STRAP: Spatio-Temporal Pattern Retrieval for Out-of-Distribution Generalization
Authors: Haoyu Zhang
WentaoZhang
Hao Miao
Xinke Jiang
Yuchen Fang
Yifan Zhang
Venue: NeurIPS 2025 poster ()
Keywords: Spatio-Temporal Graph Neural Networks; Out-of-Distribution;
Primary area: deep_learning

Abstract: Spatio-Temporal Graph Neural Networks (STGNNs) have emerged as a powerful tool for modeling dynamic graph-structured data across diverse domains. However, they often fail to generalize in Spatio-Temporal Out-of-Distribution (STOOD) scenarios, where both temporal dynamics and spatial structures evolve beyond the training distribution. To address this problem, we propose an innovative Spatio-Temporal Retrieval-Augmented Pattern Learning framework, STRAP, which enhances model generalization by integrating retrieval-augmented learning into the STGNN continue learning pipeline.
The core of STRAP is a compact and expressive pattern library that stores representative spatio-temporal patterns enriched with historical, structural, and semantic information, which is obtained and optimized during the training phase.
During inference, STRAP retrieves relevant patterns from this library based on similarity to the current input and injects them into the model via a plug-and-play prompting mechanism. This not only strengthens spatio-temporal representations but also mitigates catastrophic forgetting. Moreover, STRAP introduces a knowledge-balancing objective to harmonize new information with retrieved knowledge.
Extensive experiments across multiple real-world streaming graph datasets show that STRAP consistently outperforms state-of-the-art STGNN baselines on STOOD tasks, demonstrating its robustness, adaptability, and strong generalization capability without task-specific fine-tuning.

STRAP: Spatio-Temporal Pattern Retrieval for Out-of-Distribution Generalization
Haoyu Zhang
Wentao Zhang* Hao Miao Xinke Jiang* Yuchen Fang*, Yifan Zhang
City University of Hong Kong, Hong Kong, China
City University of Hong Kong (Dongguan), Guangdong, China Northeastern University, Shenyang. China
The Hong Kong Polytechnic University, Hong Kong, China
* University of Electronic Science and Technology of China, Chengdu, China SLAI, Shenzhen, China
hzhang2838 @ .y...uu...du.. thinkerjiang @ foxmail.com
wentaozh2001 @ @gmail.com hao.miao @ polyu.cdu.hk fyclmiss gmail.com yifan. zhang @ittyuddgeduuu
Abstract
Graph Neural Networks (STGNNs) have emerged as a powerful tool for modeling dynamic graph structurd data across diverse domains. However, they often fail to generalize in scenarios, where both temporal dynamics and spatial structures evolve beyond the training distribution. To address this problem, we propose an innovative Pentio-Temporal Gerrieval-Augmentee Pattern Learning framework, STRAP, which enhances model generalization by integrating eetrrevallaugmennee learning into the STGNN continue learning pipeline. The of STRAP is compact and expressive pattern library that stores representative spatio-temporal patterns enriched with historical, structural, and semantic information, which is obtained and optimized during the training phase. During inference. STRAP retrieves relevant patterns from this library based on similarity the current input and injects them into the model via plug-and sang--nd--lay prompting mechanism. This not only strengthens spatio-temporal representations but also mitigates catastrophic forgetting. Moreover, STRAP introduces a wewwledeebbllnccin objective to harmonize new information with retrieved knowledge. Extensive experiments across multiple streaming graph datasets show that STRAP consistently outperforms state-of-te fftte-of-the-and -he-harrt STGNN baselines on STOOD tasks, demonstrating its robustness, adaptability, and strong generalization capability without task-specific fine-tuning.
cut-oo-DDistribution (STOOD)
Introduction
Ppatio-Temporal Graph Neural Networks (STGNNs) [36, 78, 43, 53, 35] have emerged as a power-
ful paradigm for modeling complex systems that evolve over both space and time. By integrating spatial and temporal dependencies [7, 29, 12] and modeling techniques [34, 46), STGNNs have surpassed traditional spatio-temporal approaches [36, 55), making extraordinary progress in diverse domains [72]. such as traffic forecasting [66, 41], climate and weather prediction [53, 43), financial modeling [22, 28), and public health [31, 67]. However, training and deploying STGNNs on real-world streaming spatio-temporal data poses critical generalization challenges due to evolving dynamics across multiple dimensions: 1 Spatially, systems undergo restructuring through node additions and removals [51, 55], leading to dynamic topologies and heterogeneity [76, 74, 14, 73]. @ Temporally, data exhibits periodic
Indicates equal contribution. Corresponding author.
39th Conference on Neural Information Processing Systems (NeurIPS 2025).

