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Imposing constraints on the output of a Deep Neural Net is one way to improvethe quality of its predictions while loosening the requirements for labeledtraining data. Such constraints are usually imposed as soft constraints byadding new terms to the loss function that is minimized during training. Analternative is to impose them as hard constraints, which has a number oftheoretical benefits but has not been explored so far due to the perceivedintractability of the problem.  In this paper, we show that imposing hard constraints can in fact be done ina computationally feasible way and delivers reasonable results. However, thetheoretical benefits do not materialize and the resulting technique is nobetter than existing ones relying on soft constraints. We analyze the reasonsfor this and hope to spur other researchers into proposing better solutions.

Imposing Hard Constraints on Deep Networks: Promises and Limitations