ASPECT: Node-Level Adaptive Spectral Fusion for Graph Contrastive Learning

Zhuolong Li; Boxue Yang; Haopeng Chen

cs.LGApr 2, 2026

ASPECT: Node-Level Adaptive Spectral Fusion for Graph Contrastive Learning

Authors: Zhuolong Li, Boxue Yang, Haopeng Chen

Organizations: School of Computer Science, Shanghai Jiao Tong University

Abstract

Spectral graph contrastive learning often constructs low- and high-frequency views to capture complementary graph signals, but these views are commonly combined by graph-level or node-agnostic fusion rules. We show that graph-level fusion can incur irreducible regret on mixed graphs with separated node-wise spectral preferences. Motivated by this result, we propose ASPECT, a spectral graph contrastive learning method that adaptively fuses low- and high-frequency views at the node level. ASPECT learns a node-wise spectral policy and regularizes it using channel-wise contrastive evidence, enabling different nodes to use different spectral mixtures. We further introduce ASPECT-S, an optional stability-aware extension that uses generated graph-structure and feature perturbations to obtain empirical channel-wise sensitivity estimates, together with a Rayleigh-based spectral search bias for producing informative perturbations. Experiments on homophilic and heterophilic benchmarks show that ASPECT improves representation quality over competitive spectral and graph contrastive baselines, while ASPECT-S further improves performance under joint graph-structure and feature perturbations.

Figures & tables

Figure 1: Overview of ASPECT and the optional ASPECT-S branch. Top: ASPECT constructs low- and high-frequency views with learnable spectral filters, learns a node-wise spectral policy $m$ to adaptively fuse the two channels, and optimizes a clean contrastive loss $\mathcal{L}_{\mathrm{std}}$ between the fused embedding $\mathbf{Z}$ and the augmented-view embedding $\mathbf{Z}_{aug}$ . Bottom: ASPECT-S is an optional stability-aware branch used when robustness to local graph-structure or feature perturbations is desired. It generates perturbed graphs and features while fixing the clean-graph gate, and uses the resulting perturbed channel representations to obtain empirical channel-wise sensitivity estimates. The Rayleigh-based term $\Phi_{ray}$ acts as a spectral search bias for producing informative perturbations. Auxiliary losses such as the policy regularizer are omitted for clarity.

Methods	Homophilic Datasets			Heterophilic Datasets
Methods	Cora	Citeseer	Pubmed	Cornell	Texas	Wisconsin	Actor	Chameleon	Squirrel
DGI	$\text{85.88}_{\,\pm\,\text{0.95}}$	$\text{76.44}_{\,\pm\,\text{0.84}}$	$\text{82.13}_{\,\pm\,\text{0.24}}$	$\text{70.82}_{\,\pm\,\text{2.71}}$	$\text{81.48}_{\,\pm\,\text{2.79}}$	$\text{75.00}_{\,\pm\,\text{4.22}}$	$\text{32.09}_{\,\pm\,\text{1.18}}$	$\text{58.23}_{\,\pm\,\text{0.70}}$	$\text{38.80}_{\,\pm\,\text{0.76}}$
GRACE	$\text{83.27}_{\,\pm\,\text{0.74}}$	$\text{73.79}_{\,\pm\,\text{0.57}}$	$\text{81.71}_{\,\pm\,\text{0.14}}$	$\text{60.66}_{\,\pm\,\text{2.94}}$	$\text{75.74}_{\,\pm\,\text{3.12}}$	$\text{72.13}_{\,\pm\,\text{1.99}}$	$\text{31.97}_{\,\pm\,\text{1.13}}$	$\text{59.52}_{\,\pm\,\text{2.65}}$	$\text{42.68}_{\,\pm\,\text{1.10}}$
GCA	$\text{84.09}_{\,\pm\,\text{0.85}}$	$\text{75.23}_{\,\pm\,\text{1.19}}$	$\text{82.01}_{\,\pm\,\text{0.34}}$	$\text{53.11}_{\,\pm\,\text{4.01}}$	$\text{81.97}_{\,\pm\,\text{1.58}}$	$\text{73.50}_{\,\pm\,\text{2.85}}$	$\text{31.13}_{\,\pm\,\text{1.11}}$	$\text{65.54}_{\,\pm\,\text{1.10}}$	$\text{47.13}_{\,\pm\,\text{0.93}}$
GREET	$\text{85.16}_{\,\pm\,\text{0.77}}$	$\text{79.06}_{\,\pm\,\text{1.34}}$	$\text{85.64}_{\,\pm\,\text{0.28}}$	$\text{78.36}_{\,\pm\,\text{2.77}}$	$\text{78.03}_{\,\pm\,\text{3.94}}$	$\text{84.63}_{\,\pm\,\text{2.10}}$	$\text{37.12}_{\,\pm\,\text{0.67}}$	$\text{60.57}_{\,\pm\,\text{1.03}}$	$\text{42.80}_{\,\pm\,\text{1.01}}$
CCA-SSG	$\text{87.39}_{\,\pm\,\text{0.89}}$	$\text{79.60}_{\,\pm\,\text{1.01}}$	$\text{84.95}_{\,\pm\,\text{0.26}}$	$\text{78.69}_{\,\pm\,\text{4.61}}$	$\text{87.87}_{\,\pm\,\text{1.89}}$	$\text{82.88}_{\,\pm\,\text{3.58}}$	$\text{34.86}_{\,\pm\,\text{1.13}}$	$\text{59.84}_{\,\pm\,\text{1.21}}$	$\text{41.50}_{\,\pm\,\text{1.12}}$

