Spiking Graph Predictive Coding for Reliable OOD Generalization

Jing Ren; Jiapeng Du; Bowen Li; Ziqi Xu; Xin Zheng; Hong Jia; Suyu Ma; Xiwei Xu

cs.LGFeb 22, 2026

Spiking Graph Predictive Coding for Reliable OOD Generalization

Authors: Jing Ren, Jiapeng Du, Bowen Li, Ziqi Xu, Xin Zheng, Hong Jia, Suyu Ma, Xiwei Xu, +1 more

Organizations: RMIT University, Melbourne, Australia · University of Auckland, Auckland, New Zealand · CSIRO’s Data61, Melbourne, Australia · CSIRO’s Data61, Sydney, Australia

Abstract

Graphs provide a powerful basis for modeling Web-based relational data, with expressive GNNs to support the effective learning in dynamic web environments. However, real-world deployment is hindered by pervasive out-of-distribution (OOD) shifts, where evolving user activity and changing content semantics alter feature distributions and labeling criteria. These shifts often lead to unstable or overconfident predictions, undermining the trustworthiness required for Web4Good applications. Achieving reliable OOD generalization demands principled and interpretable uncertainty estimation; however, existing methods are largely post-hoc, insensitive to distribution shifts, and unable to explain where uncertainty arises especially in high-stakes settings. To address these limitations, we introduce SpIking GrapH predicTive coding (SIGHT), an uncertainty-aware plug-in graph learning module for reliable OOD Generalization. SIGHT performs iterative, error-driven correction over spiking graph states, enabling models to expose internal mismatch signals that reveal where predictions become unreliable. Across multiple graph benchmarks and diverse OOD scenarios, SIGHT consistently enhances predictive accuracy, uncertainty estimation, and interpretability when integrated with GNNs.

Figures & tables

Figure 1. Overview of the proposed framework SIGHT. In training, the encoded node representations are learned by aggregating neighbor information through GNNs. Before propagation, predictions are refined via an iterative predictive coding (PC) unit over LIF neurons. In testing, the model will be tested on datasets with covariate shift , where the input feature distribution changes while the underlying labels remain stable (i.e., $P^{\text{train}}(X)\neq P^{\text{test}}(X)$ but $P^{\text{train}}(Y|X)=P^{\text{test}}(Y|X)$ ), and with concept shift , where the meaning of labels or the feature–label relationship itself changes over time (i.e., $P^{\text{train}}(Y|X)\neq P^{\text{test}}(Y|X)$ ).

	Method	Accuracy $\uparrow$		ECE $\downarrow$		NLL $\downarrow$		BS $\downarrow$		AUROC $\uparrow$
	Method	ID	OOD	ID	OOD	ID	OOD	ID	OOD	ID	OOD
Cora	GCN	89.8 $\pm$ 0.3	43.5 $\pm$ 5.2	0.019 $\pm$ 0.003	0.391 $\pm$ 0.071	0.318 $\pm$ 0.008	2.595 $\pm$ 0.512	0.150 $\pm$ 0.004	0.919 $\pm$ 0.103	88.7 $\pm$ 0.3	59.9 $\pm$ 3.7
	+G- $\Delta$ UQ	91.3 $\pm$ 0.4	80.1 $\pm$ 4.7	0.019 $\pm$ 0.004	0.053 $\pm$ 0.031	0.270 $\pm$ 0.018	0.574 $\pm$ 0.149	0.130 $\pm$ 0.007	0.288 $\pm$ 0.068	87.3 $\pm$ 1.2	81.5 $\pm$ 2.8
	+SIGHT	93.2 $\pm$ 0.6	95.6 $\pm$ 0.2	0.015 $\pm$ 0.002	0.009 $\pm$ 0.002	0.241 $\pm$ 0.021	0.153 $\pm$ 0.010	0.105 $\pm$ 0.009	0.068 $\pm$ 0.003	86.7 $\pm$ 1.2	89.8 $\pm$ 1.5
Citeseer	GCN	82.1 $\pm$ 0.4	46.6 $\pm$ 1.9	0.026 $\pm$ 0.003	0.334 $\pm$ 0.027	0.503 $\pm$ 0.012	1.838 $\pm$ 0.051	0.252 $\pm$ 0.006	0.793 $\pm$ 0.026	84.1 $\pm$ 0.8	74.1 $\pm$ 1.6
	+G- $\Delta$ UQ	81.6 $\pm$ 0.4	71.0 $\pm$ 4.2	0.021 $\pm$ 0.008	0.066 $\pm$ 0.027	0.531 $\pm$ 0.037	0.889 $\pm$ 0.145	0.263 $\pm$ 0.010	0.416 $\pm$ 0.056	82.2 $\pm$ 1.6	76.5 $\pm$ 1.3

Table 1. Node classification accuracy and uncertainty on ID and OOD datasets with the GCN backbone. Best results are in bold , and SIGHT is marked with a . Results with the GAT backbone are in Table 6 .

