Huang,)-247.1(and)-247.1(Quoc)-247.1(V)]TJ
8.892 0 0 8.7176 68.0881 404.4774 Tm
0 Tc
[(Le.)-483(Re)14(gularized)-286(e)25(v)20(olution)-286(for)-286(image)-286(classi\223er)-286(architecture)]TJ
8.7176 0 0 8.7176 68.0881 393.8224 Tm
(search.)Tj
/F7 1 Tf
3.1639 0 TD
(AAAI)Tj
/F2 1 Tf
2.1661 0 TD
[(,)-250(2019.)]TJ
0 .99399 1 0 k
3.11 0 TD
(1)Tj
/Cs8 cs 1 scn
-10.6615 -1.2547 TD
([38])Tj
8.892 0 0 8.7176 68.0881 382.8844 Tm
[(Pengzhen)-316.2(Ren,)-333.1(Y)108(u)0(n)-316(Xiao,)-334(Xiaojun)-316(Chang,)-334(Po-Y)99(ao)-316(Huang,)]TJ
8.5869 0 0 8.7176 68.0881 372.2294 Tm
[(Zhihui)-254(Li,)-255(Xiaojiang)-254.1(Chen,)-254(and)-255.1(Xin)-254(W)81(ang.)-367(A)-254(comprehensi)25(v)16(e)]TJ
8.5433 0 0 8.7176 68.0881 361.5744 Tm
[(surv)15.1(e)16(y)-207(of)-206(neural)-206(architecture)-206(search:)-292(Challenges)-206(and)-206(solutions.)]TJ
/F7 1 Tf
8.7176 0 0 8.7176 68.0881 350.9194 Tm
[(arXiv)-250(pr)37(eprint)-250(arXiv:2006.02903)]TJ
/F2 1 Tf
13.2678 0 TD
[(,)-250(2020.)]TJ
0 .99399 1 0 k
3.11 0 TD
(1)Tj
/Cs8 cs 1 scn
-18.5994 -1.2548 TD
([39])Tj
8.892 0 0 8.7176 68.0881 339.9803 Tm
[(Y)98(a)0(o)-281(Shu,)-291(W)79(e)0(i)-282(W)79(ang,)-291(and)-281(Shaofeng)-282(Cai.)-469(Understanding)-281(ar)19(-)]TJ
8.6217 0 0 8.7176 68.0881 329.3253 Tm
[(chitectures)-252.1(learnt)-252(by)-253(cell-based)-252(neural)-252(architecture)-252(search.)-363(In)]TJ
/F7 1 Tf
8.5869 0 0 8.7176 67.9403 318.6703 Tm
[(International)-253.1(Confer)38(ence)-253.1(on)-254(Learning)-253(Repr)38(esentations)]TJ
/F2 1 Tf
21.9359 0 TD
[(,)-253(2020.)]TJ
8.7176 0 0 8.7176 68.0881 308.0153 Tm
0 .99399 1 0 k
(2)Tj
/Cs8 cs 1 scn
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(,)Tj
0 .99399 1 0 k
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(4)Tj
/Cs8 cs 1 scn
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(,)Tj
0 .99399 1 0 k
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(8)Tj
/Cs8 cs 1 scn
-4.2215 -1.2548 TD
([40])Tj
8.892 0 0 8.7176 68.0881 297.0763 Tm
[(Julien)-368.1(Siems,)-398.1(Lucas)-368.1(Zimmer)38.8(,)-398(Arber)-368(Zela,)-398(Jo)14(vita)-367(Lukasik,)]TJ
0 -1.2222 TD
[(Mar)17.9(gret)-266(K)24(euper)40(,)-271(and)-266(Frank)-266(Hutter)53(.)-418(Nas-bench-301)-266(and)-266(the)]TJ
8.6915 0 0 8.7176 68.0881 275.7672 Tm
-.0001 Tc
[(case)-250.2(for)-250.1(surrogate)-250.1(benchmarks)-251.3(for)-250.1(neural)-250.2(architecture)-250.2(search.)]TJ
/F7 1 Tf
8.7176 0 0 8.7176 68.0881 265.1132 Tm
0 Tc
