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

Yingxu Wang, Kunyu Zhang, Mengzhu Wang, Siyang Gao, Nan Yin

TL;DR

USBD reframes source-free graph domain adaptation by distilling source knowledge into a compact set of prototypes that span the entire Dirichlet energy spectrum. A bi-level optimization constructs a universal structural basis, while a spectral-aware inference module activates prototypes according to the target's spectral fingerprint, enabling instant, target-specific adaptation without retraining. The approach provides theoretical universality guarantees and generalization bounds, and empirical results show strong robustness across structure, feature, and correlation shifts with improved efficiency. This universal-basis perspective offers a principled, privacy-preserving path to robust graph transfer learning in settings with limited or no access to source data.

Abstract

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.

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

TL;DR

USBD reframes source-free graph domain adaptation by distilling source knowledge into a compact set of prototypes that span the entire Dirichlet energy spectrum. A bi-level optimization constructs a universal structural basis, while a spectral-aware inference module activates prototypes according to the target's spectral fingerprint, enabling instant, target-specific adaptation without retraining. The approach provides theoretical universality guarantees and generalization bounds, and empirical results show strong robustness across structure, feature, and correlation shifts with improved efficiency. This universal-basis perspective offers a principled, privacy-preserving path to robust graph transfer learning in settings with limited or no access to source data.

Abstract

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.
Paper Structure (38 sections, 2 theorems, 12 equations, 11 figures, 18 tables, 1 algorithm)

This paper contains 38 sections, 2 theorems, 12 equations, 11 figures, 18 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Problem Formulation
  5. Overview of USBD
  6. Universal Structural Basis Distillation
  7. Universal Basis Condensation Formulation.
  8. Semantic Fidelity via Meta-Matching.
  9. Spectral and Structural Regularization.
  10. Theoretical Guarantee of Universality.
  11. Spectral-Aware Adaptive Inference
  12. Target Spectral Fingerprinting.
  13. Spectral-Weighted Basis Activation.
  14. Adaptive Prediction.
  15. Generalization Bound Analysis.
  16. ...and 23 more sections

Key Result

theorem 1

Let $\mathcal{H}_{\text{spec}} = [0, E_{\max}]$ be the bounded spectral domain of valid Dirichlet energies. Assume the synthesized basis $\mathcal{S}_{syn} = \{G_k\}_{k=1}^K$ is optimized such that the spectral coverage loss $\mathcal{L}_{\text{span}}$ converges to zero. Let the anchors $\{\mu_k\}_{ where $\epsilon$ is the optimization residual.

Figures (11)

  • Figure 1: The key challenges in SF-GDA. (a) Unobservability of structural shifts arises from missing source data, where source model fails to represent OOD target patterns. (b) The spectral bias dilemma: GNN low-pass filters remove necessary high-frequency signals, leading to a self-reinforcing error loop. (c) The efficiency-universality trade-off highlights the difficulty of handling arbitrary target structures without high computational costs during deployment.
  • Figure 2: Proposed USBD comprises two stages: (a) Universal Structural Basis Distillation: A bi-level optimization framework distills source knowledge into compact synthetic prototypes spanning the full Dirichlet energy spectrum to capture diverse topological motifs beyond the source domain. (b) Spectral-Aware Adaptive Inference: The module identifies the target spectral fingerprint and dynamically activates optimal basis combinations of the learned prototypes for instant adaptation.
  • Figure 3: Comparison of time and GPU consumption between baseline methods and USBD during the adaptation stage.
  • Figure 4: T-SNE visualizations on M2 of the Mutagenicity dataset for USBD and baselines trained/adapted on M0$\rightarrow$M1.
  • Figure 5: Sensitivity analysis of the number of synthetic bases $K$ and balance coefficient ($\lambda_1$, $\lambda_2$) on the Mutagenicity dataset.
  • ...and 6 more figures

Theorems & Definitions (2)

  • theorem 1: Universal Spectral Covering Property
  • theorem 2: Generalization Bound via Universal Covering