The paper introduces FRESHPart, a new spectral hypergraph partitioning framework that refines spectral embeddings using Geometry Feedback and Search Feedback. By analyzing circuit and synthetic hypergraphs, the authors uncover a ray-like embedding structure that explains why projection-based partitioning works well, and show that Laplacian design and hyperedge reweighting can shape this geometry. On the Titan23 benchmark, FRESHPart reduces cut sizes by 13.09% at ε=2% and 25.21% at ε=20% compared to hMETIS, achieving the best reported results while completing all tests in under 120 seconds on a single GPU.
arXiv:2611.05729v1 Announce Type: new Abstract: With scalable Laplacian solvers now available, the next frontier is to exploit them more effectively for high-quality hypergraph partitioning. In this...
HyperFuse is a new, label‑free pipeline for fast self‑supervised node embeddings on attributed hypergraphs. It computes structural node coordinates via a spectral relaxation of hypergraph modularity, builds multi‑scale feature summaries with utility‑weighted hyperedges, and trains a lightweight encoder for only 100 epochs. In experiments on nine public hypergraphs, HyperFuse achieved 13–179× speed‑ups over baselines and matched or exceeded their accuracy on most downstream tasks.
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.
The paper introduces Selective Hypergraph Refinement (SHR), a post‑processing technique for frozen graph clustering models that does not alter model parameters, node representations, or the original graph. SHR uses an attribute hypergraph to generate candidate refinement directions and selectively updates only nodes with sufficient support, preserving the majority of original assignments. Experiments on 15 backbone‑dataset combinations show modest macro gains (up to 0.137 pp) with very few hard assignment changes, indicating a limited but measurable refinement space after training.
The paper introduces OFAG, a foundation model designed for attributed graph clustering that can be trained once and applied to diverse graphs without graph‑specific tuning. It learns a reusable clustering strategy from synthetic graphs and uses a dimension‑agnostic encoder to handle varying feature spaces, producing clustering‑friendly node representations in a single forward pass. Across ten datasets, a frozen OFAG model outperforms baselines in both speed and clustering quality, and the authors provide code and pretrained checkpoints for easy adoption.
The paper introduces a geometry‑aware graph construction method that adaptively selects Gaussian kernel bandwidths per node to align the kernel’s spectral complexity with the intrinsic dimensionality of the underlying manifold. By matching the kernel’s effective rank to a local intrinsic dimension estimate derived from a minimum spanning tree, the method operates within a manifold‑consistent log‑log scaling regime. Experiments on CIFAR‑100 demonstrate that this adaptive bandwidth approach consistently improves leave‑one‑out classification and label propagation accuracy compared to fixed‑bandwidth and other adaptive techniques.
arXiv:2605. 16836v2 Announce Type: replace-cross Abstract: Hypergraphs provide a principled framework for modeling polyadic interactions, with applications in recommendation systems, social networks, and molecular modeling.
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.
arXiv:2502.04312v3 Announce Type: replace Abstract: Contrastive learning leverages data augmentation to develop feature representation without relying on large labeled datasets. However, despite its...
arXiv:2608.27883v1 Announce Type: new Abstract: Physical systems are often modeled by solution operators that map input fields, parameters, geometries, or past states to steady or future physical sta...
The paper investigates federated hypergraph learning where local hyperedge releases can correspond to multiple global hypergraph structures, highlighting identifiability and computational challenges. It shows that pairwise assignment of latent correspondences is tractable while multi-client hyperedge matching is generally intractable, and introduces FedASTRA—a method that learns correspondence‑invariant diffusion representations via adaptive heat diffusion and masked latent prediction, communicating only model parameters. Experiments on eight real‑world datasets, including ogbn‑papers100M, demonstrate that FedASTRA achieves state‑of‑the‑art performance‑communication trade‑offs, reaching 50.07 % accuracy and 29.73 % Macro‑F1 while sending only 59.60 MiB per round.
arXiv:2606. 22180v2 Announce Type: replace-cross Abstract: Graph embedding maps graph nodes into low-dimensional vectors to support applications such as recommendation, fraud detection, and graph-based retrieval-augmented generation (GraphRAG).