SCL-GNN: Towards Generalizable Graph Neural Networks via Spurious Correlation Learning

Yuxiang Zhang; Enyan Dai

cs.LGMar 9, 2026

SCL-GNN: Towards Generalizable Graph Neural Networks via Spurious Correlation Learning

Authors: Yuxiang Zhang, Enyan Dai

Organizations: The Hong Kong University of Science and Technology (Guangzhou)

Abstract

Graph Neural Networks (GNNs) have demonstrated remarkable success across diverse tasks. However, their generalization capability is often hindered by spurious correlations between node features and labels in the graph. Our analysis reveals that GNNs tend to exploit imperceptible statistical correlations in training data, even when such correlations are unreliable for prediction. To address this challenge, we propose the Spurious Correlation Learning Graph Neural Network (SCL-GNN), a novel framework designed to enhance generalization on both Independent and Identically Distributed (IID) and Out-of-Distribution (OOD) graphs. SCL-GNN incorporates a principled spurious correlation learning mechanism, leveraging the Hilbert-Schmidt Independence Criterion (HSIC) to quantify correlations between node representations and class scores. This enables the model to identify and mitigate irrelevant but influential spurious correlations effectively. Additionally, we introduce an efficient bi-level optimization strategy to jointly optimize modules and GNN parameters, preventing overfitting. Extensive experiments on real-world and synthetic datasets demonstrate that SCL-GNN consistently outperforms state-of-the-art baselines under various distribution shifts, highlighting its robustness and generalization capabilities.

Figures & tables

Figure 1: An illustration of node classification task on an academic network for GNNs. (a) The task aims to classify the label $y$ of target node $v$ based on the compact graph $\mathcal{G}_{v}=\{\mathbf{A}_{v},\mathbf{X}_{v}$ } consisting of its neighbors. (b) Four existing relations and the notion in the network example, only the AI researcher feature of the collaborator has a positive influence for predicting that the researcher also researches AI. (c) Description and comparison of the workflow of SCL-GNN and existing works. We virtually split features into spurious and stable sets. We propose a more effective method to achieve the same goal by spurious correlation learning, instead of importing complex probability computation.

Figure 2: Illustration of SCL-GNN framework for generalizing GNN via spurious correlation learning. (a) and (b) illustrates the details of spurious correlation(abbreviated as SC) learner $f_{a}$ and backbone GNN model $f_{s}$ , respectively, (c) represent an overview of the framework, (d) and (e) respectively explain the process of spurious correlation learning and generalization via pseudo algorithms. When the training is finished, the $f_{a}$ is fixed synchronously, and we only need to evaluate GNN model with the fine-tuned model weight $\mathbf{W}^{\prime}$ .

Datasets	#Nodes	#Edges	#Features	#Classes	Distribution Shift
Cora	2708	5429	1433	7	Features
Pubmed	19717	44338	500	3	Features
Arxiv	169343	1166243	128	40	Timeline
Products	2449029	61859140	100	47	Popularity

Table 1: Details of Datasets.

Backbone	Method	Cora			Pubmed
Backbone		ID	OOD1	OOD2	ID	OOD1	OOD2
GCN	StableGNN	84.05 $\pm$ 2.16	77.31 $\pm$ 0.17	73.61 $\pm$ 0.37	71.85 $\pm$ 2.23	67.12 $\pm$ 0.76	65.73 $\pm$ 1.58
	SRGNN	91.57 $\pm$ 2.81	80.30 $\pm$ 0.21	76.31 $\pm$ 0.41	90.89 $\pm$ 4.23	82.45 $\pm$ 0.07	79.25 $\pm$ 0.17
	EERM	88.57 $\pm$ 1.24	83.50 $\pm$ 0.44	81.07 $\pm$ 0.25	82.79 $\pm$ 3.34	77.15 $\pm$ 0.24	74.43 $\pm$ 0.65
	CANET	96.25 $\pm$ 2.56	95.14 $\pm$ 0.56	93.89 $\pm$ 0.16	96.13 $\pm$ 3.32	90.67 $\pm$ 0.26	88.49 $\pm$ 0.04
	SCL-GNN	97.14 $\pm$ 1.26	95.62 $\pm$ 0.06	95.03 $\pm$ 0.09	97.24 $\pm$ 0.06	94.16 $\pm$ 0.76	91.56 $\pm$ 0.06

Table 2: Accuracy

\pm

Standard Deviation(%) for Cora and Pubmed on ID and two sets of OOD data, respectively. The distribution shift is generated on feature of nodes.