Panel of Figure 2 — Figure 2. Comparison of label distribution between training and testing sets on Twitch and CBAS.

Panel of Figure 3 — Figure 3. Comparison of feature distribution between training and testing sets on Cora, Citeseer, and Pubmed.

Dataset	# Nodes	# Edges	# Classes	# Features	Shift Type
Cora	2,708	5,429	7	1,433	Covariate
Citeseer	3,327	4,732	6	3,703	Covariate
Pubmed	19,717	44,338	3	500	Covariate
Twitch	34120	892346	2	128	Concept
CBAS	700	3962	4	4	Concept

Table 2. Statistics of the experimental datasets.

		GCN				GAT
	Model	Accuracy $\uparrow$		ECE $\downarrow$		Accuracy $\uparrow$		ECE $\downarrow$
	Model	w/o SIGHT	w/ SIGHT	w/o SIGHT	w/ SIGHT	w/o SIGHT	w/ SIGHT	w/o SIGHT	w/ SIGHT
Cora	✗	43.5 $\pm$ 5.2	95.6 $\pm$ 0.2	0.391 $\pm$ 0.071	0.009 $\pm$ 0.002	67.4 $\pm$ 4.1	96.3 $\pm$ 0.7	0.164 $\pm$ 0.026	0.008 $\pm$ 0.002
	CAGCN	40.9 $\pm$ 3.3	95.6 $\pm$ 0.2	0.439 $\pm$ 0.081	0.037 $\pm$ 0.019	67.4 $\pm$ 4.1	95.8 $\pm$ 0.7	0.255 $\pm$ 0.031	0.042 $\pm$ 0.022
	Dirichlet	42.1 $\pm$ 4.4	95.5 $\pm$ 0.1	0.412 $\pm$ 0.039	0.012 $\pm$ 0.001	65.9 $\pm$ 3.0	96.6 $\pm$ 0.4	0.174 $\pm$ 0.024	0.009 $\pm$ 0.003
	ETS	42.1 $\pm$ 5.7	95.6 $\pm$ 0.2	0.419 $\pm$ 0.055	0.009 $\pm$ 0.001	67.0 $\pm$ 3.9	95.2 $\pm$ 1.0	0.176 $\pm$ 0.017	0.011 $\pm$ 0.003

Table 3. Accuracy and ECE under distribution shifts for different post-hoc calibration models using GCN and GAT backbones, w/o and w/ SIGHT ( a ). ✗ denotes no post-hoc calibration.

Panel of Figure 4 — Figure 4. Correlation between PC error and confidence scores on the Cora, Citeseer, and Pubmed OOD sets. Higher PC errors consistently correspond to lower confidence, showing that PC residuals serve as an intrinsic measure of uncertainty.

Method	Cora	Citeseer	Pubmed	Twitch	CBAS
GCN	70.4 $\pm$ 2.8	74.1 $\pm$ 1.1	72.6 $\pm$ 1.2	53.2 $\pm$ 0.5	74.5 $\pm$ 3.8
+G- $\Delta$ UQ	83.0 $\pm$ 2.2	77.7 $\pm$ 1.0	74.8 $\pm$ 0.4	52.2 $\pm$ 4.6	72.3 $\pm$ 6.6
+SIGHT	89.0 $\pm$ 1.6	84.0 $\pm$ 1.2	85.1 $\pm$ 0.2	54.5 $\pm$ 2.4	78.1 $\pm$ 2.4
GAT	73.9 $\pm$ 2.1	78.3 $\pm$ 1.1	77.0 $\pm$ 0.6	49.5 $\pm$ 2.4	75.9 $\pm$ 4.1
+G- $\Delta$ UQ	83.3 $\pm$ 2.4	80.4 $\pm$ 1.1	82.7 $\pm$ 0.8	49.3 $\pm$ 3.9	78.3 $\pm$ 5.3
+SIGHT	88.0 $\pm$ 2.8	81.1 $\pm$ 1.8	82.1 $\pm$ 0.2	52.7 $\pm$ 3.1	83.1 $\pm$ 3.4

Table 4. AUROC results for OOD detection. Best results are in bold , and SIGHT is marked with a .

