Polarity-Asymmetric Structural Calibration for Link Sign Prediction

Qiqi Gao; Wenzhuo Song; Xueyan Liu

cs.SISep 5, 2026

Polarity-Asymmetric Structural Calibration for Link Sign Prediction

Authors: Qiqi Gao, Wenzhuo Song, Xueyan Liu

Organizations: Northeast Normal University Changchun, Jilin, China · Jilin University Changchun, Jilin, China

Abstract

Link sign prediction (LSP) aims to infer the positive or negative polarity of unobserved links in signed networks. Signed Graph Neural Networks (SGNNs) usually rely on signed-graph structural priors, including structural balance and homophily-like similarity, to guide message passing and prediction. These priors describe population-level tendencies, not guarantees for individual target edges. Their failures are especially costly under severe sign imbalance, where errors on minority and locally conflicting relations are harder to detect and correct. We propose Polarity-Asymmetric Structural Calibration (PASC), a target-edge structural-prior calibration framework for signed link prediction. PASC constructs a structure-only prior representation, estimates a target-edge structural prior score, and compares this score with a local signed-context cue to derive a conflict residual. The residual calibrates signed attention aggregation, target-edge gated fusion, and regime-adaptive optimization. Experiments on five real-world signed network datasets show that PASC consistently achieves the best Macro-F1 among representative baselines, with competitive AUC, Binary-F1, and Micro-F1. Structural-shift experiments further suggest reduced dependence on dense-neighborhood and local-closure shortcuts. Source code is available at https://github.com/iqqGGGGGGG/PASC-for-LSP.

Figures & tables

Fig. 1: Example of target-edge structural-prior unreliability. Alice and Carol share a positive neighbor Bob, so structural balance suggests a positive relation. Their local signed context, however, may provide conflicting evidence. Structural priors capture population-level tendencies but need not be reliable for every target edge.

Triads	Prior	$(+,+)$		$(+,-)/(-,+)$		$(-,-)$
Triads	Posterior	$+$	$-$	$+$	$-$	$+$	$-$
Datasets	Bitcoin-Alpha	95.7%	4.3%	63.5%	36.5%	86.6%	13.4%
	Bitcoin-OTC	95.9%	4.1%	39.3%	60.7%	90.2%	9.8%
	Wiki-RfA	88.1%	11.9%	70.8%	29.2%	66.9%	33.1%
	Slashdot	94.9%	5.1%	46.5%	53.5%	68.5%	31.5%
	Epinions	96.5%	3.5%	53.5%	46.5%	69.7%	30.3%

TABLE I: Prior-Posterior Statistics of Triangles in Signed Networks

Fig. 2: Architecture of the PASC framework for link sign prediction. PASC estimates target-edge structural prior scores, derives conflict residuals from local signed-context cues, and uses residual-guided aggregation, regime-adaptive conflict-residual optimization (PASC-S and PASC-H), and target-edge gated fusion to calibrate structural reliance under different graph regimes.

Dataset	Nodes	Edges	Pos links	Neg links	Pos/Neg
Bitcoin-Alpha 1	3,782	24,185	22,649	1,536	14.7:1
Bitcoin-OTC 1	5,881	35,591	32,028	3,563	9.0:1
Wiki-RfA 1	11,259	178,096	138,813	39,283	3.5:1
Slashdot 1	84,140	549,201	425,071	124,130	3.4:1
Epinions 1	131,827	841,371	717,667	123,704	5.8:1

TABLE II: Statistics of the datasets used in our experiments.

