# Optimal Transport Graph Neural Networks

arXiv: https://arxiv.org/abs/2006.04804 · HTML: https://mlsanity.com/paper/2006.04804/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2020.

## Built on by (most cited first, 24 of 24)

- [Template based Graph Neural Network with Optimal Transport Distances](https://mlsanity.com/paper/2205.15733/) (2022)
- [Using Optimal Transport as Alignment Objective for fine-tuning Multilingual Contextualized Embeddings](https://mlsanity.com/paper/2110.02887/) (2021)
- [Fine-Tuning Graph Neural Networks via Graph Topology induced Optimal Transport](https://mlsanity.com/paper/2203.10453/) (2022)
- [Graph Classification by Mixture of Diverse Experts](https://mlsanity.com/paper/2103.15622/) (2021)
- [Fused Gromov-Wasserstein Graph Mixup for Graph-level Classifications](https://mlsanity.com/paper/2306.15963/) (2023)
- [Graph Classification via Reference Distribution Learning: Theory and Practice](https://mlsanity.com/paper/2408.11370/) (2024)
- [Weakly Supervised Anomaly Detection via Knowledge-Data Alignment](https://mlsanity.com/paper/2402.03785/) (2024)
- [Bi-level Contrastive Learning for Knowledge-Enhanced Molecule Representations](https://mlsanity.com/paper/2306.01631/) (2023)
- [Structure-Aware E(3)-Invariant Molecular Conformer Aggregation Networks](https://mlsanity.com/paper/2402.01975/) (2024)
- [EEGNN: Edge Enhanced Graph Neural Network with a Bayesian Nonparametric Graph Model](https://mlsanity.com/paper/2208.06322/) (2022)
- [Evaluating the diversity and utility of materials proposed by generative models](https://mlsanity.com/paper/2309.12323/) (2023)
- [Multiparameter Persistent Homology for Molecular Property Prediction](https://mlsanity.com/paper/2311.10808/) (2023)
- [Differentiable Cluster Graph Neural Network](https://mlsanity.com/paper/2405.16185/) (2024)
- [Gradual Domain Adaptation for Graph Learning](https://mlsanity.com/paper/2501.17443/) (2025)
- [Optimal Transport for Brain-Image Alignment: Unveiling Redundancy and Synergy in Neural Information Processing](https://mlsanity.com/paper/2503.10663/) (2025)
- [Graph Neural Network Surrogates of Fair Graph Filtering](https://mlsanity.com/paper/2303.08157/) (2023)
- [A Quasi-Wasserstein Loss for Learning Graph Neural Networks](https://mlsanity.com/paper/2310.11762/) (2023)
- [Cross-View Topology-Aware Graph Representation Learning](https://mlsanity.com/paper/2512.02130/) (2025)
- [Revealing Combinatorial Reasoning of GNNs via Graph Concept Bottleneck Layer](https://mlsanity.com/paper/2603.02025/) (2026)
- [Balanced Coarsening for Multilevel Hypergraph Partitioning via Wasserstein Discrepancy](https://mlsanity.com/paper/2106.07501/) (2021)
- [Structure-Sensitive Graph Dictionary Embedding for Graph Classification](https://mlsanity.com/paper/2306.10505/) (2023)
- [Semi-Supervised Image Captioning Considering Wasserstein Graph Matching](https://mlsanity.com/paper/2403.17995/) (2024)
- [Graph Residual based Method for Molecular Property Prediction](https://mlsanity.com/paper/2408.03342/) (2024)
- [DiagramRAG: A Lightweight Framework to Retrieve Scientific Diagram for Figure Generation](https://mlsanity.com/paper/2605.27931/) (2026)

## Abstract (arXiv)

Current graph neural network (GNN) architectures naively average or sum node embeddings into an aggregated graph representation -- potentially losing structural or semantic information. We here introduce OT-GNN, a model that computes graph embeddings using parametric prototypes that highlight key facets of different graph aspects. Towards this goal, we successfully combine optimal transport (OT) with parametric graph models. Graph representations are obtained from Wasserstein distances between the set of GNN node embeddings and ``prototype'' point clouds as free parameters. We theoretically prove that, unlike traditional sum aggregation, our function class on point clouds satisfies a fundamental universal approximation theorem. Empirically, we address an inherent collapse optimization issue by proposing a noise contrastive regularizer to steer the model towards truly exploiting the OT geometry. Finally, we outperform popular methods on several molecular property prediction tasks, while exhibiting smoother graph representations.