Table 1: Node classification accuracy (mean

\pm

standard deviation, %) on nine homophilic and heterophilic benchmarks under the linear evaluation protocol. The main text reports representative baselines; full results are provided in Appendix C.1 . Boldface indicates the best performance and underline indicates the second-best performance.

Methods	Homophilic Datasets			Heterophilic Datasets			Avg. Drop (%)
Methods	Cora	Citeseer	Pubmed	Actor	Chameleon	Squirrel	Avg. Drop (%)
DGI	$\text{79.62}_{\,\pm\,\text{0.62}}$	$\text{72.25}_{\,\pm\,\text{0.85}}$	$\text{74.29}_{\,\pm\,\text{1.01}}$	$\text{30.28}_{\,\pm\,\text{1.32}}$	$\text{51.47}_{\,\pm\,\text{0.70}}$	$\text{32.94}_{\,\pm\,\text{0.73}}$	9.11
GRACE	$\text{77.08}_{\,\pm\,\text{1.28}}$	$\text{70.67}_{\,\pm\,\text{0.86}}$	$\text{75.25}_{\,\pm\,\text{0.60}}$	$\text{30.78}_{\,\pm\,\text{0.71}}$	$\text{51.38}_{\,\pm\,\text{1.75}}$	$\text{32.76}_{\,\pm\,\text{1.07}}$	10.03
GCA	$\text{76.39}_{\,\pm\,\text{0.92}}$	$\text{56.55}_{\,\pm\,\text{1.31}}$	$\text{71.32}_{\,\pm\,\text{0.87}}$	$\text{31.87}_{\,\pm\,\text{0.97}}$	$\text{58.75}_{\,\pm\,\text{1.09}}$	$\text{37.20}_{\,\pm\,\text{0.90}}$	12.68
GREET	$\text{78.80}_{\,\pm\,\text{1.45}}$	$\text{75.44}_{\,\pm\,\text{0.59}}$	$\text{79.47}_{\,\pm\,\text{0.57}}$	$\text{34.46}_{\,\pm\,\text{1.23}}$	$\text{51.77}_{\,\pm\,\text{1.55}}$	$\text{35.64}_{\,\pm\,\text{1.32}}$	9.61
CCA-SSG	$\text{82.79}_{\,\pm\,\text{1.28}}$	$\text{74.88}_{\,\pm\,\text{0.72}}$	$\text{77.01}_{\,\pm\,\text{0.90}}$	$\text{30.70}_{\,\pm\,\text{0.77}}$	$\text{49.63}_{\,\pm\,\text{1.09}}$	$\text{31.23}_{\,\pm\,\text{1.44}}$	12.57

Table 2: Node classification accuracy (mean

\pm

standard deviation, %) under fixed-budget joint graph-structure and feature perturbations. We report selected representative baselines in the main text and provide the full comparison in Appendix C.2 . Boldface indicates the best result and underline indicates the second-best result.

