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.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.
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.
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.
arXiv:2606.23489v2 Announce Type: replace-cross Abstract: Meshes are among the most common 3D scene representations, but directly generating meshes is challenging because the representation contains...
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:2601. 22107v2 Announce Type: replace Abstract: We introduce \textit{Prior-Informed Flow Matching (PIFM)}, a conditional flow model for graph reconstruction.
arXiv:2608. 12010v1 Announce Type: new Abstract: Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields.