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.
By Trinh Tran, Binh Nguyen, Truong X. Nghiem
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.
By Youcef Magnouche, Abderrahmane Driouch, S\'ebastien Martin, Pierre Bauguion
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...
By Yang Zhao, Jungeun Lee, Jeong hwan Jeon, Sze Zheng Yong
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.
By Shraman Pal, Can Li
arXiv:2609.36310v1 Announce Type: new
Abstract: Everywhere learning provides a principled framework for training AI models under constraints that must hold throughout the data distribution. In the du...
By Ignacio Boero, Jonathan Nixon, Alejandro Ribeiro
arXiv:2608. 09707v1 Announce Type: cross Abstract: Embedding trained neural networks as surrogates within optimisation problems is an established practice in operations research.
By Yu Liu, Jan Kronqvist, Fabricio Oliveira
arXiv:2606. 05247v1 Announce Type: new Abstract: Enforcing nonlinear inequality constraints in neural networks remains challenging, especially when the output is subject to many coupled constraints.
By Ziqian Wang, Chenxi Fang, Zhen Zhang
arXiv:2608. 02343v1 Announce Type: cross Abstract: Many operational problems are constrained sequential decision processes with large, combinatorial action spaces and interdependent feasibility constraints.
By Patrick Helm, Jan-Niklas Doerr, Joren Gijsbrechts, Stefan Minner
The paper demonstrates that tree tensor networks (TTNs) can encode arbitrary read‑once Boolean formulas, yielding polynomial‑size targets that are hard for gradient descent to learn in polynomial time, yet their loss landscapes are conditionally benign: every minimum‑norm local minimum is global. This shows that bad local minima are not the source of learning difficulty in TTNs; instead, high‑order degenerate saddle points caused by rank‑deficiency can impede learning. A case study on the parity function illustrates how TTNs can link landscape geometry to computational hardness.
By Zach Furman, Stephan W\"aldchen, Yangda Bei, Liam Hodgkinson
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...
By Veit Elser, Manish Krishan Lal
arXiv:2606. 19652v1 Announce Type: new Abstract: In this work, we introduce a training procedure for shallow neural networks that promotes robustness against adversarial attacks.
By Chao Yin, Antoine Lesage-Landry
The paper introduces ReMILP, a reformulation‑contrastive learning framework that uses self‑supervision from equivalent formulations of mixed‑integer linear programs (MILPs). By distinguishing re‑descriptions and substitutions, the method trains a graph neural network and a hypernetwork to predict how variable embeddings transform under changes of variables, achieving invariance and equivariance without solver‑derived labels. The learned representations prove useful for tasks such as binary solution, constraint activity, and integrality gap prediction, and serve as a strong initialization for fine‑tuning.
By Ousema Bouaneni, Mathis Le Bail, Cl\'ement Elliker, Ma\"el Jenny, Sonia Vanier