Backbone	Method	Arxiv			Products
Backbone		ID	OOD1	OOD2	ID	OOD1	OOD2
GCN	StableGNN	60.35 $\pm$ 0.46	57.33 $\pm$ 0.12	53.25 $\pm$ 0.49	80.23 $\pm$ 0.43	69.12 $\pm$ 0.46	67.23 $\pm$ 0.38
	SRGNN	61.02 $\pm$ 0.18	57.30 $\pm$ 0.11	46.98 $\pm$ 0.29	84.16 $\pm$ 0.42	78.12 $\pm$ 0.07	72.56 $\pm$ 0.13
	EERM	57.12 $\pm$ 0.14	53.15 $\pm$ 0.44	48.37 $\pm$ 0.19	82.42 $\pm$ 0.42	74.52 $\pm$ 0.33	72.45 $\pm$ 0.17
	CANET	62.52 $\pm$ 0.20	59.04 $\pm$ 0.22	56.12 $\pm$ 0.15	85.61 $\pm$ 0.33	78.27 $\pm$ 0.46	75.51 $\pm$ 0.19
	SCL-GNN	63.74 $\pm$ 0.36	62.15 $\pm$ 0.06	60.89 $\pm$ 0.22	88.04 $\pm$ 0.15	84.16 $\pm$ 0.09	80.07 $\pm$ 0.20

Table 3: Accuracy

\pm

Standard Deviation(%) for Arxiv and Products on ID and two sets of OOD data, respectively. The distribution shift is generated by the timeline and popularity of nodes.

Panel of Figure 3 — Figure 3: Model performance with different $\beta$ .

Figure 4: Ablation study of SCL-GNN with GCN and GAT.

Panel of Figure 5 — Figure 5: Comparison of a GCN backbone’s learning curves

Panel of Figure 6 — Figure 6: The distribution of two sets of correlations.

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CGRL: Causal-Guided Representation Learning for Node-Level Out-of-Distribution Generalization

Bowen Lu, Lianqiang Yang, Teng Li, Kun Zhang

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OOD Generalization Graph Neural Networks Causal Representation Learning Node Classification Disentangled Representation Learning

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Graph Neural Networks (GNNs) deliver strong performance on graph tasks, but their accuracy drops significantly under out-of-distribution (OOD) scenarios. Under distribution shifts, GNNs often fit environmental noise and spurious correlations instead of stable causal mechanisms, leading to weak OOD robustness and unstable predictive representations. Existing solutions based on environment invariance or causal reasoning are insufficient for node classification, as they do not explicitly model the fine-grained latent geometry required by the task. We further observe a training instability named Info-Jitter, where the mutual information between predictive representations and ground-truth labels fluctuates throughout training. To address these issues, we construct a node-classification-specific causal graph derived from the task's geometric objective. Using do-calculus to block non-causal paths caused by environmental noise, we derive a deconfounded interventional objective and a variational lower bound to disentangle representations into intra-class and inter-class components. We then propose Causal-Guided Representation Learning (CGRL), a framework with two core modules. First, a multi-branch re-weighted representation learning (RRL) module learns a causal modulation matrix to amplify causal signals and suppress environmental noise during message passing. Second, an optimization strategy combining intra-class aggregation, inter-class separation, energy-based reconstruction and supervised prediction regularizes the latent space for robust node-level generalization. Experiments on multiple benchmark datasets show that CGRL outperforms strong baselines across various distribution shifts and effectively mitigates the Info-Jitter phenomenon.

Abstract

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