[(arXiv)-250(pr)37(eprint)-250(arXiv:2008.09777)]TJ
/F2 1 Tf
13.2678 0 TD
[(,)-250(2020.)]TJ
0 .99399 1 0 k
3.11 0 TD
(11)Tj
/Cs8 cs 1 scn
-18.5994 -1.2548 TD
[([41])-556(Mingxing)-250.1(T)80(a)0(n)-251(and)-251(Quoc)-251(Le.)-362(Ef)25(\223cientnet:)-312(Rethinking)-250(model)]TJ
8.892 0 0 8.7176 68.0881 243.5191 Tm
[(scaling)-260.1(for)-259(con)39(v)20(olutional)-260(neural)-260(netw)10(orks.)-399(In)]TJ
/F7 1 Tf
18.3759 0 TD
(International)Tj
8.5694 0 0 8.7176 67.8003 232.8641 Tm
[(Confer)38(ence)-255(on)-254(Mac)15(hine)-254(Learning)]TJ
/F2 1 Tf
13.4859 0 TD
[(,)-254(pages)-255(6105\2056114,)-254(2019.)]TJ
0 .99399 1 0 k
10.656 0 TD
(1)Tj
8.7176 0 0 8.7176 48.7217 221.9251 Tm
/Cs8 cs 1 scn
([42])Tj
8.6217 0 0 8.7176 68.0881 221.9251 Tm
[(Hidenori)-252.1(T)81(anaka,)-252(Daniel)-252(K)15(unin,)-252(Daniel)-251(L)-252(Y)101(amins,)-252(and)-251(Surya)]TJ
8.7699 0 0 8.7176 68.0881 211.2701 Tm
[(Ganguli.)-357(Pruning)-248(neural)-248(netw)10(orks)-248(without)-248.1(an)15(y)-248(data)-248(by)-248(itera-)]TJ
8.5694 0 0 8.7176 68.0881 200.6151 Tm
[(ti)25(v)16(ely)-254(conserving)-255(synaptic)-254<946f>26(w)66(.)]TJ
/F7 1 Tf
13.0229 0 TD
[(Advances)-254.1(in)-254(Neur)15(al)-254(Informa-)]TJ
8.7176 0 0 8.7176 68.0881 189.96 Tm
[(tion)-250(Pr)45(ocessing)-250(Systems)]TJ
/F2 1 Tf
9.621 0 TD
[(,)-250(33,)-250(2020.)]TJ
0 .99399 1 0 k
4.61 0 TD
(3)Tj
/Cs8 cs 1 scn
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(,)Tj
0 .99399 1 0 k
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(5)Tj
/Cs8 cs 1 scn
-17.4524 -1.2548 TD
([43])Tj
8.8484 0 0 8.7176 68.0881 179.021 Tm
[(Chaoqi)-245(W)79(ang,)-246(Guodong)-245(Zhang,)-246(and)-245(Roger)-245(Grosse.)-352(Picking)]TJ
8.5433 0 0 8.7176 67.774 168.367 Tm
[(winning)-221.9(tick)11.1(ets)-222.1(before)-220.8(training)-221.9(by)-221(preserving)-222(gradient)-221<946f>25(w)67(.)-295(In)]TJ
/F7 1 Tf
8.5869 0 0 8.7176 67.9403 157.712 Tm
[(International)-253.1(Confer)38(ence)-253.1(on)-254(Learning)-253(Repr)38(esentations)]TJ
/F2 1 Tf
21.9359 0 TD
[(,)-253(2020.)]TJ
8.7176 0 0 8.7176 68.0881 147.057 Tm
0 .99399 1 0 k
(3)Tj
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(,)Tj
0 .99399 1 0 k
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(5)Tj
/Cs8 cs 1 scn
-3.2215 -1.2547 TD
([44])Tj
8.5782 0 0 8.7176 68.0881 136.1189 Tm
[(Ruochen)-252.9(W)81(ang,)-254(Minhao)-253(Cheng,)-253(Xiangning)-254(Chen,)-253(Xiaocheng)]TJ
8.8746 0 0 8.7176 67.8178 125.4639 Tm
