arXiv:2609. 29466v1 Announce Type: cross Abstract: Approximate message passing on factor graphs underlies two dominant families of probabilistic inference algorithms: expectation propagation (EP) and variational message passing (VMP).
The paper introduces the Graph Dynamics Model (GDM), a world model that learns stochastic latent dynamics over evolving graph topologies. GDM employs a sparse recurrent adjacency matrix for topology updates and a recurrent state‑space architecture for stochastic transitions, enabling it to handle partially observable, stochastic environments. The authors also propose the Graph Distribution Distance (GDD) metric, using maximum mean discrepancy with a graph kernel, to compare predicted and true joint graph state distributions, and demonstrate GDM’s superior performance and zero‑shot generalisation on large graphs.
The paper introduces S$^3$GLC, a deep graph-level clustering framework that combines global topological features—derived via a Spectral Signature based on the Hoffman-Wielandt inequality—with local neighborhood information to improve clustering of graph datasets. It also incorporates a joint manifold-preserving sparse regression module to fuse these representations while reducing noise, and a balanced clustering objective using optimal transport to prevent clustering collapse, especially in imbalanced multi-class settings. Experiments on ten real-world datasets, including REDDIT-12K and OGBG-PPA, show that S$^3$GLC outperforms fifteen state-of-the-art baselines.
SCGFM-ART is a structure‑centric graph foundation model that aligns arbitrary graphs onto a shared relational atlas using Amortized Relational Transport (ART). The atlas, defined by a finite set of relational landmarks, provides a universal coordinate system, while ART predicts end‑to‑end graph‑to‑base transport plans, eliminating costly runtime Gromov‑Wasserstein optimizations. The framework decomposes graphs into global relational response coordinates and local node‑to‑role structural correspondences, enabling unified representations that resolve structural and semantic heterogeneity across diverse graph domains.
The paper introduces Variational Bayesian Flow Network (VBFN), a graph generation model that lifts Bayesian updates to a joint Gaussian belief family with structured precisions, enabling coupled node and edge updates in a single fusion step. By constructing sample‑agnostic sparse precisions from a representation‑induced dependency graph, VBFN avoids label leakage while enforcing node‑edge consistency. Experiments on synthetic and molecular graph datasets show that VBFN improves fidelity and diversity over baseline methods.
The paper introduces Spectral Connectivity-Regularized Graph Learning (SCoGL), a method for learning sparse graphs from limited data by incorporating Laplacian spectral priors that promote global connectivity. SCoGL extends the graphical lasso objective with a connectivity prior derived from Laplacian eigenvalues and uses projected gradient descent with Armijo backtracking for optimization. Experiments demonstrate that SCoGL improves graph recovery and enhances downstream tasks such as graph signal denoising when observations are scarce.
arXiv:2606. 11831v1 Announce Type: cross Abstract: Neural relational inference (NRI) methods discover interaction graphs from trajectories through variational reasoning on discrete potential edges.
Given a collection of $N$ graphs, graph-level clustering (GLC) seeks to partition the $N$ graphs into semantically meaningful groups, which serves as a fundamental task in analyzing graph-structured d...
Training Graph Neural Networks on large graphs is challenged by the memory cost of storing all node representations across layers. We show that several existing scalable approaches can be written as structured modifications of the GNN propagation matrix, providing a unified perspective that exposes their respective limitations.
arXiv:2608.30152v1 Announce Type: new Abstract: Graph positional encodings are widely used in graph neural networks and graph Transformers, yet it remains unclear when the code itself can identify no...
arXiv:2608. 02128v1 Announce Type: new Abstract: Training Graph Neural Networks on large graphs is challenged by the memory cost of storing all node representations across layers.
arXiv:2610.27439v1 Announce Type: cross Abstract: Solving reasoning tasks supported on graphs typically requires providing a Language Reasoning Model (LRM) with a serialized description of the graph....