DSBD: Dual-Aligned Structural Basis Distillation for Graph Domain Adaptation

Yingxu Wang; Kunyu Zhang; Jiaxin Huang; Mengzhu Wang; Mingyan Xiao; Siyang Gao; Nan Yin

cs.LGApr 3, 2026

DSBD: Dual-Aligned Structural Basis Distillation for Graph Domain Adaptation

Authors: Yingxu Wang, Kunyu Zhang, Jiaxin Huang, Mengzhu Wang, Mingyan Xiao, Siyang Gao, Nan Yin

Organizations: Zhengzhou University · The Hebei University of Technology · California State Polytechnic University · The City University of Hong Kong

Abstract

Graph domain adaptation (GDA) aims to transfer knowledge from a labeled source graph to an unlabeled target graph under distribution shifts. However, existing methods are largely feature-centric and overlook structural discrepancies, which become particularly detrimental under significant topology shifts. Such discrepancies alter both geometric relationships and spectral properties, leading to unreliable transfer of graph neural networks (GNNs). To address this limitation, we propose Dual-Aligned Structural Basis Distillation (DSBD) for GDA, a novel framework that explicitly models and adapts cross-domain structural variation. DSBD constructs a differentiable structural basis by synthesizing continuous probabilistic prototype graphs, enabling gradient-based optimization over graph topology. The basis is learned under source-domain supervision to preserve semantic discriminability, while being explicitly aligned to the target domain through a dual-alignment objective. Specifically, geometric consistency is enforced via permutation-invariant topological moment matching, and spectral consistency is achieved through Dirichlet energy calibration, jointly capturing structural characteristics across domains. Furthermore, we introduce a decoupled inference paradigm that mitigates source-specific structural bias by training a new GNN on the distilled structural basis. Extensive experiments on graph and image benchmarks demonstrate that DSBD consistently outperforms state-of-the-art methods.

Figures & tables

Figure 1. The key challenges in GDA: (a) The lack of a differentiable structural substrate prevents explicit optimization of cross-domain topology. (b) Geometric alignment does not guarantee spectral consistency, leading to mismatched GNN filtering across domains. (c) Source-specific structural bias entangles message passing, resulting in aggregation mismatch under topology shift.

Figure 2. Overview of the proposed DSBD, which consists of two key steps: (1) Dual-Aligned Structural Basis Distillation, which constructs a differentiable structural substrate by distilling source knowledge into compact synthetic graphs and enforcing joint geometric and spectral alignment with the target domain; (2) Structurally Calibrated Target Inference, which eliminates source structural bias via decoupled retraining on the distilled basis, ensuring topology-aware transfer under domain shift.

Methods	MNIST				CIFAR-10
Methods	S0 $\rightarrow$ S1	S1 $\rightarrow$ S0	S0 $\rightarrow$ S2	S2 $\rightarrow$ S0	C0 $\rightarrow$ C1	C1 $\rightarrow$ C0	C0 $\rightarrow$ C2	C2 $\rightarrow$ C0
G-CRD	48.34 $\pm 2.5$	49.12 $\pm 2.4$	38.45 $\pm 2.1$	47.55 $\pm 2.0$	25.34 $\pm 1.9$	30.45 $\pm 2.1$	27.12 $\pm 2.2$	29.45 $\pm 2.5$
MuGSI	45.12 $\pm 3.2$	45.67 $\pm 3.1$	35.12 $\pm 3.5$	43.12 $\pm 3.0$	22.11 $\pm 2.6$	27.12 $\pm 3.1$	24.33 $\pm 2.8$	26.11 $\pm 2.7$
TGS	49.88 $\pm 1.8$	51.22 $\pm 1.9$	39.56 $\pm 2.2$	48.66 $\pm 2.4$	26.55 $\pm 1.6$	31.55 $\pm 1.8$	28.45 $\pm 1.9$	30.55 $\pm 2.1$
LAD-GNN	51.45 $\pm 2.1$	52.88 $\pm 2.3$	42.10 $\pm 1.9$	50.12 $\pm 2.1$	28.12 $\pm 1.7$	33.22 $\pm 2.0$	30.15 $\pm 2.1$	32.12 $\pm 1.9$
AdaGMLP	47.22 $\pm 2.7$	48.34 $\pm 2.6$	36.78 $\pm 3.1$	46.33 $\pm 2.5$	24.55 $\pm 2.4$	29.66 $\pm 2.8$	26.55 $\pm 2.6$	28.33 $\pm 2.9$

Table 1. The image classification results (in %) under edge density domain shifts (source

\rightarrow

target) on the MNIST and CIFAR-10 datasets. Bold results indicate the best performance.

