9_10_convolutional_rbm

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1、NeuralnetworksComputervision-convolutionalRBM2CONVOLUTIONALRBMConvolutionalDeepBeliefNetworksforScalableUnsupervisedLearningofHierarchicalRepresentationsTopics:ConvolutionalDeepBeliefNetworksforScalableUnsupervisedLearningofHierarchicalRepresentationsConvolutionalDeepBeliefNetworksf

2、orScalableUnsupervisedLearningofHierarchicalRepresentations(NWconvolutionalRBM,NVNH+1);thefilterweightsaresharedLeeetal.2009kacrossallthehiddenunitswithinthegroup.Inaddi-NpkP(poolinglayer)Pα•((HowaboutdesigningconvolutionalunsupervisednetworksNNWWtion,eachhiddengrouphasabias,,NNVV

3、NNHH+1);thefilterweightsareshared+1);thefilterweightsaresharedbkandallvisiblekkacrossallthehiddenunitswithinthegroup.Inaddi-acrossallthehiddenunitswithinthegroup.Inaddi-NNppkkPP(poolinglayer)(poolinglayer)unitsshareasinglebiasc.PPααNkktion,eachhiddengrouphasabiastion,eachhiddengroupha

4、sabiasbbandallvisibleandallvisibleHChi,jH(detectionlayer)‣let’sconsiderthecaseoftheRBMkkunitsshareasinglebiasunitsshareasinglebiasWedefinetheenergyfunctioncc..E(v,h)as:NNHkkkkHCChhi,ji,jHH(detectionlayer)(detectionlayer)‣couldusesameconvolutionalconnectivitybetweeninput(1v)andhiddenl

5、ayer(h)WedefinetheenergyfunctionWedefinetheenergyfunctionP(v,h)=exp(EEE(((vvv,,,hhh)))as:)as:WkZ11PP((vv,,hh)=)=exp(exp(XKEE((vXNv,,Hhh))))XNWkWWkkZZkk‣hijarethehiddenunitsofNE(v,h)=hijWrsvi+r1,j+s1NVWvV(visiblelayer)XXKKXNXNHHXNXNWWthekthfeaturemapk=1i,j=1r,s=1EE((vv,,hh)=)=h

6、hkkWWkkvv‣WkNNNNWWvvXKXNHijijrsrsii++rrXNV11,j,j++ss11rsaretheweightstotheVVVV(visiblelayer)(visiblelayer)Figure1.ConvolutionalRBMwithprobabilisticmax-kk=1=1i,ji,j=1=1r,sr,s=1=1kkthfeaturemapbkhijcvij.(1)pooling.Forsimplicity,onlygroupkofthedetectionlayerXXKKk=1XNXNHHi,j=1XNXN

7、VVi,j=1‣WFigure1.~Figure1.karetheweightswithConvolutionalRBMwithprobabilisticmax-ConvolutionalRBMwithprobabilisticmax-kkandthepooinglayerareshown.ThebasicCRBMcorre-bbkkhhijijccvvijij..(1)(1)flippedrowsandcolumnspooling.Forsimplicity,onlygrouppooling.Forsimplicity,onlygroupspondst

8、oasimplifiedstructur