Why is this autoencoder only predicting a single output regardless of input when using min-max scaling?
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Joseph Conroy
on 11 Jul 2024
Answered: Joseph Conroy
on 16 Jul 2024
Key questions:
- Why does a network predict a specific value for the output regardless of input as if the input data had no information relevant to prediction?
- Why does replacing min-max scaling with standard scaling fix this, at least occassionally?
The problem background: I am trying to train a simple image autoencoder, but I keep getting networks that only output a single image regardless of the input. Taking the difference between each output image reveals they are all exactly the same. Googling this issue, I saw a stack overflow post that this often arises with improperly dimensioned loss functions. I also saw folks mentioning issues with using the sigmoid loss function for autoencoders, but the explanations as to why never surpass guesswork. I changed the scaling from min-max scaling to standard scaling and was able to obtain a network that breaks out of the single-prediction behavior, but without understanding why, I will have no recourse but trial-and-error if it breaks again.
Notes on dimensioning loss functions: When calculating the loss between a batch of images of shape [imgDim, imgDim, 1, batchSize] the mse loss function outputs a loss of dimension [1,1,1,batchSize], but this loss function has produced defective results under min-max scaling, such as the aforementioned degeneration to a single output, as well as an initial loss three orders of magnitude above the inputs and outputs scaled to the range [0,1]. To be clear, I don't mean the learning is unstable, I mean that the absolute values of the loss are absurd.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1732728/image.png)
I tried to write my own loss function that reports a scalar value, but I encountered the same degeneration to a single prediction independent of input. I then wrote a version that reports an error tensor of the same shape as @mse, but this threw an error listed below, after the custom loss function in question.
% Version that reports a scalar
function meanAbsErr = myMae(prediction, target)
meanAbsErr = mean(abs(flatten(prediction) - flatten(target)), 'all');
end
% Version that reports [1,1,1,batchSize]
function meanAbsErr = myMae(prediction, target)
inDims = size(prediction);
meanAbsErr = mean(abs(flatten(prediction) - flatten(target)), 1);
outDims = ones(1,length(inDims)); outDims(end) = inDims(end);
meanAbsErr = reshape(meanAbsErr, outDims);
end
Value to differentiate is non-scalar. It must be a traced real dlarray scalar.
Error in mathworksDebug>modelLoss (line 213)
[gradientsE,gradientsD] = dlgradient(loss,netE.Learnables,netD.Learnables);
Error in deep.internal.dlfeval (line 17)
[varargout{1:nargout}] = fun(x{:});
Error in deep.internal.dlfevalWithNestingCheck (line 19)
[varargout{1:nargout}] = deep.internal.dlfeval(fun,varargin{:});
Error in dlfeval (line 31)
[varargout{1:nargout}] = deep.internal.dlfevalWithNestingCheck(fun,varargin{:});
Error in mathworksDebug (line 134)
[loss,gradientsE,gradientsD] = dlfeval(@modelLoss,netE,netD,X,Ztarget);
Notes on scaling
I wrote a custom scaling function that executes the same behavior as rescale except that it reports the obtained extrema to use in scaling and de-scaling unseen data.
% Min-max scaling between [lb, ub]
function [scaled,smin,smax] = myRescale(varargin)
datastruct = varargin{1}; lb = varargin{2}; ub = varargin{3};
if length(varargin) <= 3
smin = min(datastruct(:)); smax = max(datastruct(:));
else
smin = varargin{4}; smax = varargin{5};
end
scaled = (datastruct - smin) / (smax - smin) * (ub - lb) + lb;
end
% Invert scaling
function unscaled = myDescale(scaled, lb, ub, smin, smax)
unscaled = (scaled + lb ) * (smax - smin) ./ (ub - lb) + smin;
end
% Converts the data to z-scores
function [standard, center, stddev] = myStandardize(varargin)
datastruct = varargin{1};
if length(varargin) == 1
center = mean(datastruct(:)); stddev = std(datastruct(:));
else
center = varargin{2}; stddev = varargin{3};
end
standard = (datastruct - center) / stddev;
end
% Converts z-scores back to the data's scale
function destandard = myDestandardize(datastruct, center, stddev)
destandard = datastruct * stddev + center;
end
In the following code, I have removed the validation set to reduce bloat.
