dlarray/dlgradient Value to differentiate is non-scalar. It must be a traced real dlarray scalar.

Hello, I am working on auto differentiation. But it came up with a error shown as title.

data = randn (3, 5000, 100);
numChannels=size(data,1);
numObservations=size(data,3);

XTrain = data(:,:,1:floor(0.9*numObservations));
XTest = data(:,:,floor(0.9*numObservations)+1:end);

numHiddenUnits=100;
numLatentChannels=1;
layersE = [
    sequenceInputLayer(numChannels,Normalization="zscore")
    lstmLayer(numHiddenUnits,'OutputMode','sequence')
    fullyConnectedLayer(2*numLatentChannels)
    samplingLayerSeq
    ];

Unrecognized function or variable 'samplingLayerSeq'.

layersD = [
    sequenceInputLayer(numLatentChannels,Normalization="zscore")
    lstmLayer(numHiddenUnits,'OutputMode','sequence')
    fullyConnectedLayer(numChannels)
    ];
netE = dlnetwork(layersE);
netD = dlnetwork(layersD);
numEpochs = 150;
miniBatchSize = 20;
learnRate = 1e-2;
dsTrain = arrayDatastore(XTrain,IterationDimension=3);
numOutputs = 1;
mbq = minibatchqueue(dsTrain,numOutputs, ...
    MiniBatchSize = miniBatchSize, ...
    MiniBatchFcn=@preprocessMiniBatch, ...
    MiniBatchFormat="CBT", ...
    PartialMiniBatch="discard");

trailingAvgE = [];
trailingAvgSqE = [];
trailingAvgD = [];
trailingAvgSqD = [];
numObservationsTrain = size(XTrain,3);
numIterationsPerEpoch = ceil(numObservationsTrain / miniBatchSize);
numIterations = numEpochs * numIterationsPerEpoch;
monitor = trainingProgressMonitor( ...
    Metrics="Loss", ...
    Info="Epoch", ...
    XLabel="Iteration");
epoch = 0;
iteration = 0;
% Loop over epochs.
while epoch < numEpochs && ~monitor.Stop
    epoch = epoch + 1;
    % Shuffle data.
    shuffle(mbq);
    % Loop over mini-batches.
    while hasdata(mbq) && ~monitor.Stop
        iteration = iteration + 1;
        % Read mini-batch of data.
        X = next(mbq);
        % X = dlarray(X,'CBT');
        
        % 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);
    end
end
%% model loss
function [loss,gradientsE,gradientsD] = modelLoss(netE,netD,X)
% Forward through encoder.
[Z,mu,logSigmaSq] = forward(netE,X);
% Forward through decoder.
Y = forward(netD,Z);
% Calculate loss and gradients.
loss = elboLoss(Y,X,mu,logSigmaSq);
[gradientsE,gradientsD] = dlgradient(loss,netE.Learnables,netD.Learnables);
end
%% elboloss
function loss = elboLoss(Y,T,mu,logSigmaSq)
% Reconstruction loss.
reconstructionLoss = mse(Y,T);
% KL divergence.
KL = -0.5 * sum(1 + logSigmaSq - mu.^2 - exp(logSigmaSq),1);
KL = mean(KL);
% Combined loss.
loss = reconstructionLoss + KL;
end

%% preprocess minibatch
function X = preprocessMiniBatch(dataX)
% Concatenate.
X = cat(3,dataX{:});
end

%% class 
classdef samplingLayerSeq < nnet.layer.Layer

    methods
        function layer = samplingLayerSeq(args)
            % layer = samplingLayer creates a sampling layer for VAEs.
            %
            % layer = samplingLayer(Name=name) also specifies the layer 
            % name.

            % Parse input arguments.
            arguments
                args.Name = "";
            end

            % Layer properties.
            layer.Name = args.Name;
            layer.Type = "Sampling";
            layer.Description = "Mean and log-variance sampling";
            layer.OutputNames = ["out" "mean" "log-variance"];
        end

        function [Z,mu,logSigmaSq] = predict(~,X)
            % [Z,mu,logSigmaSq] = predict(~,Z) Forwards input data through
            % the layer at prediction and training time and output the
            % result.
            %
            % Inputs:
            %         X - Concatenated input data where X(1:K,:) and 
            %             X(K+1:end,:) correspond to the mean and 
            %             log-variances, respectively, and K is the number 
            %             of latent channels.
            % Outputs:
            %         Z          - Sampled output
            %         mu         - Mean vector.
            %         logSigmaSq - Log-variance vector

            % Data dimensions.
            numLatentChannels = size(X,1)/2;
            miniBatchSize = size(X,2);

            % Split statistics.
            mu = X(1:numLatentChannels,:,:);
            logSigmaSq = X(numLatentChannels+1:end,:,:);
            
            sz = size(mu);
            epsilon =randn(sz);
            % Sample output.
            % epsilon = randn(numLatentChannels,miniBatchSize,"like",X);
            sigma = exp(.5 * logSigmaSq);
            Z = epsilon .* sigma + mu;
            % Z = dlarray(Z,'CBT');
        
        end

    end
    
end

Illegal use of reserved keyword "classdef".

Answer 1

[Ben]

Your loss in modelLoss has a non-scalar T dimension since the model outputs sequences. You need to compute a scalar loss to use dlgradient. Standard approaches might be to take a sum or mean over the T dimension, but more intricate losses are common too.