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Smoothness Really Matters: A Simple Yet Effective Approach for Unsupervised Graph Domain Adaptation

Wei Chen, Guo Ye, Yakun Wang, Zhao Zhang, Libang Zhang, Daixin Wang, Zhiqiang Zhang, Fuzhen Zhuang

TL;DR

This work tackles unsupervised graph domain adaptation by addressing structural distribution shifts that undermine GNN transfer. It introduces Target-Domain Structural Smoothing (TDSS), a simple, plug-and-play approach that applies Laplacian smoothing on the target graph via neighbor sampling to stabilize node representations and improve generalization. A formal bound shows the target risk depends on source risk, domain discrepancy, and model smoothness, motivating the focus on reducing the smoothing term Φ, especially in the target domain. Empirically, TDSS consistently surpasses state-of-the-art baselines across three real-world datasets and six transfer tasks, with random-walk smoothing delivering the strongest gains and robust performance across backbone GNNs.

Abstract

Unsupervised Graph Domain Adaptation (UGDA) seeks to bridge distribution shifts between domains by transferring knowledge from labeled source graphs to given unlabeled target graphs. Existing UGDA methods primarily focus on aligning features in the latent space learned by graph neural networks (GNNs) across domains, often overlooking structural shifts, resulting in limited effectiveness when addressing structurally complex transfer scenarios. Given the sensitivity of GNNs to local structural features, even slight discrepancies between source and target graphs could lead to significant shifts in node embeddings, thereby reducing the effectiveness of knowledge transfer. To address this issue, we introduce a novel approach for UGDA called Target-Domain Structural Smoothing (TDSS). TDSS is a simple and effective method designed to perform structural smoothing directly on the target graph, thereby mitigating structural distribution shifts and ensuring the consistency of node representations. Specifically, by integrating smoothing techniques with neighborhood sampling, TDSS maintains the structural coherence of the target graph while mitigating the risk of over-smoothing. Our theoretical analysis shows that TDSS effectively reduces target risk by improving model smoothness. Empirical results on three real-world datasets demonstrate that TDSS outperforms recent state-of-the-art baselines, achieving significant improvements across six transfer scenarios. The code is available in https://github.com/cwei01/TDSS.

Smoothness Really Matters: A Simple Yet Effective Approach for Unsupervised Graph Domain Adaptation

TL;DR

This work tackles unsupervised graph domain adaptation by addressing structural distribution shifts that undermine GNN transfer. It introduces Target-Domain Structural Smoothing (TDSS), a simple, plug-and-play approach that applies Laplacian smoothing on the target graph via neighbor sampling to stabilize node representations and improve generalization. A formal bound shows the target risk depends on source risk, domain discrepancy, and model smoothness, motivating the focus on reducing the smoothing term Φ, especially in the target domain. Empirically, TDSS consistently surpasses state-of-the-art baselines across three real-world datasets and six transfer tasks, with random-walk smoothing delivering the strongest gains and robust performance across backbone GNNs.

Abstract

Unsupervised Graph Domain Adaptation (UGDA) seeks to bridge distribution shifts between domains by transferring knowledge from labeled source graphs to given unlabeled target graphs. Existing UGDA methods primarily focus on aligning features in the latent space learned by graph neural networks (GNNs) across domains, often overlooking structural shifts, resulting in limited effectiveness when addressing structurally complex transfer scenarios. Given the sensitivity of GNNs to local structural features, even slight discrepancies between source and target graphs could lead to significant shifts in node embeddings, thereby reducing the effectiveness of knowledge transfer. To address this issue, we introduce a novel approach for UGDA called Target-Domain Structural Smoothing (TDSS). TDSS is a simple and effective method designed to perform structural smoothing directly on the target graph, thereby mitigating structural distribution shifts and ensuring the consistency of node representations. Specifically, by integrating smoothing techniques with neighborhood sampling, TDSS maintains the structural coherence of the target graph while mitigating the risk of over-smoothing. Our theoretical analysis shows that TDSS effectively reduces target risk by improving model smoothness. Empirical results on three real-world datasets demonstrate that TDSS outperforms recent state-of-the-art baselines, achieving significant improvements across six transfer scenarios. The code is available in https://github.com/cwei01/TDSS.

Paper Structure

This paper contains 21 sections, 1 theorem, 23 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation
  4. Methodology
  5. Target Domain Structural Smoothing
  6. Target Risk Bound with Model Smoothness
  7. Overall Optimization
  8. Experiment
  9. Experimental Setups
  10. Datasets
  11. Baselines
  12. Implementation Details
  13. Experiment Results
  14. Performance Comparison (RQ1)
  15. Results for Various GNNs (RQ2).
  16. ...and 6 more sections

Key Result

Theorem 1

Consider two distributions $\mathbb{S}$ and $\mathbb{T}$, if a model $f$ is $(k,2r)$-cover with $\Phi$ smoothness over distributions $\mathbb{S}$ and $\mathbb{T}$, then with probability at least $1- \xi$, the following holds: where and

Figures (4)

  • Figure 1: An example of GNNs sensitivity to similar inputs. Nodes have two features; green and red represent different classes. We assume the second feature determines node class: values $\leq 0.2$ are green, and values $> 0.2$ are red.
  • Figure 2: Classification Micro-F1 comparisons between TDSS variants on six cross-domain tasks.
  • Figure 3: The Micro-F1 performances of our TDSS w.r.t varying $\lambda$, $\gamma$, $\alpha$, and $\beta$ on different transfer tasks.
  • Figure 4: Visualization of learned node embedding on D $\to$ A for different models. We use Normalized Mutual Information (NMI) zhang2015evaluating to evaluate the clustering effect, with higher values indicating better performance.

Theorems & Definitions (3)

  • Theorem 1
  • proof
  • proof