Why do I get "Encountered complex value" error when training a custom network with the "fft" function?

I'm training a neural network with "fullyConnectedLayer" and a custom loss function that has the "fft" function. "fft" should be supported for "dlarray" operations, but when I call the "dlgradient" function to calculate the gradients, I get an error:

Error using dlarray/dlgradient
Encountered complex value when computing gradient with respect to an output of fullyconnect. Convert all outputs of fullyconnect to real.

Answer 1

[MathWorks Support Team]

When the "fft" function is used in training, it might introduce complex-valued gradients during back propagation. Such complex gradients are not supported by "fullyConnectedLayer". In order to ensure that the gradients are always real-valued, in the custom loss function you can use the "real" function to cast the data as real values, before sending them to the "fft" function. For example:

function [loss, gradients] = testLoss(net, input, target)
   y = net.forward(input);
   y = stripdims(y);
   y = real(y); % <-- Cast the "y" variable as real-valued before calling "fft" on it
   yfft = fft(y,4096);
   yabs = abs(yfft);
   
   loss = sum(yabs,'all');
   gradients = dlgradient(loss,net.Learnables);
end