# Hierarchical Multi-Marginal Optimal Transport for Network Alignment

arXiv: https://arxiv.org/abs/2310.04470 · HTML: https://mlsanity.com/paper/2310.04470/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 74 references that are in the map.
- First posted on arXiv 6 Oct 2023.

## Builds on (most cited first, 30 of 32)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Learning Latent Permutations with Gumbel-Sinkhorn Networks](https://mlsanity.com/paper/1802.08665/) (2018)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Gromov-Wasserstein Learning for Graph Matching and Node Embedding](https://mlsanity.com/paper/1901.06003/) (2019)
- [Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matching](https://mlsanity.com/paper/1905.07645/) (2019)
- [Graph Optimal Transport for Cross-Domain Alignment](https://mlsanity.com/paper/2006.14744/) (2020)
- [HDMI: High-order Deep Multiplex Infomax](https://mlsanity.com/paper/2102.07810/) (2021)
- [Low-Rank Sinkhorn Factorization](https://mlsanity.com/paper/2103.04737/) (2021)
- [GOT: An Optimal Transport framework for Graph comparison](https://mlsanity.com/paper/1906.02085/) (2019)
- [Linear-Time Gromov Wasserstein Distances using Low Rank Couplings and Costs](https://mlsanity.com/paper/2106.01128/) (2021)
- [Wasserstein Embedding for Graph Learning](https://mlsanity.com/paper/2006.09430/) (2020)
- [Regularized Discrete Optimal Transport](https://mlsanity.com/paper/1307.5551/) (2013)
- [Multi-marginal optimal transport: theory and applications](https://mlsanity.com/paper/1406.0026/) (2014)
- [REGAL: Representation Learning-based Graph Alignment](https://mlsanity.com/paper/1802.06257/) (2018)
- [Online Graph Dictionary Learning](https://mlsanity.com/paper/2102.06555/) (2021)
- [KompaRe: A Knowledge Graph Comparative Reasoning System](https://mlsanity.com/paper/2011.03189/) (2020)
- [Unsupervised Hyperalignment for Multilingual Word Embeddings](https://mlsanity.com/paper/1811.01124/) (2018)
- [COPT: Coordinated Optimal Transport for Graph Sketching](https://mlsanity.com/paper/2003.03892/) (2020)
- [Wasserstein-Fisher-Rao Embedding: Logical Query Embeddings with Local Comparison and Global Transport](https://mlsanity.com/paper/2305.04034/) (2023)
- [On the complexity of the optimal transport problem with graph-structured cost](https://mlsanity.com/paper/2110.00627/) (2021)
- [COIN: Co-Cluster Infomax for Bipartite Graphs](https://mlsanity.com/paper/2206.00006/) (2022)
- [STERLING: Synergistic Representation Learning on Bipartite Graphs](https://mlsanity.com/paper/2302.05428/) (2023)
- [Wasserstein-based Graph Alignment](https://mlsanity.com/paper/2003.06048/) (2020)
- [Multi-Marginal Gromov-Wasserstein Transport and Barycenters](https://mlsanity.com/paper/2205.06725/) (2022)
- [Solving graph compression via optimal transport](https://mlsanity.com/paper/1905.12158/) (2019)
- [A Relaxed Matching Procedure for Unsupervised BLI](https://mlsanity.com/paper/2010.07095/) (2020)
- [FGOT: Graph Distances based on Filters and Optimal Transport](https://mlsanity.com/paper/2109.04442/) (2021)
- [Semi-Supervised Bilingual Lexicon Induction with Two-way Interaction](https://mlsanity.com/paper/2010.07101/) (2020)
- [Supervised Optimal Transport](https://mlsanity.com/paper/2206.13410/) (2022)

