[help please!] Error with custom training loop: Value to differentiate is not traced.

Hi!

I am using MATLAB to code a neural network with custom loss fuction these days.

I run the code and get this error: Value to differentiate is not traced. It must be a traced real dlarray scalar. Use dlgradient

inside a function called by dlfeval to trace the variables.

Here's my code:

% Generate data
sampleSize = 1000;
x = -2 + (2+2)*rand(1000,1);
e = randn(sampleSize,1);
y = (x.^2-1<=0).*(x+e) + (x.^2-1>0).*(-x+e);
data = table();
data = addvars(data, y); data = addvars(data, x);

% Define network
layers = [
    featureInputLayer(1)
    tanhLayer()
    fullyConnectedLayer(10)
    tanhLayer()
    fullyConnectedLayer(10)
    tanhLayer()
    fullyConnectedLayer(1)];
net = dlnetwork(layers);

% hyper parameters
numEpoch = 100;
learnRate = 0.0002;
gradientDecayFactor = 0.5;
squaredGradientDecayFactor = 0.999;
trailingAvg = [];
trailingAvgSqD = [];

% Training
iteration = 0;
start = tic;
for i = 1:numEpoch
    fprintf('The %.dth epoch.\n', i);
    iteration = iteration + 1;
    % Do NOT use batch
    X = dlarray(data{:,'x'},'BC');
    if canUseGPU
        X = gpuArray(X);
    end
    % get loss and gradients
    [loss,gradients] = dlfeval(@modelLoss, net, X, data);
    % update parameters
    [net,trailingAvg,trailingAvgSqD] = adamupdate(net, gradients, ...
            trailingAvg, trailingAvgSqD, iteration, ...
            learnRate, gradientDecayFactor, squaredGradientDecayFactor);
end

The 'modelLoss' function looks like:

function [loss,gradients,state] = modelLoss(net, X, data)
    % get output of network
    output = forward(net, X);
    
    % !!! where the problem is !!!
    f = extractdata(output)';
    % get sub sample according to wether f larger than 0
    % get SSE of each OLS regression in each subsample
    if height(data(f<=0,:))<5 || height(data(f>0,:))<5
        mdl = fitlme(data, 'y ~ x');
        loss = mdl.SSE;
    else
        mdl1 = fitlme(data(f<=0, :), 'y ~ x ');
        mdl2 = fitlme(data(f>0, :), 'y ~ x ');
        loss = mdl1.SSE + mdl2.SSE;
    end
    % return loss
    gradients = dlgradient(dlarray(loss), net.Learnables);
end

I've read another answer, which states that I should not use the "extractdata" function, since the gradient information will be erased.

But it seems that I must use this function because the object 'dlarray' do not support the function 'find'!

Could someone help me please!!!

Thank you so much!!!

Answer 1

[sanidhyak]

Hi @Ruihang Xie,

I understand that you are encountering the error "Value to differentiate is not traced" while training your custom neural network in MATLAB. I too faced the same issue when reproducing the provided code. This issue arises because gradient tracking is broken inside the “modelLoss” function due to the use of “extractdata” and “fitlme” functions.

To resolve this, the following workarounds are needed in the provided code:

• Remove “extractdata” function to maintain gradient tracking.
• Replace “fitlme” with a custom regression function compatible with “dlarray”.
• Use element-wise operations (.* instead of *) so that “dlarray” is compatibility.

Kindly refer to the following corrected code:

% Training loop modifications 
for i = 1:numEpoch 
    fprintf('The %.dth epoch.\n', i); 
    iteration = iteration + 1; 
    
    % Convert both X and Y to dlarrays 
    X = dlarray(data{:,'x'},'BC'); 
    Y = dlarray(data{:,'y'},'BC'); 
    
    if canUseGPU 
        X = gpuArray(X); 
        Y = gpuArray(Y); 
    end 
    
    % Get loss and gradients 
    [loss,gradients] = dlfeval(@modelLoss, net, X, Y); 
    
    % Update parameters 
    [net,trailingAvg,trailingAvgSqD] = adamupdate(net, gradients, ... 
        trailingAvg, trailingAvgSqD, iteration, ... 
        learnRate, gradientDecayFactor, squaredGradientDecayFactor); 
end 

The corrected "modelLoss" function:

function [loss,gradients] = modelLoss(net, X, Y) 
% Get network output 
output = forward(net, X); 

% Create masks while maintaining gradient tracking 
mask_neg = output <= 0; 
mask_pos = output > 0; 

% Count samples in each group 
n_neg = sum(mask_neg, 'all'); 
n_pos = sum(mask_pos, 'all'); 

% Initialize loss 
loss = dlarray(0); 

if n_neg >= 5 && n_pos >= 5 
    % Split data using masks while preserving gradients 
    X_neg = X .* mask_neg; 
    Y_neg = Y .* mask_neg; 
    X_pos = X .* mask_pos; 
    Y_pos = Y .* mask_pos; 
    
    % Calculate regression for each group 
    beta_neg = calculateBeta(X_neg(mask_neg), Y_neg(mask_neg)); 
    pred_neg = X_neg .* beta_neg; 
    loss_neg = sum((Y_neg - pred_neg).^2, 'all'); 
    
    beta_pos = calculateBeta(X_pos(mask_pos), Y_pos(mask_pos)); 
    pred_pos = X_pos .* beta_pos; 
    loss_pos = sum((Y_pos - pred_pos).^2, 'all'); 
    
    loss = loss_neg + loss_pos; 
else 
    % Single regression if groups are too small 
    beta = calculateBeta(X, Y); 
    pred = X .* beta; 
    loss = sum((Y - pred).^2, 'all'); 
end 

gradients = dlgradient(loss, net.Learnables); 
end 

Helper function:

function beta = calculateBeta(X, Y) 
XX = sum(X .* X, 'all'); 
XY = sum(X .* Y, 'all'); 
beta = XY ./ XX; 
end 

This implementation solves the error, and gradient tracking will be maintained throughout the training loop.

For further reference, please check the following MATLAB documentations on “dlarray” and “dlradient”:

• https://www.mathworks.com/help/deeplearning/ref/dlarray.html
• https://www.mathworks.com/help/deeplearning/ref/dlgradient.html

I hope this helps!

(As can be seen in the screenshot below, the error has been resolved, and training is proceeding)