Methods	Node Shift			Edge Shift			Corr. Shift		Feature Shift
Methods	M0 $\rightarrow$ M1	M0 $\rightarrow$ M2	M0 $\rightarrow$ M3	M0 $\rightarrow$ M1	M0 $\rightarrow$ M2	M0 $\rightarrow$ M3	S $\rightarrow$ SB	SB $\rightarrow$ S	P $\rightarrow$ D	D $\rightarrow$ P	C $\rightarrow$ CM	CM $\rightarrow$ C	B $\rightarrow$ BM	BM $\rightarrow$ B
G-CRD	60.4 $\pm 0.5$	55.3 $\pm 1.1$	59.6 $\pm 3.2$	73.7 $\pm 0.6$	55.3 $\pm 1.0$	58.4 $\pm 2.5$	52.8 $\pm 2.4$	53.1 $\pm 2.5$	60.7 $\pm 1.4$	71.4 $\pm 1.2$	58.7 $\pm 1.5$	71.8 $\pm 1.6$	63.8 $\pm 1.9$	83.9 $\pm 1.1$
MuGSI	45.3 $\pm 2.4$	48.6 $\pm 3.1$	56.2 $\pm 2.0$	59.8 $\pm 2.5$	55.4 $\pm 2.9$	54.2 $\pm 2.1$	49.5 $\pm 3.2$	50.2 $\pm 2.8$	57.5 $\pm 2.2$	70.1 $\pm 1.9$	55.9 $\pm 2.4$	69.4 $\pm 1.8$	61.8 $\pm 2.1$	80.5 $\pm 2.0$
TGS	53.8 $\pm 1.8$	58.2 $\pm 1.6$	50.7 $\pm 2.5$	66.4 $\pm 1.8$	63.2 $\pm 2.1$	52.8 $\pm 2.1$	50.4 $\pm 2.6$	52.5 $\pm 2.4$	59.1 $\pm 1.6$	68.7 $\pm 1.5$	57.2 $\pm 1.9$	68.1 $\pm 2.3$	65.2 $\pm 1.8$	82.1 $\pm 1.4$
LAD-GNN	58.5 $\pm 2.3$	62.4 $\pm 2.8$	53.6 $\pm 1.7$	71.2 $\pm 2.1$	72.5 $\pm 1.7$	51.4 $\pm 1.9$	51.9 $\pm 2.8$	54.0 $\pm 2.2$	59.5 $\pm 1.8$	71.8 $\pm 1.4$	56.5 $\pm 2.1$	72.3 $\pm 1.5$	64.9 $\pm 2.0$	81.8 $\pm 1.7$
AdaGMLP	51.2 $\pm 1.9$	42.8 $\pm 1.4$	55.3 $\pm 2.1$	62.1 $\pm 2.4$	58.9 $\pm 2.4$	55.6 $\pm 2.2$	49.2 $\pm 2.5$	50.9 $\pm 2.1$	55.2 $\pm 2.3$	66.9 $\pm 2.1$	53.8 $\pm 2.5$	67.5 $\pm 2.0$	60.1 $\pm 2.4$	78.6 $\pm 2.2$

Table 2. Graph classification results (in %) under node and edge density domain shifts on the Mutagenicity dataset, and under correlation shifts (Corr. Shift) and feature shifts (source

\rightarrow

target). S, SB, P, D, C, CM, B, and BM denote Spurious-Motif, Spurious-Motif_bias, PROTEINS, DD, COX2, COX2_MD, BZR, and BZR_MD, respectively. Bold indicates the best performance.