Variant	Cora		Pubmed		Actor		Squirrel
Variant	Clean	Pert.	Clean	Pert.	Clean	Pert.	Clean	Pert.
ASPECT	$\text{{88.94}}_{\,\pm\,\text{1.10}}$	$\text{{84.08}}_{\,\pm\,\text{1.41}}$	$\text{{87.75}}_{\,\pm\,\text{1.03}}$	$\text{{82.38}}_{\,\pm\,\text{0.52}}$	$\text{{42.64}}_{\,\pm\,\text{1.55}}$	$\text{36.14}_{\,\pm\,\text{0.47}}$	$\text{{59.39}}_{\,\pm\,\text{1.76}}$	$\text{{46.37}}_{\,\pm\,\text{1.08}}$
Global Fusion	$\text{87.49}_{\,\pm\,\text{0.74}}$	$\text{83.20}_{\,\pm\,\text{0.85}}$	$\text{86.93}_{\,\pm\,\text{0.68}}$	$\text{78.96}_{\,\pm\,\text{0.97}}$	$\text{41.61}_{\,\pm\,\text{0.99}}$	$\text{{37.07}}_{\,\pm\,\text{1.51}}$	$\text{57.05}_{\,\pm\,\text{0.88}}$	$\text{43.39}_{\,\pm\,\text{0.94}}$
w/o PolicyReg	$\text{87.15}_{\,\pm\,\text{1.76}}$	$\text{81.19}_{\,\pm\,\text{1.46}}$	$\text{85.40}_{\,\pm\,\text{1.90}}$	$\text{79.17}_{\,\pm\,\text{1.67}}$	$\text{41.76}_{\,\pm\,\text{2.08}}$	$\text{35.28}_{\,\pm\,\text{2.10}}$	$\text{57.92}_{\,\pm\,\text{1.00}}$	$\text{41.90}_{\,\pm\,\text{1.49}}$
ASPECT-S	$\text{{88.69}}_{\,\pm\,\text{0.72}}$	$\text{{85.30}}_{\,\pm\,\text{0.72}}$	$\text{{86.92}}_{\,\pm\,\text{0.69}}$	$\text{{84.93}}_{\,\pm\,\text{0.44}}$	$\text{{41.73}}_{\,\pm\,\text{1.30}}$	$\text{{39.20}}_{\,\pm\,\text{0.63}}$	$\text{{59.91}}_{\,\pm\,\text{0.90}}$	$\text{{50.17}}_{\,\pm\,\text{0.92}}$
w/o Rayleigh	$\text{87.91}_{\,\pm\,\text{0.99}}$	$\text{83.64}_{\,\pm\,\text{1.04}}$	$\text{86.18}_{\,\pm\,\text{1.06}}$	$\text{82.83}_{\,\pm\,\text{0.83}}$	$\text{41.22}_{\,\pm\,\text{1.43}}$	$\text{38.06}_{\,\pm\,\text{1.36}}$	$\text{58.43}_{\,\pm\,\text{1.77}}$	$\text{47.61}_{\,\pm\,\text{1.87}}$

Table 3: Ablation study on representative homophilic and heterophilic datasets. We report node classification accuracy (mean

\pm

standard deviation, %) on clean graphs and under fixed-budget joint graph-structure and feature perturbations. Bold indicates the best performance within each ASPECT or ASPECT-S block.