Dataset	Metrics	nSNE	SGCN	SNEA	SDGNN	RSGNN	SPMF	TrustSGCN	CFSE	PASC
Bitcoin-Alpha	AUC	84.25 $\pm$ 2.72	88.57 $\pm$ 0.19	89.20 $\pm$ 1.60	90.29 $\pm$ 1.27	79.68 $\pm$ 0.71	90.15 $\pm$ 0.28	86.72 $\pm$ 0.93	93.37 $\pm$ 0.40	93.61 $\pm$ 0.53
	Binary-F1	94.07 $\pm$ 5.01	97.07 $\pm$ 0.05	93.60 $\pm$ 0.47	97.23 $\pm$ 0.30	94.81 $\pm$ 0.08	97.15 $\pm$ 0.11	97.00 $\pm$ 0.04	97.81 $\pm$ 0.02	97.85 $\pm$ 0.03
	Micro-F1	89.37 $\pm$ 8.30	94.35 $\pm$ 0.11	88.55 $\pm$ 0.81	94.75 $\pm$ 0.58	90.56 $\pm$ 0.15	94.61 $\pm$ 0.21	94.30 $\pm$ 0.06	95.84 $\pm$ 0.04	95.95 $\pm$ 0.06
	Macro-F1	57.76 $\pm$ 9.71	60.28 $\pm$ 0.92	69.44 $\pm$ 1.61	72.91 $\pm$ 4.32	71.18 $\pm$ 0.49	73.24 $\pm$ 0.11	69.00 $\pm$ 0.93	79.75 $\pm$ 0.32	81.30 $\pm$ 0.36
Bitcoin-OTC	AUC	90.02 $\pm$ 0.97	91.63 $\pm$ 0.09	87.90 $\pm$ 0.68	89.69 $\pm$ 1.12	81.04 $\pm$ 0.30	89.33 $\pm$ 0.40	88.92 $\pm$ 0.54	95.00 $\pm$ 0.81	94.98 $\pm$ 0.04
	Binary-F1	96.25 $\pm$ 0.42	96.21 $\pm$ 0.13	92.31 $\pm$ 0.57	95.97 $\pm$ 0.33	92.69 $\pm$ 0.27	95.77 $\pm$ 0.03	95.57 $\pm$ 0.28	97.34 $\pm$ 0.11	97.53 $\pm$ 0.13

TABLE III: Performance comparison on five real-world datasets (mean

\pm

standard deviation). The PASC column reports the variant chosen by the pre-defined training-graph rule used in Fig. 3 .

Fig. 3: Variant Adaptability comparison of PASC-S and PASC-H under different signed-topology regimes.

Fig. 4: Ablation study of PASC. Panels (a) and (b) report the degradation (

\Delta\%

) in AUC and Macro-F1 when each component is removed.

Fig. 5: Sensitivity analysis of $\lambda_{1}$ and $\lambda_{2}$ on Wiki-RfA and Slashdot, showing stable AUC and Macro-F1 across loss-weight settings.

Dataset	Metrics	nSNE	SGCN	SNEA	SDGNN	RSGNN	SPMF	TrustSGCN	CFSE	PASC
Bitcoin-Alpha	AUC	69.53 $\pm$ 2.93	80.60 $\pm$ 1.58	83.10 $\pm$ 0.70	80.71 $\pm$ 0.81	74.31 $\pm$ 0.04	83.40 $\pm$ 0.54	79.89 $\pm$ 0.23	77.94 $\pm$ 1.39	84.52 $\pm$ 0.17
Bitcoin-Alpha	Macro-F1	49.80 $\pm$ 1.97	54.89 $\pm$ 6.16	70.17 $\pm$ 0.58	63.19 $\pm$ 3.48	66.61 $\pm$ 0.83	71.16 $\pm$ 0.19	59.46 $\pm$ 1.93	60.92 $\pm$ 2.22	72.05 $\pm$ 0.35
Bitcoin-OTC	AUC	76.48 $\pm$ 7.61	88.01 $\pm$ 0.10	85.46 $\pm$ 0.10	87.01 $\pm$ 0.13	79.34 $\pm$ 0.18	88.10 $\pm$ 0.35	87.77 $\pm$ 0.09	78.26 $\pm$ 5.80	89.09 $\pm$ 0.03
Bitcoin-OTC	Macro-F1	53.46 $\pm$ 7.69	75.71 $\pm$ 0.14	74.66 $\pm$ 0.28	75.67 $\pm$ 0.11	71.61 $\pm$ 0.28	76.75 $\pm$ 0.25	74.26 $\pm$ 0.20	68.10 $\pm$ 3.47	80.06 $\pm$ 0.26
Wiki-RfA	AUC	69.46 $\pm$ 1.30	78.81 $\pm$ 1.19	79.36 $\pm$ 0.16	77.27 $\pm$ 0.87	66.62 $\pm$ 1.17	78.84 $\pm$ 0.15	77.08 $\pm$ 3.01	72.25 $\pm$ 4.89	79.70 $\pm$ 0.13
Wiki-RfA	Macro-F1	50.08 $\pm$ 9.25	67.02 $\pm$ 1.25	66.13 $\pm$ 0.05	69.23 $\pm$ 0.21	53.81 $\pm$ 0.62	69.23 $\pm$ 0.18	65.48 $\pm$ 3.83	62.83 $\pm$ 1.48	69.24 $\pm$ 0.21

TABLE IV: Performance comparison under the Degree-Shift structural-shift protocol. For space, structural-shift tables report AUC and Macro-F1. Binary-F1 and Micro-F1 show similar trends and are omitted.