% % I intend to regularize the latent space of this autoencoder to be a
% classifier once it can accomplish basic reconstruction. Made this note so
% it's clear what's going on with the custom losses and so forth.
training = digitTrain4DArrayData;
test = digitTest4DArrayData;
%% Scaling that does not work
% Min-max scaling
xlb = 0; xub=1;
[xTrain, xTrainMin, xTrainMax] = myRescale(training, xlb, xub);
xTest = myRescale(test, xTrainMin, xTrainMax);
%% Scaling that does work. Why?
% [xTrain, xTrainCenter, sTrainStd] = myStandardize(training);
% xTest = myStandardize(test, xTrainCenter, xTrainStd);
ntrain = size(xTrain,4); IMG_DIM = size(xTrain, 1);
N_CHANNELS=size(xTrain, 3);
numLatentChannels = 64;
imageSize = [28 28 1];
%% Layer definitions
% Encoder layer
layersE = [
imageInputLayer(imageSize,Normalization="none")
convolution2dLayer(3,32,Padding="same",Stride=2)
reluLayer
convolution2dLayer(3,64,Padding="same",Stride=2)
reluLayer
fullyConnectedLayer(numLatentChannels)
tanhLayer(Name='latent')];
% Latent projection
projectionSize = [7 7 64]; enc_dim = projectionSize(1);
numInputChannels = imageSize(3);
% Decoder
layersD = [
featureInputLayer(numLatentChannels)
projectAndReshapeLayer(projectionSize)
transposedConv2dLayer(3,64,Cropping="same",Stride=2)
reluLayer
transposedConv2dLayer(3,32,Cropping="same",Stride=2)
reluLayer
transposedConv2dLayer(3,numInputChannels,Cropping="same")
sigmoidLayer(Name='Output')
];
netE = dlnetwork(layersE);
netD = dlnetwork(layersD);
%% Training Parameters
numEpochs = 150;
miniBatchSize = 20;
learnRate = 1e-3;
dsTrain = arrayDatastore(xTrain,IterationDimension=4);
numOutputs = 1;
mbq = minibatchqueue(dsTrain,numOutputs, ...
MiniBatchSize = miniBatchSize, ...
MiniBatchFormat="SSCB", ...
MiniBatchFcn=@preprocessMiniBatch,...
PartialMiniBatch="return");
%Initialize the parameters for the Adam solver.
trailingAvgE = [];
trailingAvgSqE = [];
trailingAvgD = [];
trailingAvgSqD = [];
%Calculate the total number of iterations for the training progress monitor
numIterationsPerEpoch = ceil(ntrain / miniBatchSize);
numIterations = numEpochs * numIterationsPerEpoch;
epoch = 0;
iteration = 0;
%Initialize the training progress monitor.
monitor = trainingProgressMonitor( ...
Metrics="TrainingLoss", ...
Info=["Epoch", "LearningRate"], ...
XLabel="Iteration");
%% Training
while epoch < numEpochs && ~monitor.Stop
epoch = epoch + 1;
% Shuffle data.
shuffle(mbq);
% Loop over mini-batches.
while hasdata(mbq) && ~monitor.Stop
% Assess validation criterion
iteration = iteration + 1;
% Read mini-batch of data.
X = next(mbq);
% Evaluate loss and gradients.
[loss,gradientsE,gradientsD] = dlfeval(@modelLoss,netE,netD,X);
% Update learnable parameters.
[netE,trailingAvgE,trailingAvgSqE] = adamupdate(netE, ...
gradientsE,trailingAvgE,trailingAvgSqE,iteration,learnRate);
[netD, trailingAvgD, trailingAvgSqD] = adamupdate(netD, ...
gradientsD,trailingAvgD,trailingAvgSqD,iteration,learnRate);
updateInfo(monitor, ...
LearningRate=learnRate, ...
Epoch=string(epoch) + " of " + string(numEpochs));
recordMetrics(monitor,iteration, ...
TrainingLoss=loss);
monitor.Progress = 100*iteration/numIterations;
end
end
%% Testing
dsTest = arrayDatastore(xTest,IterationDimension=4);
numOutputs = 1;
mbqTest = minibatchqueue(dsTest,numOutputs, ...
MiniBatchSize = miniBatchSize, ...
MiniBatchFcn=@preprocessMiniBatch, ...