Figure 2: Policy behavior of ASPECT on clean graphs. Left:

m_{v}

distributions. Right: binned

m_{v}

versus

b_{H,v}-b_{L,v}

. Error bars indicate within-bin variability.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Methods	Homophilic Datasets			Heterophilic Datasets
Methods	Cora	Citeseer	Pubmed	Cornell	Texas	Wisconsin	Actor	Chameleon	Squirrel
DGI	$\text{85.88}_{\,\pm\,\text{0.95}}$	$\text{76.44}_{\,\pm\,\text{0.84}}$	$\text{82.13}_{\,\pm\,\text{0.24}}$	$\text{70.82}_{\,\pm\,\text{2.71}}$	$\text{81.48}_{\,\pm\,\text{2.79}}$	$\text{75.00}_{\,\pm\,\text{4.22}}$	$\text{32.09}_{\,\pm\,\text{1.18}}$	$\text{58.23}_{\,\pm\,\text{0.70}}$	$\text{38.80}_{\,\pm\,\text{0.76}}$
MVGRL	$\text{87.36}_{\,\pm\,\text{0.64}}$	$\text{78.70}_{\,\pm\,\text{0.64}}$	$\text{86.30}_{\,\pm\,\text{0.23}}$	$\text{67.70}_{\,\pm\,\text{4.45}}$	$\text{73.11}_{\,\pm\,\text{4.47}}$	$\text{74.25}_{\,\pm\,\text{2.43}}$	$\text{32.98}_{\,\pm\,\text{0.53}}$	$\text{57.75}_{\,\pm\,\text{1.20}}$	$\text{40.25}_{\,\pm\,\text{1.14}}$
GMI	$\text{85.09}_{\,\pm\,\text{1.13}}$	$\text{76.38}_{\,\pm\,\text{0.70}}$	$\text{83.06}_{\,\pm\,\text{0.34}}$	$\text{62.79}_{\,\pm\,\text{3.85}}$	$\text{68.03}_{\,\pm\,\text{2.02}}$	$\text{62.13}_{\,\pm\,\text{2.88}}$	$\text{32.37}_{\,\pm\,\text{1.16}}$	$\text{62.47}_{\,\pm\,\text{1.52}}$	$\text{39.82}_{\,\pm\,\text{0.94}}$
GGD	$\text{87.21}_{\,\pm\,\text{1.18}}$	$\text{79.25}_{\,\pm\,\text{1.06}}$	$\text{85.38}_{\,\pm\,\text{0.25}}$	$\text{80.33}_{\,\pm\,\text{1.80}}$	$\text{82.62}_{\,\pm\,\text{1.41}}$	$\text{73.25}_{\,\pm\,\text{3.28}}$	$\text{32.27}_{\,\pm\,\text{1.17}}$	$\text{57.64}_{\,\pm\,\text{1.65}}$	$\text{40.87}_{\,\pm\,\text{0.93}}$
GraphCL	$\text{86.54}_{\,\pm\,\text{1.34}}$	$\text{78.99}_{\,\pm\,\text{1.95}}$	$\text{85.16}_{\,\pm\,\text{0.60}}$	$\text{61.48}_{\,\pm\,\text{4.69}}$	$\text{66.07}_{\,\pm\,\text{3.42}}$	$\text{60.63}_{\,\pm\,\text{2.19}}$	$\text{32.45}_{\,\pm\,\text{1.13}}$	$\text{58.49}_{\,\pm\,\text{1.23}}$	$\text{42.92}_{\,\pm\,\text{0.96}}$

Appendix

Table 4: Full clean node classification accuracy (mean

\pm

standard deviation, %) under the linear evaluation protocol. This table includes all baselines considered in our experiments. Boldface indicates the best performance and underline indicates the second-best performance.

