The paper investigates how alignment—both outer (choosing which graphs to pair) and inner (aligning node representatives)—affects permutation-equivariant graph flow matching. It connects inner alignment to transport on the graph quotient space and shows that quotient couplings can be lifted to aligned representatives, while symmetrization yields equivariant flow‑matching minimizers. Experiments on continuous graph and molecular generation demonstrate that appropriate alignment can simplify trajectories and improve few‑step generation, though the benefits vary with the type of alignment and computational budget.
By Moritz Piening, Christian Wald
arXiv:2601. 22107v2 Announce Type: replace Abstract: We introduce \textit{Prior-Informed Flow Matching (PIFM)}, a conditional flow model for graph reconstruction.
By Harvey Chen, Nicolas Zilberstein, Santiago Segarra
arXiv:2607. 04535v4 Announce Type: replace Abstract: Orthogonal and Stiefel constraints are widely used in neural network optimization to control weight geometry, improve conditioning, and stabilize signal propagation.
By Haiwen Yi, Xinyuan Song
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
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.
By Moritz Piening, Christian Wald
Continuous-time generative frameworks construct probability paths between base and target domains by optimizing time-dependent velocity fields. While theoretical targets favor straight trajectories, empirical networks develop complex path deformations.
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...
By Rongjian Liang, Zhuo Feng, Brucek Khailany
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:2606. 27455v1 Announce Type: cross Abstract: We address the problem of inferring a directed network from nodal measurements generated by linear diffusion dynamics on the sought graph.
By Rasoul Shafipour, Andrei Buciulea, Santiago Segarra, Antonio G. Marques, Gonzalo Mateos
The paper introduces Variational Bayesian Flow Network (VBFN), a graph generation model that lifts Bayesian updates to a joint Gaussian belief family with structured precisions, enabling coupled node and edge updates in a single fusion step. By constructing sample‑agnostic sparse precisions from a representation‑induced dependency graph, VBFN avoids label leakage while enforcing node‑edge consistency. Experiments on synthetic and molecular graph datasets show that VBFN improves fidelity and diversity over baseline methods.
By Yida Xiong, Jiameng Chen, Xiuwen Gong, Jia Wu, Shirui Pan, Wenbin Hu
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:2608. 11321v1 Announce Type: cross Abstract: We study spectral clustering in the presence of a confounding latent geometry.
By Konstantin Avrachenkov, Lucas S. Sibemberg, Alexander Van Werde