		GCN					GAT
	Method	Acc $\uparrow$	ECE $\downarrow$	NLL $\downarrow$	BS $\downarrow$	AUROC $\uparrow$	Acc $\uparrow$	ECE $\downarrow$	NLL $\downarrow$	BS $\downarrow$	AUROC $\uparrow$
Cora	SIGHT	95.6 $\pm$ 0.2	0.009 $\pm$ 0.002	0.153 $\pm$ 0.010	0.068 $\pm$ 0.003	89.8 $\pm$ 1.5	96.3 $\pm$ 0.7	0.008 $\pm$ 0.002	0.138 $\pm$ 0.028	0.058 $\pm$ 0.012	89.6 $\pm$ 2.1
	w/o Spik	68.4 $\pm$ 5.1	0.146 $\pm$ 0.043	1.011 $\pm$ 0.196	0.473 $\pm$ 0.084	71.4 $\pm$ 2.3	64.5 $\pm$ 5.5	0.175 $\pm$ 0.048	1.243 $\pm$ 0.230	0.551 $\pm$ 0.093	66.3 $\pm$ 4.7
	w/o PC	95.2 $\pm$ 0.3	0.020 $\pm$ 0.005	0.158 $\pm$ 0.004	0.076 $\pm$ 0.002	89.3 $\pm$ 1.4	97.1 $\pm$ 0.2	0.017 $\pm$ 0.005	0.135 $\pm$ 0.022	0.048 $\pm$ 0.006	83.3 $\pm$ 5.2
	w/o SPC	43.5 $\pm$ 5.2	0.391 $\pm$ 0.071	2.595 $\pm$ 0.512	0.919 $\pm$ 0.103	59.9 $\pm$ 3.7	67.4 $\pm$ 4.1	0.164 $\pm$ 0.026	1.072 $\pm$ 0.108	0.498 $\pm$ 0.059	71.1 $\pm$ 3.2
Citeseer	SIGHT	91.2 $\pm$ 0.4	0.024 $\pm$ 0.004	0.307 $\pm$ 0.016	0.136 $\pm$ 0.008	83.4 $\pm$ 0.8	93.4 $\pm$ 0.2	0.028 $\pm$ 0.003	0.261 $\pm$ 0.012	0.105 $\pm$ 0.005	80.8 $\pm$ 1.2

Table 5. Ablation study of SIGHT with GCN and GAT backbones. Best results are in bold .

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

	Method	Accuracy $\uparrow$		ECE $\downarrow$		NLL $\downarrow$		BS $\downarrow$		AUROC $\uparrow$
	Method	ID	OOD	ID	OOD	ID	OOD	ID	OOD	ID	OOD
Cora	GAT	90.6 $\pm$ 0.5	67.4 $\pm$ 4.1	0.015 $\pm$ 0.001	0.164 $\pm$ 0.026	0.286 $\pm$ 0.027	1.072 $\pm$ 0.108	0.137 $\pm$ 0.011	0.498 $\pm$ 0.059	88.9 $\pm$ 0.7	71.1 $\pm$ 3.2
	+G- $\Delta$ UQ	93.9 $\pm$ 0.4	80.2 $\pm$ 3.5	0.015 $\pm$ 0.002	0.061 $\pm$ 0.033	0.211 $\pm$ 0.007	0.578 $\pm$ 0.098	0.097 $\pm$ 0.004	0.291 $\pm$ 0.053	87.2 $\pm$ 1.6	81.8 $\pm$ 3.0
	+SIGHT	93.9 $\pm$ 0.9	96.3 $\pm$ 0.7	0.017 $\pm$ 0.002	0.008 $\pm$ 0.002	0.227 $\pm$ 0.036	0.138 $\pm$ 0.028	0.097 $\pm$ 0.016	0.058 $\pm$ 0.012	87.1 $\pm$ 3.0	89.6 $\pm$ 2.1
Citeseer	GAT	82.1 $\pm$ 0.4	46.6 $\pm$ 1.9	0.026 $\pm$ 0.003	0.334 $\pm$ 0.027	0.503 $\pm$ 0.012	1.838 $\pm$ 0.051	0.252 $\pm$ 0.006	0.793 $\pm$ 0.026	84.1 $\pm$ 0.8	74.1 $\pm$ 1.6
	+G- $\Delta$ UQ	81.6 $\pm$ 0.4	71.0 $\pm$ 4.2	0.021 $\pm$ 0.008	0.066 $\pm$ 0.027	0.531 $\pm$ 0.037	0.889 $\pm$ 0.145	0.263 $\pm$ 0.010	0.416 $\pm$ 0.056	82.2 $\pm$ 1.6	76.5 $\pm$ 1.3

Appendix

Table 6. Node classification accuracy and uncertainty calibration on ID and OOD datasets with the GAT backbone. Best results are in bold , and SIGHT is marked with a . Results with the GCN backbone are in Table 1 .

Panel of Figure 5 — Figure 5. Correlation between PC error and confidence scores on the Cora, Citeseer, and Pubmed ID test sets. Higher PC errors consistently correspond to lower confidence, showing that PC residuals serve as an intrinsic measure of uncertainty.

Panel of Figure 6 — Figure 6. Sensitivity analysis of SGPC under predictive coding iterations ( $K$ ), timesteps ( $T$ ), and learning rate ( $LR$ ) on AUROC are evaluated across five datasets.

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

Yuxiang Zhang, Enyan Dai

The Hong Kong University of Science and Technology (Guangzhou)

Graph Neural Networks Spurious Correlation Robustness OOD Generalization

Open paper AskPDF arXiv

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.

Abstract

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