TFWaveFormer: Temporal-Frequency Collaborative Multi-level Wavelet Transformer for Dynamic Link Prediction

Hantong Feng; Yonggang Wu; Duxin Chen; Wenwu Yu

cs.LGMar 4, 2026

TFWaveFormer: Temporal-Frequency Collaborative Multi-level Wavelet Transformer for Dynamic Link Prediction

Authors: Hantong Feng, Yonggang Wu, Duxin Chen, Wenwu Yu

Organizations: School of Cyber Science and Engineering, Southeast University, Nanjing, China · School of Mathematics, Southeast University, Nanjing, China

Abstract

Dynamic link prediction plays a crucial role in diverse applications including social network analysis, communication forecasting, and financial modeling. While recent Transformer-based approaches have demonstrated promising results in temporal graph learning, their performance remains limited when capturing complex multi-scale temporal dynamics. In this paper, we propose TFWaveFormer, a novel Transformer architecture that integrates temporal-frequency analysis with multi-resolution wavelet decomposition to enhance dynamic link prediction. Our framework comprises three key components: (i) a temporal-frequency coordination mechanism that jointly models temporal and spectral representations, (ii) a learnable multi-resolution wavelet decomposition module that adaptively extracts multi-scale temporal patterns through parallel convolutions, replacing traditional iterative wavelet transforms, and (iii) a hybrid Transformer module that effectively fuses local wavelet features with global temporal dependencies. Extensive experiments on benchmark datasets demonstrate that TFWaveFormer achieves state-of-the-art performance, outperforming existing Transformer-based and hybrid models by significant margins across multiple metrics. The superior performance of TFWaveFormer validates the effectiveness of combining temporal-frequency analysis with wavelet decomposition in capturing complex temporal dynamics for dynamic link prediction tasks.

Figures & tables

Figure 1. The proposed TFWaveFormer framework. The architecture consists of three key components: (1) feature integration, (2) multi-level wavelet transformation, and (3) temporal-frequency hybrid transformer for generating final representations.

Metr.	Datasets	DyRep	TGN	CAWN	GraphMixer	FreeDyG	DyGFormer	CorDGT	CTAN	DyGMamba	OURS
AP	Wikipedia	94.86 $\pm$ 0.06	98.45 $\pm$ 0.06	98.76 $\pm$ 0.03	97.25 $\pm$ 0.03	99.23 $\pm$ 0.01	98.82 $\pm$ 0.02	99.07 $\pm$ 0.01	96.61 $\pm$ 0.79	99.15 $\pm$ 0.02	99.33 $\pm$ 0.01
	Reddit	98.22 $\pm$ 0.04	98.63 $\pm$ 0.06	99.11 $\pm$ 0.01	97.31 $\pm$ 0.01	99.21 $\pm$ 0.01	99.11 $\pm$ 0.01	99.18 $\pm$ 0.00	97.21 $\pm$ 0.84	99.31 $\pm$ 0.01	99.32 $\pm$ 0.01
	MOOC	81.97 $\pm$ 0.49	89.15 $\pm$ 1.60	80.15 $\pm$ 0.25	82.78 $\pm$ 0.15	87.23 $\pm$ 0.45	89.01 $\pm$ 0.11	84.35 $\pm$ 0.14	84.71 $\pm$ 2.85	89.21 $\pm$ 0.08	91.24 $\pm$ 0.05
	LastFM	71.92 $\pm$ 2.21	77.07 $\pm$ 3.97	86.99 $\pm$ 0.06	75.61 $\pm$ 0.24	90.74 $\pm$ 0.14	93.00 $\pm$ 0.12	92.23 $\pm$ 0.10	86.44 $\pm$ 0.80	93.35 $\pm$ 0.20	94.64 $\pm$ 0.05
	Enron	82.38 $\pm$ 3.36	86.53 $\pm$ 1.11	89.56 $\pm$ 0.09	82.25 $\pm$ 0.16	92.51 $\pm$ 0.05	92.47 $\pm$ 0.12	91.76 $\pm$ 0.50	92.52 $\pm$ 1.20	92.65 $\pm$ 0.12	92.70 $\pm$ 0.20
	Social Evo.	88.87 $\pm$ 0.30	93.57 $\pm$ 0.17	84.96 $\pm$ 0.09	93.37 $\pm$ 0.07	94.54 $\pm$ 0.01	94.53 $\pm$ 0.01	93.81 $\pm$ 0.02	Timeout	94.77 $\pm$ 0.01	94.65 $\pm$ 0.01

Table 1. Results for transductive dynamic link prediction with Average Precision and Area Under the ROC metrics under random negative sampling strategy.

