FlatLand is a personalized federated learning approach that embeds each client’s graph data into a tailored Lorentz space, leveraging hyperbolic geometry’s negative curvature to model graph structures. The method introduces a parameter decoupling strategy that separates client‑specific heterogeneity (time‑like parameters) from shared knowledge (space‑like parameters), allowing direct aggregation without extra similarity estimation. Experiments on various federated graph learning tasks show that FlatLand outperforms existing methods, especially in low‑dimensional settings.
By Jiahong Liu, Ram Samarth B B, Xinyu Fu, Menglin Yang, Weixi Zhang, Rex Ying, Irwin King
arXiv:2606. 03307v1 Announce Type: cross Abstract: Graph foundation models (GFMs) emerged as a dominant paradigm in graph representation learning by leveraging large-scale pre-training for cross-domain inference.
By Yifan Jin, Qirui Ji, Bin Qin, Jiangmeng Li, Lixiang Liu, Fuchun Sun, Changwen Zheng
The paper introduces Constant‑Curvature Sliced Gromov‑Wasserstein (CCSGW), a new divergence for aligning probability distributions on heterogeneous constant‑curvature spaces such as hyperbolic and spherical manifolds. It extends sliced Gromov‑Wasserstein by adding geodesic‑based one‑dimensional projections for spherical spaces, enabling efficient and principled comparison across manifolds with different curvatures while preserving intrinsic geometric relationships. The authors provide theoretical analysis showing that CCSGW controls intrinsic geometric discrepancy and demonstrate consistent performance gains when integrated into mixed‑curvature learning tasks like graph anomaly detection, node classification, and multimodal learning.
By Shanglin Li, Wenjing Lu, Muyang Li, Nicu Sebe, Ziheng Chen
The paper introduces a compositional graph embedding framework based on Aitchison geometry, where nodes are represented as simplex-valued mixtures over latent archetypal factors. By embedding these mixtures using isometric log-ratio coordinates, the method preserves Aitchison distances while allowing unconstrained optimization in Euclidean space, yielding intrinsically interpretable embeddings. The approach achieves competitive performance on node classification and link prediction tasks and enables principled component restriction through subcompositional coherence, allowing analysis of how archetype groups influence representations and predictions.
By Nikolaos Nakis, Chrysoula Kosma, Panagiotis Promponas, Michail Chatzianastasis, Giannis Nikolentzos
arXiv:2608. 07029v1 Announce Type: new Abstract: Hyperbolic embeddings provide compact geometric representations of complex networks in hyperbolic spaces, but systematic comparisons of methods developed in machine learning, network science, and algorithmics remain rare.
By Robert Jankowski, Maksim Kitsak, Dorota Celi\'nska-Kopczy\'nska
The paper surveys collaborative learning methods that move beyond traditional Euclidean data to graph-structured data. It reviews foundational principles for Euclidean settings—learning effectiveness, efficiency, and privacy—and then extends the discussion to graph data, presenting a taxonomy of distribution scenarios, statistical heterogeneities, and standardized problem formulations. The survey also outlines open challenges and future research directions in this emerging field.
By R\'emi Bourgerie, \v{S}ar\=unas Girdzijauskas, Viktoria Fodor