The Flow has not summarised this story yet — read it at arXiv Machine Learning.
arXiv:2605. 22346v2 Announce Type: replace-cross Abstract: Two of the most widely used methods for analysing graph data, Adjacency Spectral Embedding and Laplacian Spectral Embedding, often produce different results when applied to the same graph.
arXiv:2601. 22107v2 Announce Type: replace Abstract: We introduce \textit{Prior-Informed Flow Matching (PIFM)}, a conditional flow model for graph reconstruction.
arXiv:2608. 04014v1 Announce Type: cross Abstract: The subdominant (minmax) ultrametric is a canonical tree-structured summary of a dissimilarity matrix, arising equivalently as the ultrametric induced by single-linkage clustering.
The paper introduces a moment-guided edge sampling framework that quantifies how local edge edits affect global graph structure using spectral moments of the random-walk transition matrix. Two complementary methods— a combinatorial closed‑form update for low‑order moments and a low‑rank approach exploiting locality and cyclic trace invariance— enable efficient computation of moment changes for single or batched edits. These moment changes serve as interpretable structural signatures, and preserving them is shown to retain key graph properties such as triangle‑weighted clustering, while also improving performance in supervised node classification and graph contrastive learning.
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.
arXiv:2511. 10234v3 Announce Type: replace-cross Abstract: While promising, graph reasoners based on Large Language Models (LLMs) lack built-in invariance to symmetries in graph representations.