Metr.	Datasets	DyRep	TGN	CAWN	GraphMixer	FreeDyG	DyGFormer	CorDGT	CTAN	DyGMamba	OURS
AP	Wikipedia	92.43 $\pm$ 0.37	97.83 $\pm$ 0.04	98.24 $\pm$ 0.03	96.65 $\pm$ 0.02	98.91 $\pm$ 0.01	98.59 $\pm$ 0.03	98.48 $\pm$ 0.02	93.58 $\pm$ 0.65	98.77 $\pm$ 0.03	98.94 $\pm$ 0.01
	Reddit	96.09 $\pm$ 0.11	97.50 $\pm$ 0.07	98.62 $\pm$ 0.01	95.26 $\pm$ 0.02	98.84 $\pm$ 0.02	98.84 $\pm$ 0.02	98.82 $\pm$ 0.01	80.07 $\pm$ 2.53	98.97 $\pm$ 0.01	98.98 $\pm$ 0.01
	MOOC	81.07 $\pm$ 0.44	89.04 $\pm$ 1.17	81.42 $\pm$ 0.24	81.41 $\pm$ 0.21	88.05 $\pm$ 0.49	86.96 $\pm$ 0.43	83.74 $\pm$ 0.51	64.99 $\pm$ 2.24	88.64 $\pm$ 0.08	90.26 $\pm$ 0.36
	LastFM	83.02 $\pm$ 1.48	81.45 $\pm$ 4.29	89.42 $\pm$ 0.07	82.11 $\pm$ 0.42	93.01 $\pm$ 0.23	94.23 $\pm$ 0.09	93.03 $\pm$ 0.18	60.40 $\pm$ 3.01	94.42 $\pm$ 0.21	95.49 $\pm$ 0.02
	Enron	74.55 $\pm$ 3.95	77.94 $\pm$ 1.02	86.35 $\pm$ 0.51	75.88 $\pm$ 0.48	89.69 $\pm$ 0.17	89.76 $\pm$ 0.34	91.65 $\pm$ 0.13	74.61 $\pm$ 1.64	89.67 $\pm$ 0.27	88.25 $\pm$ 0.27
	Social Evo.	90.04 $\pm$ 0.47	90.77 $\pm$ 0.86	79.94 $\pm$ 0.18	91.86 $\pm$ 0.06	93.10 $\pm$ 0.02	93.14 $\pm$ 0.04	92.44 $\pm$ 0.08	Timeout	93.13 $\pm$ 0.05	93.21 $\pm$ 0.02

Table 2. Results for inductive dynamic link prediction with Average Precision and Area Under the ROC Curve under random negative sampling strategy.

Panel of Figure 2 — Figure 2. Comparison performance and training time per epoch on Wikipedia and Reddit.(a) Wikipedia, (b) Reddit.

Panel of Figure 3 — Figure 3. Results of hyper-parameters sensitivity to the number of wavelet convolution kernels $m$ in dynamic link prediction experiments across different datasets. (a) Wikipedia, (b) Reddit, (c) MOOC, (d) LastFM, (e) Enron, (f) Social Evolution, (g) UCI, (h) Flights.

Panel of Figure 4 — Figure 4. Results on ablation study for dynamic link prediction Under differrent settings. (a) Transductive setting, (b) Inductive setting.

Datasets	transductive		inductive
Datasets	hist	ind	hist	ind
Wikipedia	86.21	73.36	70.08	70.07
Reddit	83.77	90.88	68.50	68.54
MOOC	88.31	82.46	79.97	79.99
LastFM	84.80	75.52	79.52	79.52
Enron	78.64	84.23	81.26	81.26

Table 3. Results for dynamic link prediction with AP under historical and inductive negative sampling strategies.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	#Nodes	#Links	Time Span	Domain
Wikipedia	9,227	157,474	1 month	Social
Reddit	10,984	672,447	1 month	Social
MOOC	7,144	411,749	17 months	Interaction
LastFM	1,980	1,293,103	1 month	Interaction
Enron	184	125,235	3 years	Social
Social Evo.	74	2,099,519	8 months	Proximity

Appendix

Table 4. Dataset Statistics.

