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sXwbvaWWArtificial Intelligence
1
Adam: A Method for Stochastic Optimization
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Adam is a type of computer algorithm used in machine learning, specifically for optimizing complex calculations. In machine learning, optimization helps improve the way models learn from data. Think of it as a smart strategy for a computer to find the best solution in a huge maze of possibilities.When a machine learning model is trained, it uses a process called 'gradient descent' to minimize errors (or, in simpler terms, to get better at its task). Imagine rolling a ball down a hill; gradient descent aims to find the lowest point in the valley – the 'optimal' spot. However, in complex problems, like those with a lot of data or parameters, this process can be like finding the lowest point in a mountain range with many valleys and ridges.Adam stands out because it's like giving the ball a GPS and a memory. It remembers the terrain it has covered (past gradients) and adapts its speed and direction accordingly. This adaptive approach helps it navigate through the complex landscape of data more efficiently.Key advantages of Adam include:Efficiency: It works fast, even with huge amounts of data or parameters.Memory-saving: It doesn't need much computer memory to run.Flexibility: It can handle a wide range of problems, even if the data or the goal keeps changing (non-stationary objectives), or if the information is very noisy or sparse.User-friendly: Its settings (hyper-parameters) are intuitive to understand and don't need much tweaking.Adam also relates to other optimization algorithms and has sound theoretical backing, proving its effectiveness. It's often compared favorably to other methods in practical scenarios. Lastly, there's a variant called AdaMax, which is a bit different and based on another mathematical concept (the infinity norm).In summary, Adam is like a highly skilled guide helping a machine learning model navigate complex terrains, making the training process faster, more efficient, and generally more effective.

Adam+dropoutFigure1:LogisticregressiontrainingnegativeloglikelihoodonMNISTimagesandIMDBmoviereviewswith10,000bag - of - words(BoW)featurevectors.trainingtopreventover - tting.Ingure1,AdagradoutperformsSGDwithNesterovmomentumbyalargemarginbothwithandwithoutdropoutnoise.AdamconvergesasfastasAdagrad.TheempiricalperformanceofAdamisconsistentwithourtheoreticalndingsinsections2and4.Sim - ilartoAdagrad,AdamcantakeadvantageofsparsefeaturesandobtainfasterconvergenceratethannormalSGDwithmomentum.6.2EXPERIMENT:MULTI - LAYERNEURALNETWORKSMulti - layerneuralnetworkarepowerfulmodelswithnon - convexobjectivefunctions.Althoughourconvergenceanalysisdoesnotapplytonon - convexproblems,weempiricallyfoundthatAdamoftenoutperformsothermethodsinsuchcases.Inourexperiments,wemademodelchoicesthatareconsistentwithpreviouspublicationsinthearea;aneuralnetworkmodelwithtwofullyconnectedhiddenlayerswith1000hiddenunitseachandReLUactivationareusedforthisexperimentwithminibatchsizeof128.First,westudydifferentoptimizersusingthestandardde
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Thesum - of - functions(SFO)method(Sohl - Dicksteinetal.,2014)isarecentlyproposedquasi - Newtonmethodthatworkswithminibatchesofdataandhasshowngoodperformanceonoptimizationofmulti - layerneuralnet - works.WeusedtheirimplementationandcomparedwithAdamtotrainsuchmodels.Figure2showsthatAdammakesfasterprogressintermsofboththenumberofiterationsandwall - clocktime.Duetothecostofupdatingcurvatureinformation,SFOis5 - 10xslowerperiterationcom - paredtoAdam,andhasamemoryrequirementthatislinearinthenumberminibatches.Stochasticregularizationmethods,suchasdropout,areaneffectivewaytopreventover - ttingandoftenusedinpracticeduetotheirsimplicity.SFOassumesdeterministicsubfunctions,andindeedfailedtoconvergeoncostfunctionswithstochasticregularization.WecomparetheeffectivenessofAdamtootherstochasticrstordermethodsonmulti - layerneuralnetworkstrainedwithdropoutnoise.Figure2showsourresults;Adamshowsbetterconvergencethanothermethods.6.3EX
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PERIMENT:CONVOLUTIONALNEURALNETWORKSConvolutionalneuralnetworks(CNNs)withseverallayersofconvolution,poolingandnon - linearunitshaveshownconsiderablesuccessincomputervisiontasks.Unlikemostfullyconnectedneuralnets,weightsharinginCNNsresultsinvastlydifferentgradientsindifferentlayers.AsmallerlearningratefortheconvolutionlayersisoftenusedinpracticewhenapplyingSGD.WeshowtheeffectivenessofAdamindeepCNNs.OurCNNarchitecturehasthreealternatingstagesof5x5convolutionltersand3x3maxpoolingwithstrideof2thatarefollowedbyafullyconnectedlayerof1000rectiedlinearhiddenunits(ReLUs).Theinputimagearepre - processedbywhitening,and6
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0.45 0.5 40 40 140 15 5 0.4 20 20 PublishedasaconferencepaperatICLR2015 101 50 RMSProp 45iterations over entire dataset 10-3 AdaDelta AdaGrad+dropout AdaGrad+dropout 10-1 10-1 102 3.0iterations over entire dataset 200iterations over entire dataset Adam Adam Adam(a) 10 3.0training cost SGDNesterov+dropout SGDNesterov+dropout 0 0 30 MNIST Multilayer Neural Network + dropout
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