[(T)79(ang,)-247(and)-247(Cho-Jui)-247(Hsieh.)-357(Rethinking)-246(architecture)-247(selection)]TJ
8.7176 0 0 8.7176 68.0881 114.8089 Tm
[(in)-250(dif)25(ferentiable)-250(nas.)-360(In)]TJ
/F7 1 Tf
9.6658 0 TD
(ICLR)Tj
/F2 1 Tf
2.167 0 TD
[(,)-250(2021.)]TJ
0 .99399 1 0 k
3.11 0 TD
(2)Tj
/Cs8 cs 1 scn
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(,)Tj
0 .99399 1 0 k
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(3)Tj
/Cs8 cs 1 scn
10.6934 70.1548 TD
([45])Tj
8.892 0 0 8.7176 319.6596 726.394 Tm
[(Xinle)-255(W)49(u)0(,)-257(Dalin)-255(Zhang,)-257(Chenjuan)-255(Guo,)-257(Chao)9(yang)-255(He,)-258(Bin)]TJ
8.5433 0 0 8.7176 319.1536 715.7391 Tm
[(Y)102(ang,)-227(and)-221(Christian)-220(S.)-221(Jensen.)-292(Autocts:)-299(Automated)-220(correlated)]TJ
8.6566 0 0 8.7176 319.6596 705.0851 Tm
[(time)-253(series)-252.1(forecasting.)]TJ
/F7 1 Tf
9.6186 0 TD
[(Pr)45(oc.)-252(VLDB)-253(Endow)75(.)]TJ
/F2 1 Tf
8.1073 0 TD
[(,)-253(15\(4\):971\205983,)]TJ
8.7176 0 0 8.7176 319.6596 694.4301 Tm
(2021.)Tj
0 .99399 1 0 k
2.61 0 TD
(1)Tj
/Cs8 cs 1 scn
-4.8315 -1.3538 TD
([46])Tj
8.6828 0 0 8.7176 319.6596 682.628 Tm
[(Sirui)-249.9(Xie,)-251(Hehui)-251(Zheng,)-251(Chunxiao)-251(Liu,)-250(and)-251(Liang)-250(Lin.)-360(Snas:)]TJ
8.7176 0 0 8.7176 319.6596 671.973 Tm
[(stochastic)-250(neural)-249.9(architecture)-250(search.)]TJ
/F7 1 Tf
15.0767 0 TD
(ICLR)Tj
/F2 1 Tf
2.167 0 TD
[(,)-250(2019.)]TJ
0 .99399 1 0 k
3.11 0 TD
(1)Tj
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0 .99399 1 0 k
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(7)Tj
/Cs8 cs 1 scn
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(,)Tj
0 .99399 1 0 k
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(13)Tj
/Cs8 cs 1 scn
-24.5751 -1.3538 TD
([47])Tj
8.6828 0 0 8.7176 319.6596 660.171 Tm
[(Y)111(uhui)-250(Xu,)-251(Lingxi)-250(Xie,)-251(Xiaopeng)-250(Zhang,)-251(Xin)-250(Chen,)-251(Guo-Jun)]TJ
8.892 0 0 8.7176 319.6596 649.5159 Tm
[(Qi,)-393(Qi)-363(T)35(ian,)-393(and)-363(Hongkai)-363(Xiong.)-730(Pc-darts:)-540(P)14(artial)-363(chan-)]TJ
8.7438 0 0 8.7176 319.6596 638.8609 Tm
[(nel)-250(connections)-250.8(for)-249.9(memory-ef)25.3(\223cient)-251(architecture)-249.7(search.)-362.9(In)]TJ
/F7 1 Tf
8.7176 0 0 8.7176 319.5116 628.2059 Tm
(ICLR)Tj
/F2 1 Tf
2.167 0 TD
[(,)-250(2020.)]TJ
0 .99399 1 0 k
3.11 0 TD
(7)Tj
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(,)Tj
0 .99399 1 0 k
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(11)Tj
