Imposing Star-Shaped Hard Constraints on the Neural Network Output

Abstract

A problem of imposing hard constraints on the neural network output can be met in many applications. We propose a new method for solving this problem for non-convex constraints that are star-shaped. A region produced by constraints is called star-shaped when there exists an origin in the region from which every point is visible. Two tasks are considered: to generate points inside the region and on the region boundary. The key idea behind the method is to generate a shift of the origin towards a ray parameterized by the additional layer of the neural network. The largest admissible shift is determined by the differentiable Ray marching algorithm. This allows us to generate points which are guaranteed to satisfy the constraints. A more accurate modification of the algorithm is also studied. The proposed method can be regarded as a generalization of the methods for convex constraints. Numerical experiments illustrate the method by solving machine-learning problems. The code implementing the method is publicly available.

Keywords

• neural network
• hard constraints
• star-shaped region
• Ray marching
• classification