  Deep Neural Networks (DNNs) outshine alternative function approximators in
many settings thanks to their modularity in composing any desired
differentiable operator. The formed parametrized functional is then tuned to
solve a task at hand from simple gradient descent. This modularity comes at the
cost of making strict enforcement of constraints on DNNs, e.g. from a priori
knowledge of the task, or from desired physical properties, an open challenge.
In this paper we propose the first provable affine constraint enforcement
method for DNNs that only requires minimal changes into a given DNN's
forward-pass, that is computationally friendly, and that leaves the
optimization of the DNN's parameter to be unconstrained, i.e. standard
gradient-based method can be employed. Our method does not require any sampling
and provably ensures that the DNN fulfills the affine constraint on a given
input space's region at any point during training, and testing. We coin this
method POLICE, standing for Provably Optimal LInear Constraint Enforcement.
Github: https://github.com/RandallBalestriero/POLICE
