I am trying to recreate the results reported in __Reducing the dimensionality of data with neural networks__ of autoencoding the __Olivetti face dataset__ with an adapted version of the MNIST digits __MatLab code__, but am having some difficulty. It seems that no matter how much tweaking I do on the number of epochs, rates, or momentum the stacked RBMs are entering the fine-tuning stage with a large amount of error and consequently fail to improve much at the fine-tuning stage. I am also experiencing a similar problem with another real-valued dataset.

For the first layer, I am using an RBM with a smaller learning rate (as described in the paper) and with:

negdata = poshidstates*vishid' + repmat(visbiases,numcases,1);

I'm fairly confident I am following the instructions found in the __supporting material__ but I cannot achieve the correct errors.

Is there something I am missing? See the code I'm using for real-valued visible unit RBMs below, and for the whole deep training. The rest of the code can be found __here__.

rbmvislinear.m:

epsilonw = 0.001; % Learning rate for weights epsilonvb = 0.001; % Learning rate for biases of visible units epsilonhb = 0.001; % Learning rate for biases of hidden units weightcost = 0.0002; initialmomentum = 0.5; finalmomentum = 0.9; [numcases numdims numbatches]=size(batchdata); if restart ==1, restart=0; epoch=1; % Initializing symmetric weights and biases. vishid = 0.1*randn(numdims, numhid); hidbiases = zeros(1,numhid); visbiases = zeros(1,numdims); poshidprobs = zeros(numcases,numhid); neghidprobs = zeros(numcases,numhid); posprods = zeros(numdims,numhid); negprods = zeros(numdims,numhid); vishidinc = zeros(numdims,numhid); hidbiasinc = zeros(1,numhid); visbiasinc = zeros(1,numdims); sigmainc = zeros(1,numhid); batchposhidprobs=zeros(numcases,numhid,numbatches); end for epoch = epoch:maxepoch, fprintf(1,'epoch %d\r',epoch); errsum=0; for batch = 1:numbatches, if (mod(batch,100)==0) fprintf(1,' %d ',batch); end %%%%%%%%% START POSITIVE PHASE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% data = batchdata(:,:,batch); poshidprobs = 1./(1 + exp(-data*vishid - repmat(hidbiases,numcases,1))); batchposhidprobs(:,:,batch)=poshidprobs; posprods = data' * poshidprobs; poshidact = sum(poshidprobs); posvisact = sum(data); %%%%%%%%% END OF POSITIVE PHASE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% poshidstates = poshidprobs > rand(numcases,numhid); %%%%%%%%% START NEGATIVE PHASE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% negdata = poshidstates*vishid' + repmat(visbiases,numcases,1);% + randn(numcases,numdims) if not using mean neghidprobs = 1./(1 + exp(-negdata*vishid - repmat(hidbiases,numcases,1))); negprods = negdata'*neghidprobs; neghidact = sum(neghidprobs); negvisact = sum(negdata); %%%%%%%%% END OF NEGATIVE PHASE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% err= sum(sum( (data-negdata).^2 )); errsum = err + errsum; if epoch>5, momentum=finalmomentum; else momentum=initialmomentum; end; %%%%%%%%% UPDATE WEIGHTS AND BIASES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% vishidinc = momentum*vishidinc + ... epsilonw*( (posprods-negprods)/numcases - weightcost*vishid); visbiasinc = momentum*visbiasinc + (epsilonvb/numcases)*(posvisact-negvisact); hidbiasinc = momentum*hidbiasinc + (epsilonhb/numcases)*(poshidact-neghidact); vishid = vishid + vishidinc; visbiases = visbiases + visbiasinc; hidbiases = hidbiases + hidbiasinc; %%%%%%%%%%%%%%%% END OF UPDATES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% end fprintf(1, '\nepoch %4i error %f \n', epoch, errsum); end

dofacedeepauto.m:

clear all close all maxepoch=200; %In the Science paper we use maxepoch=50, but it works just fine. numhid=2000; numpen=1000; numpen2=500; numopen=30; fprintf(1,'Pretraining a deep autoencoder. \n'); fprintf(1,'The Science paper used 50 epochs. This uses %3i \n', maxepoch); load fdata %makeFaceData; [numcases numdims numbatches]=size(batchdata); fprintf(1,'Pretraining Layer 1 with RBM: %d-%d \n',numdims,numhid); restart=1; rbmvislinear; hidrecbiases=hidbiases; save mnistvh vishid hidrecbiases visbiases; maxepoch=50; fprintf(1,'\nPretraining Layer 2 with RBM: %d-%d \n',numhid,numpen); batchdata=batchposhidprobs; numhid=numpen; restart=1; rbm; hidpen=vishid; penrecbiases=hidbiases; hidgenbiases=visbiases; save mnisthp hidpen penrecbiases hidgenbiases; fprintf(1,'\nPretraining Layer 3 with RBM: %d-%d \n',numpen,numpen2); batchdata=batchposhidprobs; numhid=numpen2; restart=1; rbm; hidpen2=vishid; penrecbiases2=hidbiases; hidgenbiases2=visbiases; save mnisthp2 hidpen2 penrecbiases2 hidgenbiases2; fprintf(1,'\nPretraining Layer 4 with RBM: %d-%d \n',numpen2,numopen); batchdata=batchposhidprobs; numhid=numopen; restart=1; rbmhidlinear; hidtop=vishid; toprecbiases=hidbiases; topgenbiases=visbiases; save mnistpo hidtop toprecbiases topgenbiases; backpropface;

Thanks for your time