/Cs8 cs 1 scn
-8.4814 -1.3537 TD
([48])Tj
8.892 0 0 8.7176 319.6596 616.4049 Tm
[(Chris)-318.1(Y)54(ing,)-335(Aaron)-318(Klein,)-336(Eric)-317(Christiansen,)-336(Esteban)-317(Real,)]TJ
8.8571 0 0 8.7176 319.6596 605.7499 Tm
-.0001 Tc
[(K)24.9(e)23.9(vin)-246.1(Murphy)63.9(,)-247.1(and)-247.1(Frank)-246.1(Hutter)53.9(.)-356.1(Nas-bench-101:)-306.1(T)78.9(o)23.9(w)9.9(ards)]TJ
8.5433 0 0 8.7176 319.6596 595.0948 Tm
0 Tc
[(reproducible)-199.7(neural)-199.9(architecture)-198.9(search.)-247.9(In)]TJ
/F7 1 Tf
16.9567 0 TD
(ICML)Tj
/F2 1 Tf
2.3889 0 TD
[(,)-200(pages)-200(7105\205)]TJ
8.7176 0 0 8.7176 319.4416 584.4398 Tm
[(7114,)-250(2019.)]TJ
0 .99399 1 0 k
5.11 0 TD
(5)Tj
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(,)Tj
0 .99399 1 0 k
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(11)Tj
/Cs8 cs 1 scn
-8.3065 -1.3538 TD
([49])Tj
8.6566 0 0 8.7176 319.6596 572.6378 Tm
[(Kaicheng)-251.1(Y)112(u)0(,)-251(Christian)-251(Sciuto,)-252(Martin)-251(Jaggi,)-251(Claudiu)-251(Musat,)]TJ
8.5433 0 0 8.7176 319.6596 561.9828 Tm
[(and)-234(Mathieu)-232.8(Salzmann.)-320.8(Ev)26(aluating)-234(the)-234(search)-234(phase)-234(of)-233(neural)]TJ
8.7176 0 0 8.7176 319.6596 551.3278 Tm
[(architecture)-249.9(search.)-360.1(In)]TJ
/F7 1 Tf
9.2168 0 TD
(ICLR)Tj
/F2 1 Tf
2.167 0 TD
[(,)-250(2020.)]TJ
0 .99399 1 0 k
3.11 0 TD
(1)Tj
/Cs8 cs 1 scn
-16.7153 -1.3538 TD
([50])Tj
8.892 0 0 8.7176 319.6596 539.5257 Tm
[(Arber)-304.1(Zela,)-320(Thomas)-304.2(Elsk)9.9(en,)-319(T)78(onmo)10(y)-305(Saikia,)-319(Y)98(assine)-304(Mar)19(-)]TJ
8.7874 0 0 8.7176 319.6596 528.8717 Tm
[(rakchi,)-249(Thomas)-249.1(Brox,)-250.1(and)-249(Frank)-249(Hutter)55(.)-360(Understanding)-249(and)]TJ
8.5433 0 0 8.7176 319.6596 518.2167 Tm
[(rob)20.1(ustifying)-240.9(dif)26.1(ferentiable)-241(architecture)-241(search.)-337(In)]TJ
/F7 1 Tf
19.8896 0 TD
(ICLR)Tj
/F2 1 Tf
2.1671 0 TD
[(,)-241(2020.)]TJ
8.7176 0 0 8.7176 319.0066 507.5617 Tm
0 .99399 1 0 k
(1)Tj
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(2)Tj
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0 .99399 1 0 k
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(3)Tj
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(,)Tj
0 .99399 1 0 k
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(5)Tj
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0 .99399 1 0 k
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(8)Tj
/Cs8 cs 1 scn
-6.1465 -1.3538 TD
([51])Tj
8.892 0 0 8.7176 319.6596 495.7596 Tm
