Organizations: College of Computer Science and Technology, Jilin University, Changchun, China · Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China · Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun, China · Shenzhen Institute for Advanced Study, University of Electronic Science and Technology of China, Shenzhen, China · The Chinese University of Hong Kong, Hong Kong, China
Spatial-temporal forecasting is pivotal for intelligent urban management yet remains challenging due to the intricate coupling of spatial dynamics and temporal non-stationarity. Existing approaches, while effective, often overlook two fundamental characteristics of real-world data: (1) Granularity-dependence, where dominant spatial correlations shift significantly across different time scales, and (2) Signal entanglement, where global common patterns are inextricably mixed with node-specific disturbances. In this paper, we propose a novel framework named M2Net (Multi-Scale Masked attention and Prototype network) to unify scale-specific structural learning and semantic decomposition. First, to capture the evolution of spatial dependencies, we introduce a Multi-Scale Masked attention mechanism. By downsampling temporal features into multiple resolutions, we dynamically generate scale-adaptive spatial masks, allowing the model to distinguish between micro-scale physical neighbors and macro-scale functional correlations. Second, to disentangle unique variations from shared trends, we propose a Prototype Residual Learning module. It retrieves global common patterns from a momentum-updated prototype bank and subtracts them from node representations, explicitly forcing the network to model the residual unique deviations. By integrating these two orthogonal views, i.e., structural multiscaling and semantic decomposition, our approach effectively isolates valid spatial-temporal signals from noise. Extensive experiments on real-world datasets demonstrate that M2Net outperforms state-of-the-art baselines on extensive empirical verifications.
Figures & tables
Fig. 1 : Spatial relation visualization of PEMS08. Adjacent nodes ( e.g., 74 and 75) exhibit high spatial correlation at both scales. Coarse temporal scale (c) captures more long-range, non-adjacent relationships ( e.g., nodes 80–115) compared to fine-grained scale (b).
Fig. 2 : The framework of M2Net . Our model consists of two complementary branches: (1) Multi-Scale Masked Attention (MSMA) first applies Seasonal-Trend Decomposition (STD) to input time series, then captures spatial dependencies at multiple temporal resolutions by generating scale-specific masks from multi-resolution temporal features, and (2) Prototype Residual Learning (PRL) separates global patterns from node-specific variations using a momentum-updated prototype bank P . Both branches are fused for final forecasting. The right panel shows the Seasonal Encoder (the trend encoder follows the same framework), where multi-scale masks {M(l)} modulate shared QKV projections to produce scale-specific attention outputs {Z(l)} , aggregated through LayerNorm and FFN layers.
Dataset
Sensors
Timesteps
Time Range
PEMS-BAY
325
52,116
01/2017 – 06/2017
PEMS07
883
28,224
05/2017 – 08/2017
PEMS08
170
17,856
07/2016 – 08/2016
PEMS03
358
26,208
09/2018 – 11/2018
PEMS04
307
16,992
01/2018 – 02/2018
TABLE I : Dataset statistics.
Method
PEMS-BAY
PEMS07
PEMS08
PEMS03
PEMS04
Metrics
MAE
RMSE
MAPE(%)
MAE
RMSE
MAPE(%)
MAE
RMSE
MAPE(%)
MAE
RMSE
MAPE(%)
MAE
RMSE
MAPE(%)
(a)
PDFormer
1.62
3.65
3.66
19.97
32.95
8.55
14.09
23.41
9.05
14.94
25.39
15.82
18.36
30.03
12.00
STAEformer
1.65
3.61
3.75
20.09
33.36
8.41
14.17
23.63
9.28
15.27
26.76
15.88
18.34
31.14
13.06
STDN
1.60
3.78
3.62
22.94
36.06
10.32
14.41
23.89
10.26
15.34
27.12
17.71
18.79
34.13
16.96
(b)
DGCRN
1.64
3.67
3.66
20.24
33.08
8.71
14.34
23.53
9.48
15.09
26.02
16.05
18.68
30.21
13.04
AGCRN
1.65
3.68
3.75
20.40
34.24
8.62
15.54
24.77
10.15
15.60
26.88
15.25
19.25
31.10
13.00
TABLE II: Performance comparison of different methods. “(ours)” means our proposed method M2Net . The best results are bolded and the second-best results are underlined . “(a)” denotes Transformer-based methods, “(b)” denotes GRU-based methods, “(c)” denotes CNN/GNN-based baselines, “(d)” denotes lightweight methods, “(ours)” denotes M2Net .
