The paper introduces the Generalized Graph Variational Autoencoder (GGVA), which replaces the Kullback–Leibler divergence in the standard variational graph autoencoder with any member of the Rényi–Tsallis family of order $q$. The authors show that for $q<1$ the Tsallis divergence is bounded, whereas the KL and Rényi divergences are unbounded, and that this boundedness can significantly increase the amount of posterior information retained—up to 49× more than the VGAE on several benchmark graphs. Experiments demonstrate that the GGVA’s retained information improves node classification performance, though it does not improve link‑prediction accuracy and only delays, rather than prevents, posterior collapse.
By Kleyton da Costa, Bernardo Modenesi, Ivan F. M. Menezes, Helio Lopes
arXiv:2608. 10845v1 Announce Type: cross Abstract: Spectral clustering methods for network data are commonly based on a few matrix representations, such as the adjacency matrix and the symmetric Laplacian.
By John Park, Ning Hao
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.
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.
By Violet Zheng, Jean Honorio
arXiv:2609.38161v1 Announce Type: new
Abstract: Evaluations of graph reconstruction by language models typically report a single aggregate distance between the original and the reconstructed graph. W...
By Jianru Shen
AutoGraphForge is a computational pipeline designed to automate the discovery, refutation, formalization, and proving of graph-theoretic conjectures. It generates conjectures using a Graffiti3 generator, filters out known results with a novelty filter, tests candidates against a large dataset of graphs, and refines surviving conjectures through counterexample search. The pipeline then translates each conjecture into Lean 4, verifies proofs with neural provers, and integrates the results into a formal library.
By J\'an Pastorek
arXiv:2607. 07513v1 Announce Type: new Abstract: Self-supervised learning matches supervised accuracy from a fraction of the labels, but the labeled-sample efficiency behind this has lacked a theoretical explanation.
By Adam M. Oberman
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:2511. 11927v2 Announce Type: replace-cross Abstract: Principal Component Analysis (PCA) is a standard tool for extracting a low-rank signal from noisy observations.
By Urte Adomaityte, Gabriele Sicuro, Pierpaolo Vivo
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...
By Chenghui Li, A. Martina Neuman
arXiv:2410. 09737v2 Announce Type: replace Abstract: A popular way to improve the expressive power of graph neural networks (GNNs) is to use Laplacian eigenvectors as additional node features, since they can serve both as structural identifiers and global coordinates of nodes.
By Junru Zhou, Cai Zhou, Xiyuan Wang, Pan Li, Muhan Zhang
arXiv:2505. 03649v4 Announce Type: replace-cross Abstract: Modeling of intricate relational patterns has become a cornerstone of contemporary statistical research and related data science fields.
By Bernardo Marenco, Paola Bermolen, Marcelo Fiori, Federico Larroca, Gonzalo Mateos