Panel of Figure 3 — Figure 3. T-SNE visualizations on the Mutagenicity dataset for DSBD and baselines.

Methods	M0 $\rightarrow$ M1	M1 $\rightarrow$ M0	M0 $\rightarrow$ M2	M2 $\rightarrow$ M0	M0 $\rightarrow$ M3	M3 $\rightarrow$ M0
DSBD w/o SE	64.2	61.5	65.8	50.3	53.4	54.2
DSBD w/o SP	71.5	68.1	74.2	55.6	56.5	60.1
DSBD w/o GE	69.5	66.4	71.6	53.8	54.2	57.1
DSBD w/o TG	72.4	70.6	73.9	57.1	58.6	62.3
DSBD	76.5	72.3	79.1	59.4	60.8	64.5

Table 3. The results of ablation studies on the Mutagenicity dataset. Bold results indicate the best performance.

Panel of Figure 4 — Figure 4. Sensitivity analysis of the number of synthetic bases $K$ and balance coefficient ( $\lambda_{1}$ , $\lambda_{2}$ ) on the Mutagenicity dataset.

Figure 5. Distribution of Dirichlet energy and graph density of distilled basis between DSBD and baselines.

Panel of Figure 6 — Figure 6. Visualizations of the distilled basis of DSBD with different Dirichlet energy $\Omega$ .

Appendix figures & tables22 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7. Visualization of domain shifts across different types. (a) Node distribution shift between sub-datasets of FRANKENSTEIN. (b) Edge distribution shift between sub-datasets of FRANKENSTEIN. (c) Feature distribution shift between PROTEINS and DD datasets.

Datasets	Graphs	Avg. Nodes	Avg. Edges	Classes
PROTEINS	1,113	39.1	72.8	2
NCI1	4,110	29.87	32.30	2
Mutagenicity	4,337	30.32	30.77	2
FRANKENSTEIN	4,337	16.9	17.88	2
ogbg-molhiv	41,127	25.5	27.5	2
CIFAR10	60,000	117.6	941.2	10

Appendix

Table 4. Statistics of the experimental datasets.

Panel of Figure 8 — Figure 8. T-SNE visualizations of additional baselines on the Mutagenicity dataset.

Figure 9. Full visualizations of the distilled basis of DSBD with different Dirichlet energy $\Omega$ .

Panel of Figure 10 — Figure 10. Hyperparameter sensitivity analysis of balance coefficient ( $\lambda_{\text{1}}$ , $\lambda_{\text{2}}$ ) on the PROTEINS, FRANKENSTEIN, NCI1 and ogbg-molhiv datasets.

Panel of Figure 11 — Figure 11. Hyperparameter sensitivity analysis of the number of synthetic bases $K$ on the PROTEINS, FRANKENSTEIN, NCI1 and ogbg-molhiv datasets.

Methods	M0 $\rightarrow$ M1	M1 $\rightarrow$ M0	M0 $\rightarrow$ M2	M2 $\rightarrow$ M0	M0 $\rightarrow$ M3	M3 $\rightarrow$ M0	M1 $\rightarrow$ M2	M2 $\rightarrow$ M1	M1 $\rightarrow$ M3	M3 $\rightarrow$ M1	M2 $\rightarrow$ M3	M3 $\rightarrow$ M2
DSBD w/o SE	64.2	61.5	65.8	50.3	53.4	54.2	65.1	69.5	48.2	62.8	50.9	48.7
DSBD w/o SP	71.5	68.1	74.2	55.6	56.5	60.1	72.5	76.7	53.4	69.2	56.2	53.8
DSBD w/o GE	69.5	66.4	71.6	53.8	54.2	57.1	69.8	74.2	51.5	65.7	54.1	51.6
DSBD w/o TG	72.4	70.6	73.9	57.1	58.6	62.3	74.1	78.5	54.9	71.4	59.4	55.5
DSBD	76.5	72.3	79.1	59.4	60.8	64.5	76.4	81.2	56.8	73.6	60.3	57.2

Appendix

Table 5. The results of ablation studies on the Mutagenicity dataset (source

\rightarrow