VisiFold: Long-Term Traffic Forecasting via Temporal Folding Graph and Node Visibility

Zhiwei Zhang; Xinyi Du; Weihao Wang; Xuanchi Guo; Wenjuan Han

cs.AIMar 12, 2026

VisiFold: Long-Term Traffic Forecasting via Temporal Folding Graph and Node Visibility

Authors: Zhiwei Zhang, Xinyi Du, Weihao Wang, Xuanchi Guo, Wenjuan Han

Organizations: Key Laboratory of Big Data & Artificial Intelligence in Transportation (Beijing Jiaotong University), Ministry of Education · School of Computer Science and Technology, Beijing Jiaotong University, Beijing 100044, China · Beijing Normal University, Beijing, China

Abstract

Traffic forecasting is a cornerstone of intelligent transportation systems. While existing research has made significant progress in short-term prediction, long-term forecasting remains a largely uncharted and challenging frontier. Extending the prediction horizon intensifies two critical issues: escalating computational resource consumption and increasingly complex spatial-temporal dependencies. Current approaches, which rely on spatial-temporal graphs and process temporal and spatial dimensions separately, suffer from snapshot-stacking inflation and cross-step fragmentation. To overcome these limitations, we propose VisiFold. Our framework introduces a novel temporal folding graph that consolidates a sequence of temporal snapshots into a single graph. Furthermore, we present a node visibility mechanism that incorporates node-level masking and subgraph sampling to overcome the computational bottleneck imposed by large node counts. Extensive experiments show that VisiFold not only drastically reduces resource consumption but also outperforms existing baselines in long-term forecasting tasks. Remarkably, even with a high mask ratio of 80%, VisiFold maintains its performance advantage. By effectively breaking the resource constraints in both temporal and spatial dimensions, our work paves the way for more realistic long-term traffic forecasting. The code is available at~ https://github.com/PlanckChang/VisiFold.

Figures & tables

Fig. 1 : From spatial-temporal graph to temporal folding graph. A spatial-temporal graph leads to snapshot-stacking inflation and cross-step fragmentation, thereby constraining the expansion of the forecasting horizon. Temporal folding graph collapses all attributes over time steps into a single node, thereby compressing a sequence of snapshots into a single graph.

Fig. 2 : Overview of VisiFold. VisiFold pipeline begins by building a temporal folding graph, from which token embeddings are derived via a linear transformation and fused with other embeddings. This is followed by node-level masking and subgraph sampling. The refined representations are then encoded by a Transformer encoder, and final predictions are generated by an MLP head.

Dataset	# Time Steps	Nodes	Time Range	Frequency
PEMS04	16992	307	2018/01 – 2018/02	288
PEMS08	17856	170	2016/07 – 2016/08	288
SEATTLE	8760	323	2015/01 – 2015/12	24

TABLE I : Summary of datasets.

	Method	24 Time Steps			36 Time Steps			48 Time Steps
	Method	RMSE	MAE	MAPE	RMSE	MAE	MAPE	RMSE	MAE	MAPE
PEMS04	HA	81.57	56.47	45.49	106.58	76.01	68.84	127.28	93.37	94.62
	VAR	41.09	27.19	21.42	45.44	30.48	24.51	49.46	33.50	27.28
	DCRNN	42.86	28.70	21.23	51.40	33.78	27.10	57.85	38.26	33.73
	GWNet	35.52	22.79	16.04	38.17	24.71	17.67	40.60	26.42	18.99
	GMAN	38.10	21.67	17.78	52.86	22.12	16.43	47.85	23.35	17.98

TABLE II : Performance comparison in long-term scenarios. The values of the three metrics are the smaller, the better. The best results are indicated in bold , and the second-best results are underlined . VisiFold outperforms the baselines in the long-term task.

Panel of Figure 5 — Fig. 3 : Resource consumption comparison. The numbers above the bars for Ours are absolute values, while those above the baseline indicate multiples relative to Ours . VisiFold gains a significant superiority in resource overhead.

Method	RMSE	MAE	MAPE
Full model	31.36	19.07	12.44
w/o Spatial Embedding	+8.22	+5.45	+4.20
w/o Dow Embedding	+0.19	+0.26	+0.18
w/o Tod embedding	+0.35	+0.29	+0.27

TABLE III : Ablation of embedding components. The full model reports absolute errors in PEMS04 24-step scenario; ablated variants report the error increase ( + ) relative to the full model. While all embeddings are helpful, spatial embeddings provide the majority of the contribution.

Fig. 4 : Performance and error bars of Full Model vs w/o Node Visibility . In the full version, which includes node-level masking and subgraph sampling, the average error decreases and the bar ranges narrow, indicating improved model stability and performance.

	PEMS04	PEMS08	SEATTLE
Only TFG	704	514	706
w/ Node-level Masking	-10.23%	-8.56%	-6.23%
w/ Subgraph Sampling	-1.70%	-2.33%	-4.53%
Full Model	-12.22%	-10.86%	-11.33%

TABLE IV : Memory overhead (MB) of the ablation of node visibility. Only TFG uses absolute numbers, while the results with node visibility are reported as percentage reductions.