Method
PEMS03
PEMS04
PEMS08
Metrics
MAE
RMSE
MAPE(%)
MAE
RMSE
MAPE(%)
MAE
RMSE
MAPE(%)
w/o MSMA
14.96
25.65
15.70
18.33
30.25
12.56
14.13
23.27
9.24
Mask-T
14.65
25.05
15.32
18.33
30.43
12.54
14.06
23.20
9.20
Mask-S
14.77
25.72
16.32
18.24
30.05
12.39
14.16
23.32
9.25
w/o Dec
14.82
25.96
15.57
18.31
30.16
12.67
14.07
23.16
9.20
A-Dual
14.90
25.64
15.33
18.30
30.17
12.50
14.11
23.29
9.23
TABLE III : Ablation study results.
Models
RAST
STDN
GWNet
STID
Metrics
✗
✓
Impr(%)
✗
✓
Impr(%)
✗
✓
Impr(%)
✗
✓
Impr(%)
PEMS03
MAE
15.94
15.82
↑ 0.75
15.34
15.34
-
14.55
14.43
↑ 0.82
15.41
15.27
↑ 0.91
RMSE
27.17
27.13
↑ 0.15
27.12
26.84
↑ 1.03
25.66
25.01
↑ 2.53
27.42
25.10
↑ 8.46
PEMS04
MAE
19.48
19.14
↑ 1.75
18.79
18.79
-
18.80
18.73
↑ 0.37
18.47
18.36
↑ 0.60
RMSE
31.08
30.61
↑ 1.51
34.13
32.13
↑ 5.86
30.33
30.19
↑ 0.46
30.02
29.91
↑ 0.37
PEMS08
MAE
15.14
14.90
↑ 1.59
14.41
14.27
↑ 0.97
14.59
14.53
↑ 0.41
14.22
14.13
↑ 0.63
TABLE IV : Compatibility analysis of PRL module across different baseline models on PEMS03, PEMS04 and PEMS08.
Method
PEMS03
PEMS04
PEMS08
Metrics
MAE
RMSE
MAPE(%)
MAE
RMSE
MAPE(%)
MAE
RMSE
MAPE(%)
Global Mean
14.75
26.76
15.76
18.40
30.50
12.76
14.14
23.23
9.28
K-means Cluster
14.74
25.57
15.55
18.29
30.20
12.57
14.10
23.19
9.22
Soft Cluster
14.68
25.80
15.33
18.29
30.21
12.68
14.06
23.23
9.21
M2Net
14.65
24.68
15.17
18.20
29.89
12.43
14.02
23.10
9.15
TABLE V : Analysis of residual construction strategies for PRL on PEMS03, PEMS04 and PEMS08.
Fig. 3 : Power Spectral Density (PSD) and Low/High-Frequency Energy comparison of global, prototype, and residual representations on PEMS08.
Fig. 4 : Hyper-parameter analysis.
Dataset
PEMS08
PEMS07
Metrics
Train Time (s)
Infer Time (s)
Params (K)
Mem Usage (MB)
Train Time (s)
Infer Time (s)
Params (K)
Mem Usage (MB)
D2 STGNN
34.94
4.55
391
8296
672.45
87.32
405
15613
STAEFormer
35.11
4.56
1223
8018
458.81
55.29
1908
22919
STWave
31.47
5.25
882
5660
247.83
39.87
882
8539
STDN
39.93
4.79
5876
9028
293.39
31.05
4489
9213
RAST
15.58
4.79
265
1244
76.78
20.78
311
3253
TABLE VI : Efficiency comparison on PEMS08 and PEMS07.
Method
PEMS03
PEMS04
PEMS08
Metrics
MAE
RMSE
MAPE(%)
MAE
RMSE
MAPE(%)
MAE
RMSE
MAPE(%)
Continuous Similarity
14.81
27.19
15.67
18.28
30.16
12.55
14.02
23.15
9.33
Adaptive Attention
14.72
25.83
15.34
18.34
30.31
12.51
14.08
23.12
9.21
M2Net
14.65
24.68
15.17
18.20
29.89
12.43
14.02
23.10
9.15
TABLE VII : Comparative analysis of MSMA module on PEMS03, PEMS04 and PEMS08.
Fig. 5 : Compatibility analysis of MSMA with STAEFormer on PEMS04 and PEMS08.
Fig. 6 : Case study of multi-scale mask for node 91.
