高阶信息如何加速神经网络训练？.pdf

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1、How high-order informationtheneural networkacceleratestraining？Xunpeng HuangBytedance AILab MLNLCNov 2020#page#OutlinePreliminariesAccelerate neural network training with second momentsApproximate Hessian with a low computational complexitySummaryReferences#page#PreliminariesAccelerate neural networ

2、k training with second momentsApproximate Hessian with a low computational complexitySummaryReferences#page#An brieFintroduction to optimizersand theirapplicationsiteration20000：810Figure: Logistic regression and SVM classificationMost optimization problems are solved by different optimizersMany tas

3、ks in CV and NLP can be Formulated as some optimizationproblems.#page#An brieFintroduction to optimizers and their applicationsOptimization problemsStochastic problems:arg minx F(x)= EeF(x,e）Finite sum problems:arg minx F(x)=1/nZiF（x）where x Fx） denote the parameters and the objective Functions.Opti

4、mizersUpdate rulesGDX+1=Xt-VF（x）Newton methodXt+1=xt-2F（xt)F(xtTable: Deterministic optimizersOptimizersUpdate rulesGDXt+1=X-Vf，（Xe）SVRG6xm+1=xcm-7:(Vfam(xm)-VFam(xt,o)+VF（XC,0）Stochastic Newton7-”ia，（xe)/i.（xeXt+1=X-7VTable: Stochastic optimizers#page#High-order optimization in convex settingsCore

5、ProblemWhy can we accelerate the convergence via high-order inFormation？In most First-order optimizers， the step size depends on the gradientLipschitz continuous constant L in the objective Function， which defined as:）（x-y）+L/2.1x-y1VxywehaveF(x）fy）+VFy）0806-0.40.206081122214-0.2-0.4-0.6-0.8#page#Hi

6、gh-order optimization in convex settingsAnswer to the core problemHigh-order information provides adaptive step sizes during iterationsFor GD：Xt+1=X-7:Vf（xe）f（x)+F（xe)（x-x）台Xt+1=argminX+1/（2me)lx-xe|1For Newton method:xt+1=x-2f（x:)fx）xt+1=argminf（xe)+Vf（xe)（x-xe）+（x-x)f（xe)（x-x）#page#PreliminariesAc