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

- [Quantization Meets dLLMs: A Systematic Study of Post-training Quantization for Diffusion LLMs](https://mlsanity.com/paper/2508.14896/) (2025)
- [SelfElicit: Your Language Model Secretly Knows Where is the Relevant Evidence](https://mlsanity.com/paper/2502.08767/) (2025)
- [Pave Your Own Path: Graph Gradual Domain Adaptation on Fused Gromov-Wasserstein Geodesics](https://mlsanity.com/paper/2505.12709/) (2025)
- [PyG-SSL: A Graph Self-Supervised Learning Toolkit](https://mlsanity.com/paper/2412.21151/) (2024)
- [Can Graph Neural Networks Learn Language with Extremely Weak Text Supervision?](https://mlsanity.com/paper/2412.08174/) (2024)
- [APEX2: Adaptive and Extreme Summarization for Personalized Knowledge Graphs](https://mlsanity.com/paper/2412.17336/) (2024)
- [Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting](https://mlsanity.com/paper/2505.18442/) (2025)
- [Causality-Aware Spatiotemporal Graph Neural Networks for Spatiotemporal Time Series Imputation](https://mlsanity.com/paper/2403.11960/) (2024)
- [Joint Optimal Transport and Embedding for Network Alignment](https://mlsanity.com/paper/2502.19334/) (2025)
- [PLANETALIGN: A Comprehensive Python Library for Benchmarking Network Alignment](https://mlsanity.com/paper/2505.21366/) (2025)
- [Hierarchical LoRA MoE for Efficient CTR Model Scaling](https://mlsanity.com/paper/2510.10432/) (2025)
- [Harnessing Consistency for Robust Test-Time LLM Ensemble](https://mlsanity.com/paper/2510.13855/) (2025)
- [Prune as You Generate: Online Rollout Pruning for Faster and Better RLVR](https://mlsanity.com/paper/2603.24840/) (2026)
- [AIM: Attributing, Interpreting, Mitigating Data Unfairness](https://mlsanity.com/paper/2406.08819/) (2024)
- [InterFormer: Effective Heterogeneous Interaction Learning for Click-Through Rate Prediction](https://mlsanity.com/paper/2411.09852/) (2024)
- [Graph Data Selection for Domain Adaptation: A Model-Free Approach](https://mlsanity.com/paper/2505.17293/) (2025)
- [Optimizing Distributional Geometry Alignment with Optimal Transport for Generative Dataset Distillation](https://mlsanity.com/paper/2512.00308/) (2025)
- [Predict, Don't Iterate: Efficient Adaptive-Length Infilling for Diffusion Language Models](https://mlsanity.com/paper/2609.02108/) (2026)
- [Fine-grained Graph Rationalization](https://mlsanity.com/paper/2312.07859/) (2023)
- [Graph homophily booster: Reimagining the role of discrete features in heterophilic graph learning](https://mlsanity.com/paper/2602.07256/) (2026)
- [AvAtar: Learning to Align via Active Optimal Transport](https://mlsanity.com/paper/2605.24395/) (2026)
- [Geometry-Aware Dataset Condensation for Diffusion Model Training](https://mlsanity.com/paper/2606.05883/) (2026)
- [Emotion-Cause Pair Extraction in Conversations via Semantic Decoupling and Graph Alignment](https://mlsanity.com/paper/2604.19547/) (2026)
- [Revisiting On-policy Adversarial Black-Box Distillation: Calibrating Groupwise Reward Geometry for Effective Advantage Construction](https://mlsanity.com/paper/2609.39757/) (2026)

## Abstract (arXiv)

Finding node correspondence across networks, namely multi-network alignment, is an essential prerequisite for joint learning on multiple networks. Despite great success in aligning networks in pairs, the literature on multi-network alignment is sparse due to the exponentially growing solution space and lack of high-order discrepancy measures. To fill this gap, we propose a hierarchical multi-marginal optimal transport framework named HOT for multi-network alignment. To handle the large solution space, multiple networks are decomposed into smaller aligned clusters via the fused Gromov-Wasserstein (FGW) barycenter. To depict high-order relationships across multiple networks, the FGW distance is generalized to the multi-marginal setting, based on which networks can be aligned jointly. A fast proximal point method is further developed with guaranteed convergence to a local optimum. Extensive experiments and analysis show that our proposed HOT achieves significant improvements over the state-of-the-art in both effectiveness and scalability.