Say we train a (discriminative) CNN to predict age from images of faces. Is there a direct way of obtaining the homologous generative network (ie, from a scalar age to an image of a face) ? The backward pass during training should be doing something similar in order to propagate the gradients from age to the face.
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There is probably no good way to do this, since it is possible to discriminate age without modeling the whole space of faces. If you also happened to have a density model of faces $X$ as well, perhaps you could use MCMC to sample from $P(X|y) \propto P(y|X)P(X)$.
