  In the last few years the systematic adoption of deep learning to visual
generation has produced impressive results that, amongst others, definitely
benefit from the massive exploration of convolutional architectures. In this
paper, we propose a general approach to visual generation that combines
learning capabilities with logic descriptions of the target to be generated.
The process of generation is regarded as a constrained satisfaction problem,
where the constraints describe a set of properties that characterize the
target. Interestingly, the constraints can also involve logic variables, while
all of them are converted into real-valued functions by means of the t-norm
theory. We use deep architectures to model the involved variables, and propose
a computational scheme where the learning process carries out a satisfaction of
the constraints. We propose some examples in which the theory can naturally be
used, including the modeling of GAN and auto-encoders, and report promising
results in problems with the generation of handwritten characters and face
transformations.
