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Given CRF potentials, one can write down the marginal predictions after only passing the initial messages from factors to variables. This paper incorporates that parametric form into a neural network, and fits it directly to minimize training error. This architecture appears to be empirically successful on a meaningful benchmark. I found the framing of the work partially misleading: As far as I can tell, the cost function reported doesn't care about structured prediction just pixel-wise errors, and no CRF model is actually fitted. To me "structured CRF prediction" means that there is a joint distribution over the labels given an input.