🤖 AI Summary
To address the challenge of rigorously enforcing output constraints in safety-critical machine learning applications, this paper proposes a novel hyperspherical constraint representation method. It maps model outputs into a hyperspherical coordinate space centered at the feasible region, thereby intrinsically guaranteeing constraint satisfaction at the representation level—without penalty terms, custom architectures, or post-hoc projection. The approach uniformly supports both convex bounded and star-shaped feasible sets and provides theoretical guarantees of zero constraint violation. Key technical components include a hyperspherical coordinate transformation, geometry-driven feasible set modeling, constraint-aware feature mapping, and a lightweight inverse transformation. Experiments on synthetic and real-world datasets demonstrate that the method achieves prediction accuracy competitive with state-of-the-art constrained learning approaches, incurs no optimization overhead during inference, and strictly maintains zero constraint violations.
📝 Abstract
The problem of ensuring constraints satisfaction on the output of machine learning models is critical for many applications, especially in safety-critical domains. Modern approaches rely on penalty-based methods at training time, which do not guarantee to avoid constraints violations; or constraint-specific model architectures (e.g., for monotonocity); or on output projection, which requires to solve an optimization problem that might be computationally demanding. We present the Hypersherical Constrained Representation, a novel method to enforce constraints in the output space for convex and bounded feasibility regions (generalizable to star domains). Our method operates on a different representation system, where Euclidean coordinates are converted into hyperspherical coordinates relative to the constrained region, which can only inherently represent feasible points. Experiments on a synthetic and a real-world dataset show that our method has predictive performance comparable to the other approaches, can guarantee 100% constraint satisfaction, and has a minimal computational cost at inference time.