{"ID":2856253,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.11227","arxiv_id":"2510.11227","title":"Enforcing convex constraints in Graph Neural Networks","abstract":"Many machine learning applications require outputs that satisfy complex, dynamic constraints. This task is particularly challenging in Graph Neural Network models due to the variable output sizes of graph-structured data. In this paper, we introduce ProjNet, a Graph Neural Network framework which satisfies input-dependant constraints. ProjNet combines a sparse vector clipping method with the Component-Averaged Dykstra (CAD) algorithm, an iterative scheme for solving the best-approximation problem. We establish a convergence result for CAD and develop a GPU-accelerated implementation capable of handling large-scale inputs efficiently. To enable end-to-end training, we introduce a surrogate gradient for CAD that is both computationally efficient and better suited for optimization than the exact gradient. We validate ProjNet on four classes of constrained optimisation problems: linear programming, two classes of non-convex quadratic programs, and radio transmit power optimization, demonstrating its effectiveness across diverse problem settings.","short_abstract":"Many machine learning applications require outputs that satisfy complex, dynamic constraints. This task is particularly challenging in Graph Neural Network models due to the variable output sizes of graph-structured data. In this paper, we introduce ProjNet, a Graph Neural Network framework which satisfies input-depend...","url_abs":"https://arxiv.org/abs/2510.11227","url_pdf":"https://arxiv.org/pdf/2510.11227v1","authors":"[\"Ahmed Rashwan\",\"Keith Briggs\",\"Chris Budd\",\"Lisa Kreusser\"]","published":"2025-10-13T10:10:46Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Graph Neural Network\"]","has_code":false}