# Pave Your Own Path: Graph Gradual Domain Adaptation on Fused Gromov-Wasserstein Geodesics

arXiv: https://arxiv.org/abs/2505.12709 · HTML: https://mlsanity.com/paper/2505.12709/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 67 of its 98 references that are in the map.
- First posted on arXiv 19 May 2025.

## Builds on (most cited first, 30 of 67)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Return of Frustratingly Easy Domain Adaptation](https://mlsanity.com/paper/1511.05547/) (2015)
- [Bridging Theory and Algorithm for Domain Adaptation](https://mlsanity.com/paper/1904.05801/) (2019)
- [Unsolved Problems in ML Safety](https://mlsanity.com/paper/2109.13916/) (2021)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [DLOW: Domain Flow for Adaptation and Generalization](https://mlsanity.com/paper/1812.05418/) (2018)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Understanding Self-Training for Gradual Domain Adaptation](https://mlsanity.com/paper/2002.11361/) (2020)
- [G-Mixup: Graph Data Augmentation for Graph Classification](https://mlsanity.com/paper/2202.07179/) (2022)
- [Contextual Stochastic Block Models](https://mlsanity.com/paper/1807.09596/) (2018)
- [Progressive Domain Adaptation for Object Detection](https://mlsanity.com/paper/1910.11319/) (2019)
- [Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matching](https://mlsanity.com/paper/1905.07645/) (2019)
- [Out-Of-Distribution Generalization on Graphs: A Survey](https://mlsanity.com/paper/2202.07987/) (2022)
- [Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties](https://mlsanity.com/paper/1811.02834/) (2018)
- [Transfer Learning of Graph Neural Networks with Ego-graph Information Maximization](https://mlsanity.com/paper/2009.05204/) (2020)
- [Discrete-state Continuous-time Diffusion for Graph Generation](https://mlsanity.com/paper/2405.11416/) (2024)
- [Graph Transfer Learning via Adversarial Domain Adaptation with Graph Convolution](https://mlsanity.com/paper/1909.01541/) (2019)
- [Low-Rank Sinkhorn Factorization](https://mlsanity.com/paper/2103.04737/) (2021)
- [Empowering Graph Representation Learning with Test-Time Graph Transformation](https://mlsanity.com/paper/2210.03561/) (2022)
- [GOT: An Optimal Transport framework for Graph comparison](https://mlsanity.com/paper/1906.02085/) (2019)
- [Debiased Self-Training for Semi-Supervised Learning](https://mlsanity.com/paper/2202.07136/) (2022)
- [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)
- [Structural Re-weighting Improves Graph Domain Adaptation](https://mlsanity.com/paper/2306.03221/) (2023)

## Built on by (most cited first, 17 of 17)

- [Quantization Meets dLLMs: A Systematic Study of Post-training Quantization for Diffusion LLMs](https://mlsanity.com/paper/2508.14896/) (2025)
- [Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting](https://mlsanity.com/paper/2505.18442/) (2025)
- [PLANETALIGN: A Comprehensive Python Library for Benchmarking Network Alignment](https://mlsanity.com/paper/2505.21366/) (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)
- [Graph Data Selection for Domain Adaptation: A Model-Free Approach](https://mlsanity.com/paper/2505.17293/) (2025)
- [Subspace Alignment for Vision-Language Model Test-time Adaptation](https://mlsanity.com/paper/2601.08139/) (2026)
- [Mixture of Sequence: Theme-Aware Mixture-of-Experts for Long-Sequence Recommendation](https://mlsanity.com/paper/2604.20858/) (2026)
- [Predict, Don't Iterate: Efficient Adaptive-Length Infilling for Diffusion Language Models](https://mlsanity.com/paper/2609.02108/) (2026)
- [Continual Low-Rank Adapters for LLM-based Generative Recommender Systems](https://mlsanity.com/paper/2510.25093/) (2025)
- [Saffron-1: Safety Inference Scaling](https://mlsanity.com/paper/2506.06444/) (2025)
- [Graph homophily booster: Reimagining the role of discrete features in heterophilic graph learning](https://mlsanity.com/paper/2602.07256/) (2026)
- [ReMix: Reinforcement routing for mixtures of LoRAs in LLM finetuning](https://mlsanity.com/paper/2603.10160/) (2026)
- [AvAtar: Learning to Align via Active Optimal Transport](https://mlsanity.com/paper/2605.24395/) (2026)
- [Rethinking the Flow-Based Gradual Domain Adaptation: A Semi-Dual Optimal Transport Perspective](https://mlsanity.com/paper/2602.01179/) (2026)
- [Structuring and Tokenizing Distributed User Interest Context for Generative Recommendation](https://mlsanity.com/paper/2606.20554/) (2026)
- [Data-Efficient Agentic Graph Domain Adaptation via Reliability-Aware Prototype Learning](https://mlsanity.com/paper/2609.14045/) (2026)

## Abstract (arXiv)

Graph neural networks, despite their impressive performance, are highly vulnerable to distribution shifts on graphs. Existing graph domain adaptation (graph DA) methods often implicitly assume a mild shift between source and target graphs, limiting their applicability to real-world scenarios with large shifts. Gradual domain adaptation (GDA) has emerged as a promising approach for addressing large shifts by gradually adapting the source model to the target domain via a path of unlabeled intermediate domains. Existing GDA methods exclusively focus on independent and identically distributed (IID) data with a predefined path, leaving their extension to non-IID graphs without a given path an open challenge. To bridge this gap, we present Gadget, the first GDA framework for non-IID graph data. First (theoretical foundation), the Fused Gromov-Wasserstein (FGW) distance is adopted as the domain discrepancy for non-IID graphs, based on which, we derive an error bound on node, edge and graph-level tasks, showing that the target domain error is proportional to the length of the path. Second (optimal path), guided by the error bound, we identify the FGW geodesic as the optimal path, which can be efficiently generated by our proposed algorithm. The generated path can be seamlessly integrated with existing graph DA methods to handle large shifts on graphs, improving state-of-the-art graph DA methods by up to 6.8% in accuracy on real-world datasets.