Generative Modeling on Metric Graphs via Neural Optimal Transport

• URL: http://arxiv.org/abs/2606.16273v1
• Date: Mon, 15 Jun 2026 06:21:50 GMT
• Title: Generative Modeling on Metric Graphs via Neural Optimal Transport
• Abstract summary: We introduce, to our knowledge, the first deep generative modeling framework for distributions continuously supported on compact metric graphs.<n>Our method embeds the graph into a smooth ambient space, solves an entropic Kantorovich problem via a neural semidual parameterization.<n>We demonstrate scalability on real-world urban mobility data by our model on one million Uber pickup locations in Manhattan, New York City.
• Score: 40.19067516813213
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce, to our knowledge, the first deep generative modeling framework for probability distributions continuously supported on compact metric graphs. Given source and target measures on a metric graph, our method embeds the graph into a smooth ambient space, solves an entropic Kantorovich problem via a neural semidual parameterization, and projects generated samples back onto the original graph. We study two embedded geometries: an extrinsic Euclidean realization and the intrinsic tropical Abel--Jacobi embedding into the Jacobian torus. In both cases, the resulting generator is graph-supported by construction. We prove that, in the joint limit of increasing neural expressivity, the learned generator converges weakly to a valid transport coupling between the original graph measures. Empirically, across a range of geometrically distinct graphs, our method matches or improves upon heuristic transport baselines based on discrete graph OT, while scaling more favorably. Finally, we demonstrate scalability on real-world urban mobility data by training our model on one million Uber pickup locations in Manhattan, New York City.

Related papers

• Graph Transformer GANs with Graph Masked Modeling for Architectural Layout Generation [153.92387500677023]
  We present a novel graph Transformer generative adversarial network (GTGAN) to learn effective graph node relations. The proposed graph Transformer encoder combines graph convolutions and self-attentions in a Transformer to model both local and global interactions. We also propose a novel self-guided pre-training method for graph representation learning.
  arXiv  Detail & Related papers  (2024-01-15T14:36:38Z)
• Heterogeneous Graph Learning for Acoustic Event Classification [22.526665796655205]
  Graphs for audiovisual data are constructed manually which is difficult and sub-optimal. We develop a new model, heterogeneous graph crossmodal network (HGCN) that learns the crossmodal edges. Our proposed model can adapt to various spatial and temporal scales owing to its parametric construction, while the learnable crossmodal edges effectively connect the relevant nodes.
  arXiv  Detail & Related papers  (2023-03-05T13:06:53Z)
• Graph Generation with Diffusion Mixture [57.78958552860948]
  Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. We propose a generative framework that models the topology of graphs by explicitly learning the final graph structures of the diffusion process.
  arXiv  Detail & Related papers  (2023-02-07T17:07:46Z)
• GrannGAN: Graph annotation generative adversarial networks [72.66289932625742]
  We consider the problem of modelling high-dimensional distributions and generating new examples of data with complex relational feature structure coherent with a graph skeleton. The model we propose tackles the problem of generating the data features constrained by the specific graph structure of each data point by splitting the task into two phases. In the first it models the distribution of features associated with the nodes of the given graph, in the second it complements the edge features conditionally on the node features.
  arXiv  Detail & Related papers  (2022-12-01T11:49:07Z)
• Latent Graph Inference using Product Manifolds [0.0]
  We generalize the discrete Differentiable Graph Module (dDGM) for latent graph learning. Our novel approach is tested on a wide range of datasets, and outperforms the original dDGM model.
  arXiv  Detail & Related papers  (2022-11-26T22:13:06Z)
• Unveiling the Sampling Density in Non-Uniform Geometric Graphs [69.93864101024639]
  We consider graphs as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius. In a social network communities can be modeled as densely sampled areas, and hubs as nodes with larger neighborhood radius. We develop methods to estimate the unknown sampling density in a self-supervised fashion.
  arXiv  Detail & Related papers  (2022-10-15T08:01:08Z)
• Template based Graph Neural Network with Optimal Transport Distances [11.56532171513328]
  Current Graph Neural Networks (GNN) architectures rely on two important components: node features embedding through message passing, and aggregation with a specialized form of pooling. We propose in this work a novel point of view, which places distances to some learnable graph templates at the core of the graph representation. This distance embedding is constructed thanks to an optimal transport distance: the Fused Gromov-Wasserstein (FGW) distance.
  arXiv  Detail & Related papers  (2022-05-31T12:24:01Z)
• Optimal Transport Graph Neural Networks [31.191844909335963]
  Current graph neural network (GNN) architectures naively average or sum node embeddings into an aggregated graph representation. We introduce OT-GNN, a model that computes graph embeddings using parametric prototypes.
  arXiv  Detail & Related papers  (2020-06-08T14:57:39Z)
• Wasserstein-based Graph Alignment [56.84964475441094]
  We cast a new formulation for the one-to-many graph alignment problem, which aims at matching a node in the smaller graph with one or more nodes in the larger graph. We show that our method leads to significant improvements with respect to the state-of-the-art algorithms for each of these tasks.
  arXiv  Detail & Related papers  (2020-03-12T22:31:59Z)
• Block-Approximated Exponential Random Graphs [77.4792558024487]
  An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large graphs. We propose an approximative framework to such non-trivial ERGs that result in dyadic independence (i.e., edge independent) distributions. Our methods are scalable to sparse graphs consisting of millions of nodes.
  arXiv  Detail & Related papers  (2020-02-14T11:42:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.