Recreating MATLAB RegressionLayer as custom RegressionLayer?

MATLAB Documentation (https://www.mathworks.com/help/deeplearning/ref/regressionlayer.html) says the regression layer using the half-mean-squared-error as the loss function in the regression layer. I'd like to replicate this layer myself, similar to the MAE loss function tutorial (https://www.mathworks.com/help/deeplearning/ug/define-custom-regression-output-layer.html), so that I can ultimately start tweaking it. For now though, I just want to replicate it exactly.

I think the correct (GPU implemented) loss function in the fowardLoss layer would be as follows:

R = size(Y,3); MSE = sum((Y-T).*(Y-T),3)/(R*2); N = size(Y,4); loss = sum(MSE)/N;

However, I'm not sure about the backwardLoss implementation. My best guess would be:

R = size(Y,3); N = size(Y,4); dLdY = (Y-T)/(N*R);

Is this correct?