Fig. 5 : Analysis of mask ratio. We report the second-best performance from TABLE II as a reference. Even when 90% of the nodes are masked, we still observe performance gains. During training, both per-epoch time and memory consumption decrease as the mask ratio increases.

Method	RMSE	MAE	MAPE
Node-level	7.22	3.82	11.87
AllZero	+0.08	+0.05	+0.05
PartialZero	+0.09	+0.04	+0.05
RandomValue	+0.15	+0.07	+0.14

TABLE V : Masking strategies comparison. Node-level masking surpasses other strategies.

Fig. 6 : Analysis of subgraph size. We report the second-best performance from TABLE II as a reference. When the subgraph is relatively small, resource consumption generally follows a linear pattern; however, as the subgraph grows large enough to affect padding values, fluctuations occur in the right part. Selecting subgraph size requires a balance between performance and efficiency.

	Method	24 Time Steps			36 Time Steps			48 Time Steps
	Method	RMSE	MAE	MAPE	RMSE	MAE	MAPE	RMSE	MAE	MAPE
PEMS04	TFG	31.70	19.36	12.84	32.57	19.92	13.23	33.90	20.70	13.61
PEMS04	SF	37.37	22.98	15.46	37.85	23.30	15.65	38.11	23.60	16.16
PEMS08	TFG	25.60	15.19	10.05	26.81	15.99	10.69	27.75	16.66	11.10
PEMS08	SF	35.92	21.45	13.75	36.70	21.76	14.09	36.48	21.59	14.15

TABLE VI : Comparison of folding strategies. The SF counterpart folding along the spatial dimension inferior to the TFG.

Fig. 7 : Illustration of traffic flow on the first day at Node 72, 95, and 111 in PEMS04. Node 72 and Node 95, being neighborhoods, exhibit similar flow patterns. Surprisingly, Node 111 also shows a similar trend, although it is not spatially adjacent to Node 72 and Node 95.

Dataset	Setting	24 Time Steps			36 Time Steps			48 Time Steps
Dataset	Setting	RMSE	MAE	MAPE	RMSE	MAE	MAPE	RMSE	MAE	MAPE
PEMS04	VisiFold	31.36	19.07	12.44	32.52	19.78	12.92	33.23	20.27	13.35
	Node-specific $E_{tod}$ and $E_{dow}$	31.64	19.32	12.57	32.93	20.07	13.02	33.52	20.53	13.48
	w/ Leader token (shared)	32.02	19.52	12.89	33.15	20.29	13.28	33.88	20.76	13.95
	w/ Leader token (exclusive)	32.03	19.62	13.09	32.92	20.16	13.92	35.01	21.22	13.80
PEMS08	VisiFold	25.31	14.73	9.84	26.51	15.48	10.38	27.49	16.35	10.98

TABLE VII : Analysis of node-specific temporal embeddings and subgraph interaction scheme.

Panel of Figure 15 — Fig. 8 : Visualizations of $E_{tod}$ , $E_{dow}$ , and $E_{s}$ .

Fig. 9 : Error analysis. VisiFold has learned the main trend patterns, but the prediction accuracy reduces during the traffic peak.

Hyperparameter	PEMS04	PEMS08	SEATTLE
Mask ratio	0.2	0.2	0.2
Subgraph size	50	30	50
Embedding dim	64	32	64
Feed-forward dim	1024	1024	1024
Heads	4	4	4
Layers	1	1	1

TABLE VIII : Key Hyperparameter Settings.

Traffic Forecasting

Traffic forecasting predicts future flows, speeds, demand, travel times, and congestion from spatial, temporal, and contextual data.

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Aug 2, 2024J/K move · Enter open · S save

Spatio-Temporal Partial Sensing Forecast for Long-term Traffic

Zibo Liu, Zhe Jiang, Zelin Xu, Tingsong Xiao+4

Department of Computer & Information Science & Engineering, University of Florida · Department of Computer Science, University of Kentucky

Long-Term Time Series Forecasting Spatiotemporal Forecasting Traffic Forecasting

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Traffic forecasting uses recent measurements by sensors installed at chosen locations to forecast the future road traffic. Existing work either assumes all locations are equipped with sensors or focuses on short-term forecast. This paper studies partial sensing forecast of long-term traffic, assuming sensors are available only at some locations. The problem is challenging due to the unknown data distribution at unsensed locations, the intricate spatio-temporal correlation in long-term forecasting, as well as noise to traffic patterns. We propose a Spatio-temporal Long-term Partial sensing Forecast model (SLPF) for traffic prediction, with several novel contributions, including a rank-based embedding technique to reduce the impact of noise in data, a spatial transfer matrix to overcome the spatial distribution shift from sensed locations to unsensed locations, and a multi-step training process that utilizes all available data to successively refine the model parameters for better accuracy. Extensive experiments on several real-world traffic datasets demonstrate its superior performance. Our source code is at https://github.com/zbliu98/SLPF

Abstract

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