Panel of Figure 5 — Figure 5. Results of hyper-parameters sensitivity study to the number of wavelet convolution kernels $m$ in dynamic link prediction experiments across different datasets. (a) UN Trade, (b) Contact.

NSS	Datasets	JODIE	DyRep	TGAT	TGN	CAWN	EdgeBank	TCL	GraphMixer	FreeDyG	DyGFormer	TFWaveFormer
hist	Wikipedia	83.01 $\pm$ 0.66	79.93 $\pm$ 0.56	87.38 $\pm$ 0.22	86.86 $\pm$ 0.33	71.21 $\pm$ 1.67	73.35 $\pm$ 0.00	89.05 $\pm$ 0.39	90.90 $\pm$ 0.10	76.13 $\pm$ 1.65	82.23 $\pm$ 2.54	86.21 $\pm$ 1.09
	Reddit	80.03 $\pm$ 0.36	79.83 $\pm$ 0.31	79.55 $\pm$ 0.20	81.22 $\pm$ 0.61	80.82 $\pm$ 0.45	73.59 $\pm$ 0.00	77.14 $\pm$ 0.16	78.44 $\pm$ 0.18	83.08 $\pm$ 0.50	81.57 $\pm$ 0.67	83.77 $\pm$ 0.43
	MOOC	78.94 $\pm$ 1.25	75.60 $\pm$ 1.12	82.19 $\pm$ 0.62	87.06 $\pm$ 1.93	74.05 $\pm$ 0.95	60.71 $\pm$ 0.00	77.06 $\pm$ 0.41	77.77 $\pm$ 0.92	80.59 $\pm$ 0.29	85.85 $\pm$ 0.66	88.31 $\pm$ 0.37
	LastFM	74.35 $\pm$ 3.81	74.92 $\pm$ 2.46	71.59 $\pm$ 0.24	76.87 $\pm$ 4.64	69.86 $\pm$ 0.43	73.03 $\pm$ 0.00	59.30 $\pm$ 2.31	72.47 $\pm$ 0.49	83.41 $\pm$ 0.67	81.57 $\pm$ 0.48	84.80 $\pm$ 0.45
	Enron	69.85 $\pm$ 2.70	71.19 $\pm$ 2.76	64.07 $\pm$ 1.05	73.91 $\pm$ 1.76	64.73 $\pm$ 0.36	76.53 $\pm$ 0.00	70.66 $\pm$ 0.39	77.98 $\pm$ 0.92	78.87 $\pm$ 0.82	75.63 $\pm$ 0.73	78.64 $\pm$ 0.35
	Social Evo.	87.44 $\pm$ 6.78	93.29 $\pm$ 0.43	95.01 $\pm$ 0.44	94.45 $\pm$ 0.56	85.53 $\pm$ 0.38	80.57 $\pm$ 0.00	94.74 $\pm$ 0.31	94.93 $\pm$ 0.31	97.79 $\pm$ 0.23	97.38 $\pm$ 0.14	96.96 $\pm$ 0.21

Appendix

Table 5. AP for transductive dynamic link prediction with historical, and inductive negative sampling strategies. NSS is the abbreviation of Negative Sampling Strategies.

