Hello - I’m working on a Convolutional Autoencoder model where I’m optimizing one cost on output layer and other cost on the bottleneck layer. Please see the picture  below(I took it from a published paper). Please note I’m not minimizing any clustering loss on the bottleneck layer. My cost is a different one. I know how to back propagate the reconstruction loss but I’m not sure how to back propagate the gradient of the cost which I’m optimizing on the output of the bottleneck layer. Can anyone please help? Thank you.
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