MiniBatchFormat="SSCB");
YTest = modelPredictions(netE,netD,mbqTest);
reconerr = mean(flatten(xTest-YTest),1);
figure
histogram(reconerr)
xlabel("Reconstruction Error")
ylabel("Frequency")
title("Test Data")
numImages = 64;
ndisplay = 10;
figure
I = imtile(YTest(:,:,:,1:numImages));
imshow(I)
title("Reconstructed Images")
%% Functions
function [loss,gradientsE,gradientsD] = modelLoss(netE,netD,X)
% Forward through encoder.
Z = forward(netE,X);
% Forward through decoder.
Xrecon = forward(netD,Z);
% Calculate loss and gradients.
loss = regularizedLoss(Xrecon,X);
[gradientsE,gradientsD] = dlgradient(loss,netE.Learnables,netD.Learnables);
end
function loss = regularizedLoss(Xrecon,X)
% Image Reconstruction loss.
reconstructionLoss = mse(Xrecon, X);
% Combined loss.
loss = reconstructionLoss;
end
function Xrecon = modelPredictions(netE,netD,mbq)
Xrecon = [];
% Loop over mini-batches.
while hasdata(mbq)
X = next(mbq);
% Pass through encoder
Z = predict(netE,X);
% Pass through decoder to get reconstructed images
XGenerated = predict(netD,Z);
% Extract and concatenate predictions.
Xrecon = cat(4,Xrecon,extractdata(XGenerated));
end
end
function X = preprocessMiniBatch(Xcell)
% Concatenate.
X = cat(4,Xcell{:});
end
end
6 Comments
Matt J
on 12 Jul 2024
Your code does not run here in the online environment, see below.
clear, close all, clc
% % I intend to regularize the latent space of this autoencoder to be a
% classifier once it can accomplish basic reconstruction. Made this note so
% it's clear what's going on with the custom losses and so forth.
training = digitTrain4DArrayData;
test = digitTest4DArrayData;
%% Scaling that does not work
% Min-max scaling
xlb = 0; xub=1;
[xTrain, xTrainMin, xTrainMax] = myRescale(training, xlb, xub);
xTest = myRescale(test, xTrainMin, xTrainMax);
%% Scaling that does work. Why?
% [xTrain, xTrainCenter, sTrainStd] = myStandardize(training);
% xTest = myStandardize(test, xTrainCenter, xTrainStd);
ntrain = size(xTrain,4); IMG_DIM = size(xTrain, 1);
N_CHANNELS=size(xTrain, 3);
numLatentChannels = 64;
imageSize = [28 28 1];
%% Layer definitions
% Encoder layer
layersE = [
imageInputLayer(imageSize,Normalization="none")
convolution2dLayer(3,32,Padding="same",Stride=2)
reluLayer
convolution2dLayer(3,64,Padding="same",Stride=2)
reluLayer
fullyConnectedLayer(numLatentChannels)
tanhLayer(Name='latent')];
% Latent projection
projectionSize = [7 7 64]; enc_dim = projectionSize(1);
numInputChannels = imageSize(3);
% Decoder
layersD = [
featureInputLayer(numLatentChannels)
projectAndReshapeLayer(projectionSize)
transposedConv2dLayer(3,64,Cropping="same",Stride=2)
reluLayer
transposedConv2dLayer(3,32,Cropping="same",Stride=2)
reluLayer
transposedConv2dLayer(3,numInputChannels,Cropping="same")
sigmoidLayer(Name='Output')
];
netE = dlnetwork(layersE);
netD = dlnetwork(layersD);
%% Training Parameters
numEpochs = 150;
miniBatchSize = 20;
learnRate = 1e-3;
dsTrain = arrayDatastore(xTrain,IterationDimension=4);
numOutputs = 1;
mbq = minibatchqueue(dsTrain,numOutputs, ...
MiniBatchSize = miniBatchSize, ...
MiniBatchFormat="SSCB", ...
MiniBatchFcn=@preprocessMiniBatch,...
PartialMiniBatch="return");
%Initialize the parameters for the Adam solver.
trailingAvgE = [];
trailingAvgSqE = [];
trailingAvgD = [];
trailingAvgSqD = [];
%Calculate the total number of iterations for the training progress monitor
numIterationsPerEpoch = ceil(ntrain / miniBatchSize);
numIterations = numEpochs * numIterationsPerEpoch;
epoch = 0;
iteration = 0;
%Initialize the training progress monitor.
monitor = trainingProgressMonitor( ...