Metrics
MAE
RMSE
MAPE(%)
Train Time (s)
Infer Time (s)
Params (K)
Batch Size
STAEformer
21.30
34.56
17.63
2226.32
247.46
3318
8
DGCRN
20.53
34.40
16.79
2157.33
618.62
371
32
STWave
20.56
33.98
15.14
551.74
91.33
882
64
RAST
20.64
34.47
16.63
323.59
101.54
1491
64
M2Net
20.05
33.69
15.97
350.46
50.77
325
64
TABLE VIII : Scalability evaluation on GBA dataset.
As a core task in intelligent transportation systems, traffic forecasting plays a critical role in urban traffic management. Accurate traffic forecasting relies on modeling complex spatiotemporal dependencies, which is inherently challenging due to spatial heterogeneity in traffic systems.Despite significant progress, most existing methods are still limited to pairwise spatial dependency modeling, making it difficult to capture dynamic high-order interactions among nodes with similar traffic patterns. To address this issue, we propose PHGNet, a novel spatiotemporal forecasting framework based on prototype-guided hypergraph construction. At the core of PHGNet, a prototype learning mechanism is designed to adaptively assign pattern-similar nodes to hyperedges, thereby capturing high-order interactions with time-varying structures. To improve the reliability of dynamic hypergraph construction, we further develop a global-local node representation module to extract time-consistent features. For forecasting, iterative residual refinement and Temporal Query Attention are introduced to improve forecasting accuracy while supporting efficient parallel decoding. Extensive experiments on multiple real-world datasets demonstrate that PHGNet achieves superior predictive performance compared with state-of-the-art methods.
Ruiwen Gu, Yahao Liu, Zhenyu Liu +2
Shenzhen Ubiquitous Data Enabling Key Lab Shenzhen International Graduate School, Tsinghua University, Shenzhen, China · School of Computer Science and Engineering University of Electronic Science and Technology of China, Chengdu, China
Accurate spatiotemporal pattern analysis is critical in fields such as urban traffic, meteorology, and public health monitoring. However, existing methods face performance bottlenecks, typically yielding only incremental gains and often exhibiting limited cross-domain transferability. We analyze this bottleneck through spatial and temporal entropy measures, which are used as diagnostic indicators of spatiotemporal complexity mismatch rather than as guarantees that entropy alignment alone yields better forecasting. Empirically, larger mismatch is often accompanied by higher prediction uncertainty, especially under a fixed model-capacity budget. Guided by this diagnostic, we propose a scalable, adaptive framework that harmonizes spatial and temporal feature representations. Spatial dimensionality is compressed via low-rank matrix embedding to preserve essential structure, while an extended temporal horizon captures long-range dependencies and mitigates cumulative errors arising from temporal heterogeneity. Extensive experiments on urban traffic, meteorological, and epidemic datasets demonstrate substantial accuracy gains and broad applicability across the evaluated domains, suggesting that the framework is promising for a wide range of spatiotemporal tasks beyond the current study. The code is available on GitHub at https://github.com/ST-Balance/ST-Balance.
Jing Chen, Shixiang Pan, Yujie Fan +3
School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou, 310018, China · Key Laboratory of New Industrial Internet Control Technology, Hangzhou, 310018, China · College of Economics, China Jiliang University, Hangzhou, 314423, China
Spatiotemporal forecasting is critical for real-world applications like traffic management, yet capturing reliable interactions remains challenging under noisy and non-stationary conditions. Existing methods primarily rely on historical spatial priors, often failing to account for evolving temporal correlations and suffering from systematic errors. In this work, we propose a nested forecasting framework that couples future macro-level regional trends with micro-level historical observations, enabling top-down guidance from abstract future representations for fine-grained forecasting. Specifically, we employ a spectral clustering-based approach to construct semantically coherent regions, providing both theoretical and empirical evidence that this representation effectively filters systematic noise while preserving essential trends. Building on this, we develop a progressive coarse-to-fine predictor to integrate these representative features into the inference process. This enables the model to leverage trend predictions to anticipate dynamic anomalies, such as periodic offsets, in advance. Furthermore, extensive experiments on multiple high-dimensional datasets demonstrate that our method consistently outperforms state-of-the-art baselines, validating the effectiveness of future macro-guided nested forecasting.
Yinghao Ai, Yukai Zhou, Ruoxi Jiang +8
National Key Laboratory for Novel Software Technology, Nanjing University, China · Shanghai Academy of AI for Science, Shanghai · Department of Computer Science and Technology, Nanjing University +3