[(Arber)-391.1(Zela,)-427(Julien)-391.1(Siems,)-427.1(and)-391.1(Frank)-390.1(Hutter)54(.)-820(Nas-bench-)]TJ
8.8135 0 0 8.7176 319.0066 485.1046 Tm
[(1shot1:)-308.9(Benchmarking)-247.9(and)-248.9(dissecting)-247.9(one-shot)-247.9(neural)-249(archi-)]TJ
8.7176 0 0 8.7176 319.6596 474.4496 Tm
[(tecture)-250(search.)-360(In)]TJ
/F7 1 Tf
7.2179 0 TD
(ICLR)Tj
/F2 1 Tf
2.167 0 TD
[(,)-250(2020.)]TJ
0 .99399 1 0 k
3.11 0 TD
(2)Tj
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0 .99399 1 0 k
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(5)Tj
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(,)Tj
0 .99399 1 0 k
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(11)Tj
/Cs8 cs 1 scn
-16.7164 -1.3538 TD
([52])Tj
8.5433 0 0 8.7176 319.6596 462.6476 Tm
[(Miao)-244.9(Zhang,)-246.9(Huiqi)-244.9(Li,)-247(Shirui)-244.9(P)15(an,)-247(Xiaojun)-245(Chang,)-247(Zongyuan)]TJ
8.7438 0 0 8.7176 319.6596 451.9926 Tm
[(Ge,)-248.9(and)-248(Ste)24.1(v)15(e)0(n)-248(Su.)-358(Dif)25(ferentiable)-248(neural)-249(architecture)-249(search)]TJ
8.613 0 0 8.7176 319.6596 441.3385 Tm
[(in)-253(equi)25(v)26(alent)-254(space)-254(with)-253(e)16(xploration)-253(enhancement.)]TJ
/F7 1 Tf
20.5879 0 TD
(Advances)Tj
8.6566 0 0 8.7176 319.6596 430.6835 Tm
[(in)-252(Neur)15(al)-252(Information)-253(Pr)46(ocessing)-252(Systems)]TJ
/F2 1 Tf
16.8924 0 TD
[(,)-252(33:13341\20513351,)]TJ
8.7176 0 0 8.7176 319.6596 420.0285 Tm
(2020.)Tj
0 .99399 1 0 k
2.61 0 TD
(1)Tj
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-4.8315 -1.3538 TD
([53])Tj
8.5433 0 0 8.7176 319.6596 408.2264 Tm
[(Miao)-206.9(Zhang,)-215.9(Huiqi)-206.9(Li,)-216.1(Shirui)-205.9(P)15(an,)-217(Xiaojun)-207(Chang,)-216(and)-207(Ste)25(v)16(e)0(n)]TJ
8.6305 0 0 8.7176 319.6596 397.5714 Tm
[(Su.)-362.9(Ov)15(ercoming)-252(multi-model)-253(for)19(getting)-253(in)-252(one-shot)-252(nas)-253(with)]TJ
8.892 0 0 8.7176 319.6596 386.9164 Tm
[(di)25(v)14(ersity)-336(maximization.)-644(In)]TJ
/F7 1 Tf
11.3585 0 TD
[(Pr)44(oceedings)-336(of)-335(the)-336(IEEE/CVF)]TJ
-11.3909 -1.2222 TD
[(Confer)35.9(ence)-376.1(on)-376(Computer)-376(V)72(ision)-376(and)-376(P)79(attern)-377(Reco)10(gnition)]TJ
/F2 1 Tf
23.5586 0 TD
(,)Tj
8.7176 0 0 8.7176 319.6596 365.6064 Tm
[(pages)-249.9(7809\2057818,)-250.1(2020.)]TJ
0 .99399 1 0 k
10.137 0 TD
(1)Tj
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-12.3585 -1.3538 TD
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