# USBD: Universal Structural Basis Distillation for Source-Free Graph Domain Adaptation

arXiv: https://arxiv.org/abs/2602.08431 · HTML: https://mlsanity.com/paper/2602.08431/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 64 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Builds on (most cited first, 30 of 46)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2002.08546/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Discovering Invariant Rationales for Graph Neural Networks](https://mlsanity.com/paper/2201.12872/) (2022)
- [Exploiting the Intrinsic Neighborhood Structure for Source-free Domain Adaptation](https://mlsanity.com/paper/2110.04202/) (2021)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [Accurate Learning of Graph Representations with Graph Multiset Pooling](https://mlsanity.com/paper/2102.11533/) (2021)
- [Source-free Domain Adaptation via Avatar Prototype Generation and Adaptation](https://mlsanity.com/paper/2106.15326/) (2021)
- [Out-Of-Distribution Generalization on Graphs: A Survey](https://mlsanity.com/paper/2202.07987/) (2022)
- [Attracting and Dispersing: A Simple Approach for Source-free Domain Adaptation](https://mlsanity.com/paper/2205.04183/) (2022)
- [Shift-Robust GNNs: Overcoming the Limitations of Localized Graph Training Data](https://mlsanity.com/paper/2108.01099/) (2021)
- [Source-Free Unsupervised Domain Adaptation: A Survey](https://mlsanity.com/paper/2301.00265/) (2022)
- [Empowering Graph Representation Learning with Test-Time Graph Transformation](https://mlsanity.com/paper/2210.03561/) (2022)
- [SAMGPT: Text-free Graph Foundation Model for Multi-domain Pre-training and Cross-domain Adaptation](https://mlsanity.com/paper/2502.05424/) (2025)
- [GOOD-D: On Unsupervised Graph Out-Of-Distribution Detection](https://mlsanity.com/paper/2211.04208/) (2022)
- [CoCo: A Coupled Contrastive Framework for Unsupervised Domain Adaptive Graph Classification](https://mlsanity.com/paper/2306.04979/) (2023)
- [Confidence May Cheat: Self-Training on Graph Neural Networks under Distribution Shift](https://mlsanity.com/paper/2201.11349/) (2022)
- [Path Neural Networks: Expressive and Accurate Graph Neural Networks](https://mlsanity.com/paper/2306.05955/) (2023)
- [Rethinking Propagation for Unsupervised Graph Domain Adaptation](https://mlsanity.com/paper/2402.05660/) (2024)
- [Source-Free Progressive Graph Learning for Open-Set Domain Adaptation](https://mlsanity.com/paper/2202.06174/) (2022)
- [LEAD: Learning Decomposition for Source-free Universal Domain Adaptation](https://mlsanity.com/paper/2403.03421/) (2024)
- [Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts](https://mlsanity.com/paper/2403.05026/) (2024)
- [SF(DA)2: Source-free Domain Adaptation Through the Lens of Data Augmentation](https://mlsanity.com/paper/2403.10834/) (2024)

## Built on by (most cited first, 9 of 9)

- [Modeling Higher-Order Brain Interactions via a Multi-View Information Bottleneck Framework for fMRI-based Psychiatric Diagnosis](https://mlsanity.com/paper/2604.17713/) (2026)
- [DSBD: Dual-Aligned Structural Basis Distillation for Graph Domain Adaptation](https://mlsanity.com/paper/2604.03154/) (2026)
- [Learning beyond Site Bias for OOD Generalization in Brain Networks](https://mlsanity.com/paper/2605.06050/) (2026)
- [BrainRiem: Riemannian Prototype Learning for Source-Free Cross-Site Brain Network Diagnosis](https://mlsanity.com/paper/2606.29200/) (2026)
- [MOLAR: Learning Multimodal Molecular Representations from Noisy Labels](https://mlsanity.com/paper/2606.18390/) (2026)
- [Safe-Subspace Pseudo-Label Refinement for Source-Free Graph Domain Adaptation](https://mlsanity.com/paper/2606.00808/) (2026)
- [Data-Efficient Agentic Graph Domain Adaptation via Reliability-Aware Prototype Learning](https://mlsanity.com/paper/2609.14045/) (2026)
- [Beyond Site Agreement: Re-estimation for Brain Network Generalization](https://mlsanity.com/paper/2609.34611/) (2026)
- [Learning Propagation Geometry from Message-Passing Feedback](https://mlsanity.com/paper/2609.34711/) (2026)

## Abstract (arXiv)

SF-GDA is pivotal for privacy-preserving knowledge transfer across graph datasets. Although recent works incorporate structural information, they implicitly condition adaptation on the smoothness priors of sourcetrained GNNs, thereby limiting their generalization to structurally distinct targets. This dependency becomes a critical bottleneck under significant topological shifts, where the source model misinterprets distinct topological patterns unseen in the source domain as noise, rendering pseudo-label-based adaptation unreliable. To overcome this limitation, we propose the Universal Structural Basis Distillation, a framework that shifts the paradigm from adapting a biased model to learning a universal structural basis for SF-GDA. Instead of adapting a biased source model to a specific target, our core idea is to construct a structure-agnostic basis that proactively covers the full spectrum of potential topological patterns. Specifically, USBD employs a bi-level optimization framework to distill the source dataset into a compact structural basis. By enforcing the prototypes to span the full Dirichlet energy spectrum, the learned basis explicitly captures diverse topological motifs, ranging from low-frequency clusters to high-frequency chains, beyond those present in the source. This ensures that the learned basis creates a comprehensive structural covering capable of handling targets with disparate structures. For inference, we introduce a spectral-aware ensemble mechanism that dynamically activates the optimal prototype combination based on the spectral fingerprint of the target graph. Extensive experiments on benchmarks demonstrate that USBD significantly outperforms state-of-the-art methods, particularly in scenarios with severe structural shifts, while achieving superior computational efficiency by decoupling the adaptation cost from the target data scale.