arXiv:2509. 12484v2 Announce Type: replace Abstract: We propose a novel neural network architecture, called Non-Trainable Modification (NTM), for computing Nash equilibria in stochastic differential games (SDGs) on graphs.
arXiv:2508. 18173v2 Announce Type: replace Abstract: The discovery of symbolic governing equations is a central goal in science; yet, it remains challenging particularly for graph dynamical systems, where the network topology further shapes the system behavior.
The paper introduces Graph-Guided Quasimetric Dense Reward (G2QDR), a framework that learns a state connectivity model to predict pairwise connectivity strengths in asymmetric environments. These strengths are converted into scalar auxiliary dense rewards, offering continuous guidance across hierarchical levels. G2QDR can be integrated into any existing Goal-Conditioned Hierarchical Reinforcement Learning architecture and shows empirical performance improvements in sparse reward settings with modest computational cost.
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.
The paper presents a graph-based framework for large-scale railway network management that combines a hierarchical Bayesian model with a Gaussian Process on a graph kernel to model spatially correlated maintenance environments, and a topology-aware Multi-Agent Reinforcement Learning system using graph neural networks and Transformers to optimize network-level policies. It demonstrates scalability by training agents on small network segments and deploying them zero-shot on larger, unseen networks, achieving superior performance over heuristics and standard MARL baselines while reducing training time. The approach addresses the computational challenges of centralized methods and the coordination gaps of decentralized methods in complex, long-horizon infrastructure asset management.
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:2607. 07330v1 Announce Type: cross Abstract: Hypergraph neural networks have shown powerful capability in modeling higher-order relations, yet their predictive uncertainty remains underexplored.
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.
arXiv:2507. 05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms.
arXiv:2608. 14856v1 Announce Type: cross Abstract: Computing Nash equilibria in interdependent security (IDS) games on networks is computationally expensive: best-response dynamics may need hundreds of iterations per instance, and downstream tasks such as auditing, stress-testing, and incentive design often require repeatedly re-solving the game under parameter perturbations.
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:2606. 26662v1 Announce Type: cross Abstract: Graph Neural Differential Equations (GNDEs) model continuous-time graph dynamics by parameterizing Neural ODE velocity fields with Graph Neural Networks.
arXiv:2606. 27780v1 Announce Type: new Abstract: World models are often used for planning by rolling learned dynamics forward.