The paper introduces “GraphPDHG,” a message‑passing neural network that aligns with the Chambolle‑Pock Primal–Dual Hybrid Gradient algorithm to solve general graph saddle‑point problems. The authors prove that “GraphPDHG” can efficiently simulate PDHG and can learn an accelerated version of the algorithm. Experiments demonstrate that the learned warm start improves second‑order optimizers and that alignment with PDHG yields better size generalization compared to standard GNN baselines.
arXiv:2602.13106v2 Announce Type: replace-cross Abstract: In recent years, there has been growing interest in understanding neural architectures' ability to learn to execute discrete algorithms, a li...
arXiv:2601. 23207v2 Announce Type: replace-cross Abstract: Understanding what graph neural networks can learn, especially their ability to learn to execute algorithms, remains a central theoretical challenge.
arXiv:2605. 09382v2 Announce Type: replace Abstract: The Linear Assignment Problem is a fundamental combinatorial optimization task where classical exact solvers ensure optimality but suffer from an $\mathcal{O}(N^{3})$ bottleneck, while recent neural approximations struggle with scalability and exactness.
arXiv:2508. 08005v4 Announce Type: replace-cross Abstract: The Maximum Clique Problem (MCP) is an NP-hard problem with wide-ranging applications in fields such as bioinformatics, network science, and social computing, yet no single algorithm consistently outperforms all others across diverse graph instances.
arXiv:2509. 18930v3 Announce Type: replace-cross Abstract: Neural algorithmic reasoning (NAR) is a paradigm that trains neural networks to execute classic algorithms by supervised learning.
The paper introduces SHSP, a Structure-Aware Hierarchical Solution Prediction framework for Mixed-Integer Linear Programming. SHSP replaces one-shot marginal decoding with a hierarchical conditional decoding that sequentially predicts variables based on a coupling graph derived from constraints, and includes a confidence-aware mask-and-repair step to correct errors. Experiments on four MILP benchmarks show SHSP reduces the solution gap by an average of 54% compared to existing one-shot methods.
Mixed-Integer Linear Programming (MILP) is a fundamental optimization paradigm in combinatorial optimization and has been widely applied across real-world domains. Due to its NP-hard nature, obtaining...
arXiv:2512. 01113v2 Announce Type: replace-cross Abstract: Algorithmic reasoning -- the ability to perform step-by-step logical inference -- is a synthetic benchmark for evaluating multi-step reasoning abilities, designed for graph neural networks and also for transformer models.
arXiv:2603. 02462v2 Announce Type: replace-cross Abstract: A key challenge in developing unified neural solvers for combinatorial optimization (CO) is the efficient generalization of models from a given set of tasks to new tasks unseen during initial training.
arXiv:2509. 24256v2 Announce Type: replace-cross Abstract: The pretrain-transfer paradigm, which underpins the success of large language models (LLMs), has demonstrated the immense power of creating foundation models that learn generalizable representations from vast datasets.
arXiv:2601. 16510v3 Announce Type: replace-cross Abstract: Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost.
arXiv:2607. 22467v1 Announce Type: new Abstract: Data scarcity poses a fundamental challenge in training generative models to produce initial guesses for parametric optimization problems that are otherwise numerically expensive to solve.