NSS	Datasets	JODIE	DyRep	TGAT	TGN	CAWN	EdgeBank	TCL	GraphMixer	FreeDyG	DyGFormer	TFWaveFormer
hist	Wikipedia	80.77 $\pm$ 0.73	77.74 $\pm$ 0.33	82.87 $\pm$ 0.22	82.74 $\pm$ 0.32	67.84 $\pm$ 0.64	77.27 $\pm$ 0.00	85.76 $\pm$ 0.46	87.68 $\pm$ 0.17	75.17 $\pm$ 1.72	78.80 $\pm$ 1.95	83.09 $\pm$ 2.03
	Reddit	80.52 $\pm$ 0.32	80.15 $\pm$ 0.18	79.33 $\pm$ 0.16	81.11 $\pm$ 0.19	80.27 $\pm$ 0.30	78.58 $\pm$ 0.00	76.49 $\pm$ 0.16	77.80 $\pm$ 0.12	81.90 $\pm$ 0.21	80.54 $\pm$ 0.29	82.01 $\pm$ 0.37
	MOOC	82.75 $\pm$ 0.83	81.06 $\pm$ 0.94	80.81 $\pm$ 0.67	88.00 $\pm$ 1.80	71.57 $\pm$ 1.07	61.90 $\pm$ 0.00	72.09 $\pm$ 0.56	76.68 $\pm$ 1.40	81.99 $\pm$ 0.25	87.04 $\pm$ 0.35	89.14 $\pm$ 0.27
	LastFM	75.22 $\pm$ 2.36	74.65 $\pm$ 1.98	64.27 $\pm$ 0.26	77.97 $\pm$ 3.04	67.88 $\pm$ 0.24	78.09 $\pm$ 0.00	47.24 $\pm$ 3.13	64.21 $\pm$ 0.73	78.54 $\pm$ 0.41	78.78 $\pm$ 0.35	80.60 $\pm$ 0.27
	Enron	75.39 $\pm$ 2.37	74.69 $\pm$ 3.55	61.85 $\pm$ 1.43	77.09 $\pm$ 2.22	65.10 $\pm$ 0.34	79.59 $\pm$ 0.00	67.95 $\pm$ 0.88	75.27 $\pm$ 1.14	75.74 $\pm$ 0.72	76.55 $\pm$ 0.52	80.30 $\pm$ 0.76
	Social Evo.	90.06 $\pm$ 3.15	93.12 $\pm$ 0.34	93.08 $\pm$ 0.59	94.71 $\pm$ 0.53	87.43 $\pm$ 0.15	85.81 $\pm$ 0.00	93.44 $\pm$ 0.68	94.39 $\pm$ 0.31	97.42 $\pm$ 0.02	97.28 $\pm$ 0.07	97.19 $\pm$ 0.15

Appendix

Table 6. AUC-ROC for transductive dynamic link prediction with historical, and inductive negative sampling strategies.

NSS	Datasets	JODIE	DyRep	TGAT	TGN	CAWN	TCL	GraphMixer	FreeDyG	DyGFormer	TFWaveFormer
hist	Wikipedia	68.69 $\pm$ 0.39	62.18 $\pm$ 1.27	84.17 $\pm$ 0.22	81.76 $\pm$ 0.32	67.27 $\pm$ 1.63	82.20 $\pm$ 2.18	87.60 $\pm$ 0.30	68.57 $\pm$ 5.01	71.42 $\pm$ 4.43	70.08 $\pm$ 5.12
	Reddit	62.34 $\pm$ 0.54	61.60 $\pm$ 0.72	63.47 $\pm$ 0.36	64.85 $\pm$ 0.85	63.67 $\pm$ 0.41	60.83 $\pm$ 0.25	64.50 $\pm$ 0.26	64.64 $\pm$ 0.38	65.37 $\pm$ 0.60	68.50 $\pm$ 0.68
	MOOC	63.22 $\pm$ 1.55	62.93 $\pm$ 1.24	76.73 $\pm$ 0.29	77.07 $\pm$ 3.41	74.68 $\pm$ 0.68	74.27 $\pm$ 0.53	74.00 $\pm$ 0.97	71.29 $\pm$ 0.57	80.82 $\pm$ 0.30	79.97 $\pm$ 0.50
	LastFM	70.39 $\pm$ 4.31	71.45 $\pm$ 1.76	76.27 $\pm$ 0.25	66.65 $\pm$ 6.11	71.33 $\pm$ 0.47	65.78 $\pm$ 0.65	76.42 $\pm$ 0.22	77.87 $\pm$ 0.54	76.35 $\pm$ 0.52	79.52 $\pm$ 0.50
	Enron	65.86 $\pm$ 3.71	62.08 $\pm$ 2.27	61.40 $\pm$ 1.31	62.91 $\pm$ 1.16	60.70 $\pm$ 0.36	67.11 $\pm$ 0.62	72.37 $\pm$ 1.37	73.01 $\pm$ 0.88	67.07 $\pm$ 0.62	81.26 $\pm$ 0.37
	Social Evo.	88.51 $\pm$ 0.87	88.72 $\pm$ 1.10	93.97 $\pm$ 0.54	90.66 $\pm$ 1.62	79.83 $\pm$ 0.38	94.10 $\pm$ 0.31	94.01 $\pm$ 0.47	96.69 $\pm$ 0.14	96.82 $\pm$ 0.16	95.85 $\pm$ 0.24

Appendix

Table 7. AP for inductive dynamic link prediction with historical, and inductive negative sampling strategies.

