arXiv Machine Learning

Balancing Symmetry and Efficiency in Graph Flow Matching

arXiv:2602. 18084v2 Announce Type: replace Abstract: Equivariance is central to graph generative models, as it ensures the model respects the permutation symmetry of graphs.

arXiv Machine Learning
4d ago

Alignment Matters Inside and Out in Equivariant Graph Flow Matching

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 Machine Learning
1d ago

CrossGMN: Graph Metanetworks for Cross-Architecture Weight-Space Transformations

CrossGMN introduces a graph metanetwork that processes a trained source network and an initialized target network simultaneously, enabling equivariant cross‑architecture weight‑space transformations. By preserving symmetry through cross‑network message passing, CrossGMN can refine target network initializations while remaining invariant to source permutations and equivariant to target permutations. Experiments demonstrate that CrossGMN accelerates knowledge distillation, transfers across datasets without retraining, and unifies compression from diverse source architectures into a common target architecture.

By Adir Dayan, Yam Eitan, Haggai Maron
arXiv Machine Learning
Aug 28

Gromov-Monge Flow Matching for Equivariant Graph Generation

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
arXiv AI
Sep 16

GraphIFE: Rethinking Graph Imbalance Node Classification via Invariant Learning

GraphIFE addresses the class imbalance problem in graph-structured data by tackling a quality inconsistency issue in synthesized nodes. The framework uses graph invariant learning to strengthen embedding space representations and identify invariant features, leading to improved performance on minority classes. Experiments show that GraphIFE consistently outperforms various baselines across multiple datasets.

By Fanlong Zeng, Wensheng Gan, Kangjie Chen, Philip S. Yu
Hugging Face Trending Papers
Aug 12

Reducing Symmetry Increase in Equivariant Neural Networks

Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields. Despite their remarkable capacity for representing geometric structures, ENNs suffer from degraded expressivity when processing symmetric inputs: the output representations are invariant to transformations that extend beyond the input's symmetries.