Homogeneous Linear Inequality Constraints for Neural Network Activations
This addresses the need for efficient constrained neural networks in applications like generative modeling, though it is incremental as it builds on existing constraint methods.
The paper tackles the problem of imposing homogeneous linear inequality constraints on neural network activations to combine data-driven training with prior knowledge, achieving a speed-up of up to two orders of magnitude over projection methods at inference time.
We propose a method to impose homogeneous linear inequality constraints of the form $Ax\leq 0$ on neural network activations. The proposed method allows a data-driven training approach to be combined with modeling prior knowledge about the task. One way to achieve this task is by means of a projection step at test time after unconstrained training. However, this is an expensive operation. By directly incorporating the constraints into the architecture, we can significantly speed-up inference at test time; for instance, our experiments show a speed-up of up to two orders of magnitude over a projection method. 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 an 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.