Pinet: Optimizing hard-constrained neural networks with orthogonal projection layers

• URL: http://arxiv.org/abs/2508.10480v1
• Date: Thu, 14 Aug 2025 09:32:09 GMT
• Title: Pinet: Optimizing hard-constrained neural networks with orthogonal projection layers
• Authors: Panagiotis D. Grontas, Antonio Terpin, Efe C. Balta, Raffaello D'Andrea, John Lygeros,
• Abstract summary: We introduce an output layer for networks that ensures satisfaction of convex constraints.<n>Our approach, $Pi$net, leverages operator splitting for rapid and reliable projections in the forward pass.
• Score: 5.227723778971733
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $\Pi$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem for backpropagation. We deploy $\Pi$net as a feasible-by-design optimization proxy for parametric constrained optimization problems and obtain modest-accuracy solutions faster than traditional solvers when solving a single problem, and significantly faster for a batch of problems. We surpass state-of-the-art learning approaches in terms of training time, solution quality, and robustness to hyperparameter tuning, while maintaining similar inference times. Finally, we tackle multi-vehicle motion planning with non-convex trajectory preferences and provide $\Pi$net as a GPU-ready package implemented in JAX with effective tuning heuristics.

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