arXiv:2607. 24338v1 Announce Type: new Abstract: Unsupervised graph representation learning aims to derive meaningful node embeddings by capturing both structural and attribute information without relying on labeled data.
Positional encodings (PEs) enhance the power of graph neural networks (GNNs), both theoretically and empirically. Two of the most popular families of PEs - spectral (e.
arXiv:2609.13920v1 Announce Type: cross Abstract: Persistent Gaussian perturbations have been shown to prevent asymptotic oversmoothing in recurrent Graph Neural Networks (GNNs) by ensuring a positiv...
arXiv:2607. 10074v1 Announce Type: new Abstract: Graph machine learning provides powerful tools for understanding complex networks and learning meaningful node representations.
The paper presents provable guarantees for a spectral method that recovers binary node labels on signed graphs with edge‑flip noise. It provides graph‑structure‑agnostic bounds on approximate inference accuracy and maximum angle deviation, using matrix concentration and eigenvector perturbation techniques. The results connect to the Cheeger constant and are validated with synthetic experiments, marking the first theoretical analysis of this spectral approach.
arXiv:2602.15239v3 Announce Type: replace Abstract: Transformers have achieved remarkable success across domains, motivating the rise of Graph Transformers (GTs) as attention-based architectures for...
arXiv:2607. 21607v1 Announce Type: cross Abstract: Graph Neural Networks propagate information through local message passing, but the graph topologies themselves can silently prevent any amount of training from solving long-range tasks.
Modern sensing, communication, and learning systems generate heterogeneous network signals, with local data differing in dimension, modality, and geometric structure. Processing such data requires a mathematical framework capable of simultaneously modeling heterogeneous local signal spaces and the transformations relating them.
arXiv:2608. 01318v1 Announce Type: cross Abstract: Modern sensing, communication, and learning systems generate heterogeneous network signals, with local data differing in dimension, modality, and geometric structure.
arXiv:2606. 03315v1 Announce Type: new Abstract: Graph foundation models aim to learn transferable knowledge from diverse graphs for generalization to unseen graphs and tasks.
The paper introduces higher-order positional encodings that enrich graph representations by incorporating topological information from lifted incidence structures, without altering existing graph learning backbones. It theoretically shows that these encodings can mix graph Laplacian frequencies beyond what scalar spectral filters achieve, and demonstrates their effectiveness on Graph Transformers for datasets like ZINC and synthetic benchmarks. The approach bridges graph positional encodings and topological deep learning, enabling standard models to exploit higher-order interactions.
HyPE-GT introduces a framework that generates learnable hyperbolic positional encodings for Graph Transformers, enabling the capture of complex hierarchical relationships in graph-structured data. Unlike traditional Euclidean encodings, HyPE’s hyperbolic encodings can be selected to suit specific downstream tasks and help mitigate oversmoothing in deep Graph Neural Networks. Experiments on molecular benchmarks and large-scale Open Graph Benchmark datasets demonstrate improved performance, while additional tests on Coauthor and Copurchase networks confirm HyPE’s effectiveness in controlling oversmoothing.