$M^2Net$: Unifying Scale-Specific Structures and Prototype Decomposition for Spatial-Temporal Forecasting

Chengyang Zhou; Zijian Zhang; Hao Miao; Chunxu Zhang; Ziming Liu; Chao Tang; Juncheng Hu; Irwin King

cs.AIOct 17, 2026

$M^2Net$ : Unifying Scale-Specific Structures and Prototype Decomposition for Spatial-Temporal Forecasting

Authors: Chengyang Zhou, Zijian Zhang, Hao Miao, Chunxu Zhang, Ziming Liu, Chao Tang, Juncheng Hu, Irwin King

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 ·

Abstract

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 $M^2Net$ (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 $M^2Net$ outperforms state-of-the-art baselines on extensive empirical verifications.

Figures & tables

Panel of Figure 1 — 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

M^{2}Net

. 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

\mathbf{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

\{\mathbf{M}^{(l)}\}

modulate shared QKV projections to produce scale-specific attention outputs

\{\mathbf{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

M^{2}Net

. 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

M^{2}Net

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	$\uparrow$ 0.75	15.34	15.34	-	14.55	14.43	$\uparrow$ 0.82	15.41	15.27	$\uparrow$ 0.91
PEMS03	RMSE	27.17	27.13	$\uparrow$ 0.15	27.12	26.84	$\uparrow$ 1.03	25.66	25.01	$\uparrow$ 2.53	27.42	25.10	$\uparrow$ 8.46
PEMS04	MAE	19.48	19.14	$\uparrow$ 1.75	18.79	18.79	-	18.80	18.73	$\uparrow$ 0.37	18.47	18.36	$\uparrow$ 0.60
PEMS04	RMSE	31.08	30.61	$\uparrow$ 1.51	34.13	32.13	$\uparrow$ 5.86	30.33	30.19	$\uparrow$ 0.46	30.02	29.91	$\uparrow$ 0.37
PEMS08	MAE	15.14	14.90	$\uparrow$ 1.59	14.41	14.27	$\uparrow$ 0.97	14.59	14.53	$\uparrow$ 0.41	14.22	14.13	$\uparrow$ 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
$M^{2}Net$	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.

Panel of Figure 8 — Fig. 3 : Power Spectral Density (PSD) and Low/High-Frequency Energy comparison of global, prototype, and residual representations on PEMS08.

Panel of Figure 9 — 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)
$D^{2}$ 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
$M^{2}Net$	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.

Panel of Figure 12 — 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
$M^{2}Net$	20.05	33.69	15.97	350.46	50.77	325	64

TABLE VIII : Scalability evaluation on GBA dataset.

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PHGNet: Prototype-Guided Hypergraph Construction for Heterogeneous Spatiotemporal Forecasting

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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.

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