arXiv:2606. 18106v1 Announce Type: new Abstract: This paper explores the problem of finding the minimum zero-forcing set on undirected graphs and proposes an adapted machine-learning framework to solve the problem.
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 a physics-inspired neural framework that combines graph neural networks with statistical‑mechanics principles to solve large‑scale graph coloring problems. By using a planting‑based supervised signal, symmetry‑breaking regularization, and iterative noise‑annealed neural dynamics, the model navigates complex solution landscapes and scales quadratically with graph size. It generalizes from small training graphs to instances up to 20 times larger, demonstrating that neural architectures can learn scalable algorithmic strategies effective in hard connectivity regions.
The paper introduces a novel end‑to‑end, size‑agnostic graph reinforcement learning framework for the one‑dimensional bin packing problem (1D‑BPP). It models packing as a Markov decision process on an item‑compatibility graph, where a graph neural network actor‑critic policy learns to merge compatible partial bins. Empirical results on the BPPLIB benchmark show that the learned policy reduces the mean optimality gap of a constructive heuristic from 2.66 % to 2.31 %, performs competitively against other learned methods, and outperforms a state‑of‑the‑art learned solver on the hardest benchmark family.
The maximum independent set (MIS) problem is a fundamental NP-hard combinatorial optimization problem with applications in scheduling, resource allocation, and network analysis. Exact solvers can prov...
The paper extends the Strong Expressive Lottery Ticket Hypothesis to relational and temporal graph neural networks by proving that sufficiently large RGNNs contain sparse subnetworks preserving 1‑relational Weisfeiler‑Leman expressivity. It derives a probabilistic lower bound for random pruning to achieve such subnetworks and shows that common TGNNs and cross‑graph message passing can be reformulated as RGNNs to inherit these guarantees. Experiments validate the bound, compare it to empirical probabilities on synthetic data, and explore the relationship between pre‑training expressivity, optimization behavior, and prediction quality on temporal and molecular benchmarks.
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...
We address liquidity placement in the Bitcoin Lightning Network (LN): given a fixed budget, which channels should a node open to maximize its routing capacity? We cast this as a budget-constrained combinatorial optimization problem on graphs, selecting $k$ edge additions that maximize $s$--$t$ max-flow, a theory-grounded measure of routing capacity, and solve it with graph reinforcement learning.
arXiv:2606. 03923v1 Announce Type: new Abstract: Graph coloring seeks to assigns colors to a graph's nodes so that adjacent nodes receive different colors, using as few colors as possible.
arXiv:2607. 08703v1 Announce Type: new Abstract: We address liquidity placement in the Bitcoin Lightning Network (LN): given a fixed budget, which channels should a node open to maximize its routing capacity?
The paper introduces a dataset‑free approach to generate planar graph embeddings that meet strict structural and geometric constraints. By integrating parametric graph grammars with safe reinforcement learning, the authors formulate the task as a constrained Markov decision process and use action projection to keep actions within safe sets. Their method consistently outperforms classical and deep generative baselines on a new benchmark suite for constrained, goal‑directed planar graph generation.
The paper investigates how sparsity impacts the expressivity of graph neural networks, focusing on relational and temporal variants. It extends the Strong Expressive Lottery Ticket Hypothesis to multi-relational and temporal domains, proving that sufficiently large RGNNs contain sparse subnetworks that preserve 1‑RWL expressivity and providing a probabilistic bound for random pruning. Experiments validate the theoretical bounds, compare them to empirical results on synthetic data, and explore the relationship between pre‑training expressivity, optimization behavior, and prediction quality on temporal and molecular benchmarks.
The paper presents a graph-based framework for large-scale railway network management, combining a hierarchical Bayesian model with a Gaussian Process on a graph kernel to infer spatially correlated maintenance environments from Swiss Federal Railways data. It introduces a topology-aware Multi-Agent Reinforcement Learning system that uses graph neural networks and Transformers to optimize network-level policies. The approach demonstrates scalability via zero-shot transfer learning, enabling agents trained on small network segments to perform effectively on unseen large networks, outperforming heuristics and standard MARL baselines while reducing training time.