Linear Inequality Constraints for Neural Network Activations

We propose a method to impose linear inequality constraints on neural network activations. The proposed method allows a data-driven training approach to be combined with modeling prior knowledge about the task. Our algorithm computes a suitable parameterization of the feasible set at initialization and uses standard variants of stochastic gradient descent to find solutions to the constrained network. Thus, the modeling constraints are always satisfied during training. Crucially, our approach avoids to solve a sub-optimization problem at each training step or to manually trade-off data and constraint fidelity with additional hyperparameters. We consider constrained generative modeling as an important application domain and experimentally demonstrate the proposed method by constraining a variational autoencoder.