Methods	Homophilic Datasets			Heterophilic Datasets			Avg. Drop (%)
Methods	Cora	Citeseer	Pubmed	Actor	Chameleon	Squirrel	Avg. Drop (%)
DGI	$\text{79.62}_{\,\pm\,\text{0.62}}$	$\text{72.25}_{\,\pm\,\text{0.85}}$	$\text{74.29}_{\,\pm\,\text{1.01}}$	$\text{30.28}_{\,\pm\,\text{1.32}}$	$\text{51.47}_{\,\pm\,\text{0.70}}$	$\text{32.94}_{\,\pm\,\text{0.73}}$	9.11
MVGRL	$\text{77.93}_{\,\pm\,\text{0.76}}$	$\text{70.31}_{\,\pm\,\text{1.00}}$	$\text{73.57}_{\,\pm\,\text{0.49}}$	$\text{27.00}_{\,\pm\,\text{0.52}}$	$\text{54.62}_{\,\pm\,\text{1.09}}$	$\text{39.31}_{\,\pm\,\text{1.13}}$	10.35
GMI	$\text{79.23}_{\,\pm\,\text{0.56}}$	$\text{70.67}_{\,\pm\,\text{0.85}}$	$\text{73.51}_{\,\pm\,\text{0.66}}$	$\text{28.88}_{\,\pm\,\text{0.96}}$	$\text{52.01}_{\,\pm\,\text{1.27}}$	$\text{32.07}_{\,\pm\,\text{1.15}}$	12.14
GGD	$\text{80.72}_{\,\pm\,\text{0.61}}$	$\text{71.00}_{\,\pm\,\text{0.83}}$	$\text{72.97}_{\,\pm\,\text{0.70}}$	$\text{30.29}_{\,\pm\,\text{1.60}}$	$\text{50.92}_{\,\pm\,\text{1.51}}$	$\text{32.23}_{\,\pm\,\text{1.19}}$	11.89
GraphCL	$\text{78.54}_{\,\pm\,\text{0.89}}$	$\text{72.40}_{\,\pm\,\text{1.19}}$	$\text{73.94}_{\,\pm\,\text{0.70}}$	$\text{31.04}_{\,\pm\,\text{0.56}}$	$\text{49.93}_{\,\pm\,\text{0.88}}$	$\text{31.69}_{\,\pm\,\text{1.44}}$	12.65

Appendix

Table 5: Full node classification accuracy (mean

\pm

standard deviation, %) under fixed-budget joint graph-structure and feature perturbations. Metattack perturbs 10% of edges and feature masking corrupts 10% of node features. This table includes all baselines considered in the perturbation evaluation. Boldface indicates the best result and underline indicates the second-best result.

Panel of Figure 3 — Figure 3: Variable-budget perturbation performance. Classification accuracy (%) as the perturbation budget increases. For each budget, graph-structure perturbations are generated by Metattack and feature perturbations are applied by masking the same percentage of node features. ASPECT-S degrades more gracefully than representative baselines across both homophilic and heterophilic datasets, suggesting that the optional stability-aware branch improves performance under the evaluated joint graph-structure and feature perturbation protocol.

Method	URL	Commit
DGI	https://github.com/PetarV-/DGI	61baf67
MVGRL	https://github.com/kavehhassani/mvgrl	628ed2b
GMI	https://github.com/zpeng27/GMI	3491e8c
GGD	https://github.com/zyzisastudyreallyhardguy/graph-group-discrimination	7cf72db
GRACE	https://github.com/CRIPAC-DIG/GRACE	51b4496
GCA	https://github.com/CRIPAC-DIG/GCA	cd6a9f0

Appendix

Table 6: Codes & commit numbers.

Parameter	Cora	Citeseer	Pubmed	Cornell	Texas	Wisconsin	Actor	Chameleon	Squirrel
Epochs	2000	500	1000	500	500	2000	500	2000	1500
Patience	180	160	40	160	100	20	120	40	140
LR ( $\eta$ )	0.00013	0.00106	0.00011	0.00073	0.00010	0.00214	0.00398	0.00335	0.00121
LR 1 ( $\eta_{1}$ )	0.00044	0.00357	0.00535	0.00025	0.00486	0.00016	0.00233	0.00228	0.00157
LR 2 ( $\eta_{2}$ )	0.00915	0.00199	0.00183	0.00295	0.00137	0.00170	0.00054	0.00818	0.00817
LR α ( $\eta_{\alpha}$ )	0.14373	26.1982	1.48472	2.63077	0.18482	12.8336	95.5903	12.7409	0.15628

Appendix

Table 7: Hyperparameters used for each dataset

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