mlsanityData to 14 Oct 2026

AT-SKM-Net: An Accelerated Trainable Sampling Kaczmarz-Motzkin Framework for Linear Hard-Constraint Feasibility on Dynamic Graphs

arXiv 2609.30088 ↗First posted 24 Sep 2026cs.LG cs.AI math.OCcited by 0

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Abstract (arXiv)

Graph-structured optimization with linear constraints is fundamental to critical infrastructure but faces scalability limits due to massive strict hard constraints and high dimensionality. While recent projection-based methods such as Trainable Sampling Kaczmarz-Motzkin Net (T-SKM-Net) guarantee feasibility, they face high computational costs in dynamic environments by processing the entire constraint set and requiring expensive matrix factorizations. To bridge this gap, we propose the Accelerated Trainable-SKM (AT-SKM) Net framework. To concentrate computation on the active constraints and eliminate redundant calculations, we introduce a hybrid sampling strategy guided by a topology-aware heterogeneous GNN model. To efficiently handle topological shifts in graph-based constraints, we employ a Cholesky Update mechanism that theoretically reduces the equality projection complexity from O(N^3) to O(N^2) under low-rank perturbations. Experiments on random geometric graphs, N-1 Security-Constrained DC-OPF, and minimum-cost gas transport problem demonstrate that AT-SKM reduces iteration counts by up to 85% and achieves 2.95x-7.29x SKM layer speedups, while maintaining zero constraint violations.

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References · 25

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13 more
  1. 2014Screening Tests for Lasso Problemscited by 15
  2. 2018Statistical Learning For DC Optimal Power Flowcited by 12
  3. 2023A New Computationally Simple Approach for Implementing Neural Networks with Output Hard Constraintscited by 12
  4. 2025Enforcing Hard Linear Constraints in Deep Learning Models with Decision Rulescited by 10
  5. 2016A Sampling Kaczmarz-Motzkin Algorithm for Linear Feasibilitycited by 9
  6. 2025End-to-End Probabilistic Framework for Learning with Hard Constraintscited by 9
  7. 2020Sampling Kaczmarz Motzkin Method for Linear Feasibility Problems: Generalization & Accelerationcited by 7
  8. 2024GRANOLA: Adaptive Normalization for Graph Neural Networkscited by 7
  9. 2024GLinSAT: The General Linear Satisfiability Neural Network Layer By Accelerated Gradient Descentcited by 7
  10. 2023SCQPTH: an efficient differentiable splitting method for convex quadratic programmingcited by 5
  11. 2025Enforcing convex constraints in Graph Neural Networkscited by 2
  12. 2025Warm-starting active-set solvers using graph neural networkscited by 2
  13. 2025T-SKM-Net: Trainable Neural Network Framework for Linear Constraint Satisfaction via Sampling Kaczmarz-Motzkin Methodcited by 1

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