NSS	Datasets	JODIE	DyRep	TGAT	TGN	CAWN	TCL	GraphMixer	FreeDyG	DyGFormer	TFWaveFormer
hist	Wikipedia	61.86 $\pm$ 0.53	57.54 $\pm$ 1.09	78.38 $\pm$ 0.20	75.75 $\pm$ 0.29	62.04 $\pm$ 0.65	79.79 $\pm$ 0.96	82.87 $\pm$ 0.21	65.400 $\pm$ 4.81	68.33 $\pm$ 2.82	68.78 $\pm$ 3.00
	Reddit	61.69 $\pm$ 0.39	60.45 $\pm$ 0.37	64.43 $\pm$ 0.27	64.55 $\pm$ 0.50	64.94 $\pm$ 0.21	61.43 $\pm$ 0.26	64.27 $\pm$ 0.13	63.60 $\pm$ 0.31	64.81 $\pm$ 0.25	66.93 $\pm$ 0.39
	MOOC	64.48 $\pm$ 1.64	64.23 $\pm$ 1.29	74.08 $\pm$ 0.27	77.69 $\pm$ 3.55	71.68 $\pm$ 0.94	69.82 $\pm$ 0.32	72.53 $\pm$ 0.84	73.60 $\pm$ 0.87	80.77 $\pm$ 0.63	81.95 $\pm$ 0.53
	LastFM	68.44 $\pm$ 3.26	68.79 $\pm$ 1.08	69.89 $\pm$ 0.28	66.99 $\pm$ 5.62	67.69 $\pm$ 0.24	55.88 $\pm$ 1.85	70.07 $\pm$ 0.20	71.24 $\pm$ 0.41	70.73 $\pm$ 0.37	72.38 $\pm$ 0.34
	Enron	65.32 $\pm$ 3.57	61.50 $\pm$ 2.50	57.84 $\pm$ 2.18	62.68 $\pm$ 1.09	62.25 $\pm$ 0.40	64.06 $\pm$ 1.02	68.20 $\pm$ 1.62	70.09 $\pm$ 0.65	65.78 $\pm$ 0.42	81.59 $\pm$ 0.38
	Social Evo.	88.53 $\pm$ 0.55	87.93 $\pm$ 1.05	91.87 $\pm$ 0.72	92.10 $\pm$ 1.22	83.54 $\pm$ 0.24	93.28 $\pm$ 0.60	93.62 $\pm$ 0.35	96.94 $\pm$ 0.17	96.91 $\pm$ 0.09	96.52 $\pm$ 0.05

Appendix

Table 8. AUC-ROC for inductive dynamic link prediction with historical, and inductive negative sampling strategies.

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A Hybrid TGN-SEAL Model for Dynamic Graph Link Prediction

Nafiseh Sadat Sajadi, Behnam Bahrak, Mahdi Jafari Siavoshani

Department of Computer Engineering, Sharif University of Technology, Tehran, Iran. · Tehran Institute for Advanced Studies, Khatam University, Tehran, Iran.

Temporal GNNs Link Prediction Temporal Link Prediction Dynamic Graph Learning

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Predicting links in sparse, continuously evolving networks is a central challenge in network science. Conventional heuristic methods and deep learning models, including Graph Neural Networks (GNNs), are typically designed for static graphs and thus struggle to capture temporal dependencies. Snapshot-based techniques partially address this issue but often encounter data sparsity and class imbalance, particularly in networks with transient interactions such as telecommunication call detail records (CDRs). Temporal Graph Networks (TGNs) model dynamic graphs by updating node embeddings over time; however, their predictive accuracy under sparse conditions remains limited. In this study, we improve the TGN framework by extracting enclosing subgraphs around candidate links, enabling the model to jointly learn structural and temporal information. Experiments on a sparse CDR, email, message dataset show that our approach increases average precision by at least 2% over standard TGNs, demonstrating the advantages of integrating local topology for robust link prediction in dynamic networks.

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