The paper introduces Bayesian matrix-valued graphs (BMVG), where each edge is represented by a symmetric positive-definite matrix instead of a scalar weight, allowing the capture of direction-dependent interactions in scientific graphs. Using the affine-invariant Riemannian metric, BMVG quantifies deformation magnitude and signed directions of edge changes across contexts, and demonstrates competitive performance against existing methods in precision recovery and structural change detection. Experiments on weather data and TCGA-BRCA gene networks show that BMVG can reveal context-dependent reconfigurations in spatial coupling and gene-module interactions.
Many scientific graphs attach several variables to each node, so a single scalar edge weight cannot describe direction-dependent interactions. We model each edge by a symmetric positive-definite (SPD)...
arXiv:2608. 04460v1 Announce Type: cross Abstract: The quantitative analysis of 3D neuronal morphologies requires capturing both graph topology and spatial geometry.
arXiv:2607. 20896v1 Announce Type: new Abstract: Spatial transcriptomics assays remain costly and technically demanding, restricting transcriptome-wide profiling to specialist settings and preventing routine clinical deployment.
arXiv:2604.02535v2 Announce Type: replace Abstract: Dimensionality reduction (DR) involves two longstanding trade-offs. First, preserving local neighborhoods can come at the cost of global structure....
arXiv:2507.23559v2 Announce Type: replace-cross Abstract: Certain data are naturally modeled by networks or weighted graphs, be they biological networks or mobility networks. When there is no canonic...
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 Gromov-Monge Flow Matching, a method that incorporates permutation-equivariance into generative graph models by aligning graph pairs up to node relabeling using the Gromov–Monge distance. It shows theoretically that quotient couplings can be lifted to aligned representatives without extra cost and that symmetrization yields equivariant flow-matching minimizers, even for categorical endpoints. Practically, the authors build minibatch couplings with Gromov–Wasserstein relaxations and optional outer assignments, improving sample quality in continuous graph and categorical molecular generation while remaining compatible with standard equivariant architectures.
arXiv:2606. 08258v1 Announce Type: cross Abstract: Understanding and comparing structures in scalar fields is a central challenge in scientific visualization, with applications ranging from feature analysis to temporal and structural comparison.
arXiv:2607. 22381v1 Announce Type: new Abstract: Curvature notions on graphs, particularly Ollivier-Ricci and Forman, have emerged as powerful tools for addressing fundamental issues in Graph Neural Networks (GNNs) such as oversmoothing and oversquashing, but rely almost exclusively on local edge-level comparisons and therefore fail to certify how information actually propagates over long distances.
arXiv:2511. 03170v3 Announce Type: replace-cross Abstract: The quantitative structure-activity relationship assumes a smooth mapping between molecular structure and biological activity.
arXiv:2608. 15306v1 Announce Type: cross Abstract: High-throughput single-cell and spatial transcriptomic technologies provide high-resolution snapshots of heterogeneous cellular states, but their destructive nature prevents repeated measurements of the same cells over time.
arXiv:2407. 07357v3 Announce Type: replace Abstract: Predicting signed interactions in biological networks is crucial for understanding drug mechanisms and facilitating drug repurposing.