# SnareNet: Flexible Repair Layers for Neural Networks with Hard Constraints

arXiv: https://arxiv.org/abs/2602.09317 · HTML: https://mlsanity.com/paper/2602.09317/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 47 references that are in the map.
- First posted on arXiv 10 Feb 2026.

## Builds on (most cited first, 30 of 31)

- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [End-to-End Training of Deep Visuomotor Policies](https://mlsanity.com/paper/1504.00702/) (2015)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [A Survey of Deep Learning Techniques for Autonomous Driving](https://mlsanity.com/paper/1910.07738/) (2019)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Challenges in Training PINNs: A Loss Landscape Perspective](https://mlsanity.com/paper/2402.01868/) (2024)
- [Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction](https://mlsanity.com/paper/1905.10866/) (2019)
- [Constrained-CNN losses for weakly supervised segmentation](https://mlsanity.com/paper/1805.04628/) (2018)
- [FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scale](https://mlsanity.com/paper/2507.12144/) (2025)
- [DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow](https://mlsanity.com/paper/1910.14448/) (2019)
- [Imposing Hard Constraints on Deep Networks: Promises and Limitations](https://mlsanity.com/paper/1706.02025/) (2017)
- [HardNet: Hard-Constrained Neural Networks with Universal Approximation Guarantees](https://mlsanity.com/paper/2410.10807/) (2024)
- [Constrained Deep Networks: Lagrangian Optimization via Log-Barrier Extensions](https://mlsanity.com/paper/1904.04205/) (2019)
- [RAYEN: Imposition of Hard Convex Constraints on Neural Networks](https://mlsanity.com/paper/2307.08336/) (2023)
- [Physics-Informed Neural Networks with Hard Linear Equality Constraints](https://mlsanity.com/paper/2402.07251/) (2024)
- [Learning to Solve Optimization Problems with Hard Linear Constraints](https://mlsanity.com/paper/2208.10611/) (2022)
- [FSNet: Feasibility-Seeking Neural Network for Constrained Optimization with Guarantees](https://mlsanity.com/paper/2506.00362/) (2025)
- [Training neural networks under physical constraints using a stochastic augmented Lagrangian approach](https://mlsanity.com/paper/2009.07330/) (2020)
- [Pinet: Optimizing hard-constrained neural networks with orthogonal projection layers](https://mlsanity.com/paper/2508.10480/) (2025)
- [Graph-based Time Series Clustering for End-to-End Hierarchical Forecasting](https://mlsanity.com/paper/2305.19183/) (2023)
- [Optimization Learning](https://mlsanity.com/paper/2501.03443/) (2025)
- [Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints](https://mlsanity.com/paper/2507.08124/) (2025)
- [Physically Valid Biomolecular Interaction Modeling with Gauss-Seidel Projection](https://mlsanity.com/paper/2510.08946/) (2025)

## Built on by (most cited first, 2 of 2)

- [SLP-ProbHard: Probabilistic Hard-Constrained Learning via Structural Latent Parameterization](https://mlsanity.com/paper/2609.33515/) (2026)
- [Only Project Once: Projection-Adaptive Loss for Exact Constraint Satisfaction](https://mlsanity.com/paper/2610.04572/) (2026)

## Abstract (arXiv)

Neural networks are increasingly used as fast surrogate models across various domains, but unconstrained predictions can violate physical, operational, or safety requirements. We propose SnareNet, a feasibility-controlled architecture to learn mappings whose outputs must satisfy input-dependent constraints. SnareNet appends a differentiable repair layer that navigates in the constraint map's range space, steering iterates toward feasibility and producing a repaired output that satisfies constraints to a user-specified tolerance. We stabilize end-to-end training by adaptive relaxation, a new training paradigm that snares the neural network at initialization and shrinks it into the feasible set, enabling early exploration and strict feasibility later in training. On optimization learning and trajectory planning benchmarks, SnareNet consistently attains improved objective quality while satisfying constraints more reliably than prior work, and it is the first to enforce non-convex constraints at medium-to-high precision robustly across instances.