mlsanityData to 14 Oct 2026

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

arXiv 2508.10480 ↗First posted 14 Aug 2025cs.LG cs.AI math.OCcited by 19

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Abstract (arXiv)

We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, Pinet, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem for backpropagation. We deploy Pinet 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 by orders of magnitude 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 Pinet as a GPU-ready package implemented in JAX.

Key facts. Cited by 19 papers in the map (data through 14 Oct 2026). Builds on 44 of its 75 references that are in the map. First posted on arXiv 14 Aug 2025.

Builds on

44 of 75 references.

References · 44

  1. 2017Deep reinforcement learning from human preferencescited by 3,912
  2. 2021Convex optimizationcited by 2,515
  3. 2016CVXPY: A Python-Embedded Modeling Language for Convex Optimizationcited by 641
  4. 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 623
  5. 2019Deep Equilibrium Modelscited by 615
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32 more
  1. 2022Tutorial on amortized optimizationcited by 83
  2. 2019Learning Optimal Solutions for Extremely Fast AC Optimal Power Flowcited by 77
  3. 2020Lagrangian Duality for Constrained Deep Learningcited by 74
  4. 2019Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Predictioncited by 67
  5. 2022Theseus: A Library for Differentiable Nonlinear Optimizationcited by 65
  6. 2022Self-Supervised Primal-Dual Learning for Constrained Optimizationcited by 61
  7. 2021Physics-Informed Neural Networks for AC Optimal Power Flowcited by 54
  8. 2017Imposing Hard Constraints on Deep Networks: Promises and Limitationscited by 43
  9. 2021Nonsmooth Implicit Differentiation for Machine Learning and Optimizationcited by 43
  10. 2019Online Mixed-Integer Optimization in Millisecondscited by 38
  11. 2021Universal Approximation Under Constraints is Possible with Transformerscited by 32
  12. 2023Learning to Warm-Start Fixed-Point Optimization Algorithmscited by 32
  13. 2023RAYEN: Imposition of Hard Convex Constraints on Neural Networkscited by 30
  14. 2022Motion Planning around Obstacles with Convex Optimizationcited by 27
  15. 2025Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modelingcited by 27
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  17. 2024Learning diffusion at lightspeedcited by 22
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  19. 2021Efficient differentiable quadratic programming layers: an ADMM approachcited by 19
  20. 2025ENFORCE: Nonlinear Constrained Learning with Adaptive-depth Neural Projectioncited by 17
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 5; 2026: 14.

19 papers.

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  2. 2025Safe Reinforcement Learning using Action Projection: Safeguard the Policy or the Environment?cited by 5
  3. 2026LMI-Net: Linear Matrix Inequality--Constrained Neural Networks via Differentiable Projection Layerscited by 4
  4. 2026Soft-Radial Projection for Constrained End-to-End Learningcited by 3
  5. 2025SynthPix: A lightspeed PIV image generatorcited by 2
  6. 2026SnareNet: Flexible Repair Layers for Neural Networks with Hard Constraintscited by 2
  7. 2026HardNet++: Nonlinear Constraint Enforcement in Neural Networkscited by 2
  8. 2026Cheap Thrills: Effective Amortized Optimization Using Inexpensive Labelscited by 1
  9. 2026Parametric Nonconvex Optimization via Convex Surrogatescited by 1
  10. 2026AdamFLIP: Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN Trainingcited by 1
  11. 2026DiffSlack: Learning under Nonlinear Inequality Constraints via Learnable Slack Variablescited by 1
  12. 2025Self-Certifying Primal-Dual Optimization Proxies for Large-Scale Batch Economic Dispatchcited by 0
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  3. 2026NLPOpt-Net: A Learning Method for Nonlinear Optimization with Feasibility Guaranteescited by 0
  4. 2026Broximal Gradient Descent: A Projection-Free Sister of Projected Gradient Descentcited by 0
  5. 2026GCPO: Diagnosing and Constraining Subspace Geometry in Rollout RL for LLMscited by 0
  6. 2026SLP-ProbHard: Probabilistic Hard-Constrained Learning via Structural Latent Parameterizationcited by 0
  7. 2026Only Project Once: Projection-Adaptive Loss for Exact Constraint Satisfactioncited by 0