Dataset	Metrics	nSNE	SGCN	SNEA	SDGNN	RSGNN	SPMF	TrustSGCN	CFSE	PASC
Bitcoin-Alpha	AUC	66.02 $\pm$ 5.45	79.98 $\pm$ 0.70	79.17 $\pm$ 0.87	79.77 $\pm$ 1.50	73.37 $\pm$ 0.35	79.00 $\pm$ 0.43	80.09 $\pm$ 2.12	76.10 $\pm$ 1.27	81.67 $\pm$ 0.15
Bitcoin-Alpha	Macro-F1	49.44 $\pm$ 1.68	60.74 $\pm$ 1.07	65.82 $\pm$ 0.62	62.49 $\pm$ 3.51	62.19 $\pm$ 0.11	65.48 $\pm$ 0.49	60.38 $\pm$ 2.60	59.48 $\pm$ 1.97	67.53 $\pm$ 0.38
Bitcoin-OTC	AUC	73.00 $\pm$ 2.18	83.86 $\pm$ 0.21	82.79 $\pm$ 2.38	83.87 $\pm$ 0.21	76.38 $\pm$ 0.02	83.20 $\pm$ 0.95	84.05 $\pm$ 0.21	80.66 $\pm$ 1.99	85.33 $\pm$ 0.10
Bitcoin-OTC	Macro-F1	59.85 $\pm$ 5.63	70.81 $\pm$ 0.71	72.80 $\pm$ 1.57	69.35 $\pm$ 0.45	69.68 $\pm$ 0.21	71.84 $\pm$ 0.47	65.48 $\pm$ 0.93	69.90 $\pm$ 0.92	74.36 $\pm$ 0.54
Wiki-RfA	AUC	80.28 $\pm$ 2.19	80.52 $\pm$ 0.10	84.12 $\pm$ 0.20	81.99 $\pm$ 0.62	71.48 $\pm$ 0.10	80.95 $\pm$ 0.07	80.47 $\pm$ 0.71	83.00 $\pm$ 0.87	84.19 $\pm$ 0.23
Wiki-RfA	Macro-F1	44.53 $\pm$ 4.91	69.06 $\pm$ 2.20	75.08 $\pm$ 0.28	71.66 $\pm$ 0.68	71.91 $\pm$ 0.32	73.66 $\pm$ 0.07	64.89 $\pm$ 0.39	73.95 $\pm$ 0.82	75.28 $\pm$ 0.51

TABLE V: Performance comparison under the Structural-Shortcut-Shift structural-shift protocol. For space, structural-shift tables report AUC and Macro-F1. Binary-F1 and Micro-F1 show similar trends and are omitted.

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While signed social recommendation has shown great potential by modeling both trust and distrust relations, its effectiveness is often hindered by structural noise and data sparsity. In this work, we first identify a fundamental inconsistency across the structural, propagation, and semantic layers of existing models, which leads to biased representations learned from sparse or noisy datasets. Furthermore, we observe that most existing methods treat the observed graph as fixed, failing to bridge the gap between noisy topologies and reliable social semantics. To address these issues, we propose a unified framework named SSC-Loop that treats signed social recommendation as the maximization of structural consistency. SSC-Loop includes three dedicated modules: ESA-DA for structural consistency, a P/N/O propagation mechanism for propagation consistency, and a contrastive learning objective for semantic consistency. Experiments on Epinions demonstrate that SSC-Loop achieves strong performance on explicit signed social rating prediction, while auxiliary results on Slashdot under a derived link-existence setting further suggest its ability to exploit signed social structures. Source code is available at https://github.com/Refrainwww/SSC-Loop.

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