Metrics="TrainingLoss", ...
Info=["Epoch", "LearningRate"], ...
XLabel="Iteration");
%% Training
while epoch < numEpochs && ~monitor.Stop
epoch = epoch + 1;
% Shuffle data.
shuffle(mbq);
% Loop over mini-batches.
while hasdata(mbq) && ~monitor.Stop
% Assess validation criterion
iteration = iteration + 1;
% Read mini-batch of data.
X = next(mbq);
% Evaluate loss and gradients.
[loss,gradientsE,gradientsD] = dlfeval(@modelLoss,netE,netD,X);
% Update learnable parameters.
[netE,trailingAvgE,trailingAvgSqE] = adamupdate(netE, ...
gradientsE,trailingAvgE,trailingAvgSqE,iteration,learnRate);
[netD, trailingAvgD, trailingAvgSqD] = adamupdate(netD, ...
gradientsD,trailingAvgD,trailingAvgSqD,iteration,learnRate);
updateInfo(monitor, ...
LearningRate=learnRate, ...
Epoch=string(epoch) + " of " + string(numEpochs));
recordMetrics(monitor,iteration, ...
TrainingLoss=loss);
monitor.Progress = 100*iteration/numIterations;
end
end
%% Testing
dsTest = arrayDatastore(xTest,IterationDimension=4);
numOutputs = 1;
mbqTest = minibatchqueue(dsTest,numOutputs, ...
MiniBatchSize = miniBatchSize, ...
MiniBatchFcn=@preprocessMiniBatch, ...
MiniBatchFormat="SSCB");
YTest = modelPredictions(netE,netD,mbqTest);
reconerr = mean(flatten(xTest-YTest),1);
figure
histogram(reconerr)
xlabel("Reconstruction Error")
ylabel("Frequency")
title("Test Data")
numImages = 64;
ndisplay = 10;
figure
I = imtile(YTest(:,:,:,1:numImages));
imshow(I)
title("Reconstructed Images")
%% Functions
function [loss,gradientsE,gradientsD] = modelLoss(netE,netD,X)
% Forward through encoder.
Z = forward(netE,X);
% Forward through decoder.
Xrecon = forward(netD,Z);
% Calculate loss and gradients.
loss = regularizedLoss(Xrecon,X);
[gradientsE,gradientsD] = dlgradient(loss,netE.Learnables,netD.Learnables);
end
% Min-max scaling between [lb, ub]
function [scaled,smin,smax] = myRescale(varargin)
datastruct = varargin{1}; lb = varargin{2}; ub = varargin{3};
if length(varargin) <= 3
smin = min(datastruct(:)); smax = max(datastruct(:));
else
smin = varargin{4}; smax = varargin{5};
end
scaled = (datastruct - smin) / (smax - smin) * (ub - lb) + lb;
end
% Invert scaling
function unscaled = myDescale(scaled, lb, ub, smin, smax)
unscaled = (scaled + lb ) * (smax - smin) ./ (ub - lb) + smin;
end
% Converts the data to z-scores
function [standard, center, stddev] = myStandardize(varargin)
datastruct = varargin{1};
if length(varargin) == 1
center = mean(datastruct(:)); stddev = std(datastruct(:));
else
center = varargin{2}; stddev = varargin{3};
end
standard = (datastruct - center) / stddev;
end
% Converts z-scores back to the data's scale
function destandard = myDestandardize(datastruct, center, stddev)
destandard = datastruct * stddev + center;
end
function loss = regularizedLoss(Xrecon,X)
% Image Reconstruction loss.
reconstructionLoss = mse(Xrecon, X);
% Combined loss.
loss = reconstructionLoss;
end
function Xrecon = modelPredictions(netE,netD,mbq)
Xrecon = [];
% Loop over mini-batches.
while hasdata(mbq)
X = next(mbq);
% Pass through encoder
Z = predict(netE,X);
% Pass through decoder to get reconstructed images
XGenerated = predict(netD,Z);
% Extract and concatenate predictions.
Xrecon = cat(4,Xrecon,extractdata(XGenerated));
end
end
function X = preprocessMiniBatch(Xcell)
% Concatenate.
X = cat(4,Xcell{:});
end
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