The article "Constraint Learning by Optimizing over Trained Neural Networks: A Pragmatic Tutorial" discusses the emerging paradigm of embedding trained machine learning models, particularly neural networks, into optimization problems. It explains how constraints can be learned from data or objectives approximated to simplify models, while addressing challenges of size and speed. The tutorial offers practical guidance and demonstrates benefits through a case study that shows smaller, sparser networks can improve efficiency.
arXiv:2605.24437v2 Announce Type: replace Abstract: We present a novel framework for embedding hard constraint satisfaction into neural network (NN) architectures, specifically feedforward neural net...
arXiv:2605. 30456v2 Announce Type: replace Abstract: Many learning tasks in science and engineering are characterized by sparse datasets, which limits the effectiveness of purely data-driven approaches.
arXiv:2512.20270v2 Announce Type: replace-cross Abstract: Many engineering tasks require solving families of nonlinear constrained optimization problems, parametrized in setting-specific variables. T...
arXiv:2606. 13803v1 Announce Type: new Abstract: Enforcing functional inequality constraints such as monotonicity and convexity in neural networks is a fundamental challenge in many industrial and scientific applications.
The paper introduces PolyFormer, a physics-informed machine learning framework that learns compact polytopic representations of complex constraints. By transforming constraint-induced geometry into efficient polytopic reformulations, PolyFormer reduces optimization complexity and enables the use of standard solvers. Evaluations on large‑scale resource aggregation, network‑constrained optimization, and uncertainty‑aware optimization show up to 6,400‑fold speedups and 99.87% memory savings while keeping feasibility and objective errors low.
CG4AI is a column generation framework that trains AI models while enforcing linear constraints on their outputs. It constructs a convex combination of models, using a master linear program to set mixture weights and a pricing subproblem to generate new models guided by dual variables, focusing on the most violated constraints. The method is applied to MNIST digit classification—demonstrating constraint learning, adversarial robustness, error correction, and output relabeling—and to multi‑commodity flow routing, achieving feasible predictors with higher accuracy than single‑model baselines.
arXiv:2502.06774v5 Announce Type: replace Abstract: Ensuring neural networks adhere to domain-specific constraints is crucial for addressing safety and trustworthiness while also enhancing inference...
The paper presents a Constraint Acquisition Tool that creates size‑independent constraint programs from input data and both positive and negative example solutions across multiple problem instances. It first derives size‑specific models using common patterns in global and binary constraints, then generalizes these into a model that can be applied to unseen data. The tool outputs MiniZinc code and a textual model description, and its effectiveness is demonstrated on the PTHG21 Challenge problems.
HUANet is a deep neural network architecture that unrolls the Alternating Direction Method of Multipliers (ADMM) into a trainable model for accelerating parametric constrained convex optimization. It embeds a hard‑constrained neural network in each ADMM iteration, using a differentiable correction stage to enforce affine equalities of the primal subproblem. The method also incorporates first‑order optimality conditions into a self‑supervised training loss, and numerical experiments on benchmark problems and a control application demonstrate its effectiveness in speeding up constrained convex optimization.
arXiv:2610.01519v1 Announce Type: cross Abstract: Neuro-Symbolic (NeSy) predictors incorporate prior knowledge into the prediction process of neural networks, ensuring that outputs satisfy specified...
arXiv:2602.17493v2 Announce Type: replace-cross Abstract: We develop a method for training neural networks on Boolean data in which the values at all nodes are strictly $\pm 1$, and the resulting mod...
The paper introduces a constraint‑aware training objective that externalizes program analysis constraints used during inference, avoiding redundant learning of these constraints during model training. It presents three theorems demonstrating that this approach can reduce model size and improve data efficiency. A controlled synthetic experiment confirms that constraint‑aware training achieves lower prediction loss than standard cross‑entropy training at the same parameter count and data volume.