Autoencoder input x, output y, not x_hat

Hello everyone,

what is the term for an autoencoder, that is trained not to reconstruct X, but to create another output y instead. I’ve heard the term somewhere, but can’t remember it.
For example the autoencoder the autoencoder is trained on the MNIST dataset not to reconstruct the given number X_hat, but to create an image of another number Y.
The loss function would be like that:

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