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fluctuations [30], abrupt changes [5], and long-term drifts [62]. @ Spatio-temporally coupling between space and time also produces synergistic impact and further results in joint distribution shifts [75, 59, 25), which may significantly impair STGNN generalization in dynamic scenarios.
This highly dynamic nature of spatio-temporal data causes traditional STGNN models face severe STOOD (Spatio-Temporaa Temporal Out-Or-Disse -f--isstrbbution) problems, leading to degraded performance for con- ventional models [82]. Existing efforts solve this critical problem as follows [68]: Backbone-based methods (Pretrain, Retrain), which either directly apply a model trained on historical data to new data without further training (Pretrain) or completely retrain the whole model from scratch using the new data (Retrain); @ Architecture-bat based methods (TrafficStream [10], ST-LLRR [54], STKEE [63], EAC (9]), which modify model architectures; ① Regularization based methods like EWC [42), which constrain model parameter updates; ! Replay- based methods (Replay [16]), which reuse historical samples. Despite their progress, these approaches face the following limitations: backbone methods suffer catastrophic forgetting [40, 60), sochitecture-basee approaches struggle with stability-plastical trade-offs [58], regularization methods over-constrain adaptation [23], and replay techniques fail to distinguish between relevant and irrelevant historical knowledge [81. The root cause of the above deficiency is the insufficient exploitation of historical information and current information. Considering the distribution shifts in spatio-temporal graph data, historical information only partially benefits current predictions [70, 15], while some may introduce noise and even negative impacts. Thus, the key chal- lenge remains identifying which historical knowledge components provide the most valuable in- formation gain for current predictions under complex pratio-temorral distribution shifts [8, 21J.
Instead of learning from the historical data and overwriting the model parameters to store the patterns implicitly, we propose to explicitly store the key similar patterns found in historical data to overcome the above limitations. The explicit storage can largely help to keep more historical information without memorizing it by updating the model parameters. Such external storage mechanisms are also capable of being cooperated with any STGNN- backbones to enhance their ability to address STOOD problems. To this end, we need to handle the following challenges:
C1. How to Effectively Identify and Efficiently Store Contributive Patterns? Current approaches either concentrate solely on spatial aspects or rely on fixed datasets through updating the model parameters, For one thing, such a narrow focus prevents them from capturing richer and more complete historical patterns that could provide significant information gain. In addition, the information memorized in the model parameters is limited, especially for the STOOD tasks. Effectively identifying the most informative spatio-temporal patterns from historical data that maximize information gain for current predictions and storing these patterns efficiently are the cornerstones to solving the STOOD problem.
graphs trained on static
C2. How to Optimally Balance the Integration of Historical Extracted Patterns with Current Observations? Existing approaches face difficulties in accurately matching relevant patterns with the current observations due to insufficient similarity metrics and retrieval criteria. This limits the model's s ability to fully exploit informative historical knowledge. On the other hand, excessive reliance on pattern matching may lead to overfitting to historical cases, blurring the boundary between prediction and retrieval. Therefore, a key challenge lies in developing mechanisms that can appropriately balance the incorporation of historical patterns with current data, ensuring both flexibility and robustness in prediction tasks.
evolving
To address the two aforementioned challenges, we propose the Opatio-Temporr Pattern Learning (STRAP) framework. We construct pattern library with a three-dimensional key-value architecture, where pattern keys serve as efficient retrieval indices and pattern values encapsulate rich contextual information.
At its core, STRAP maintains specialized collections for spatial, temporal, and spatio-temporal patterns. Pattern keys extracted using geometric topological and properties (e.g.. graph curvature, clustering coefficients) and time series characteristics (e.g.. wavelet transformations). optimized for similarity matching. Pattern values, generated through a dedicated STGNN backbone, preserve the essential features needed for downstream tasks. Specifically, STRAP employs a two-phase mechanism: (1) similarity- based retrieval that matches current graph features with historical pattern keys, and (2) feature enhancement through fusion of retrieved pattern values with current representations. As such, Cl is addressed by constructing and updating the external pattern library based on past retrieval values, and retrieving the similar patterns from the library for the downstream tasks. Furthermore, to solve pattern extraction captures cross- diss-dimmali dependencies.
C2, our approach for

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while an adaptive fusion and training mechanism calibrates the influence of historical patterns. In summary, our key contributions are as follows:
We propose STRAP, a novel plug and play framework tailored for STOOD scenarios, which constructs key-value pattern library that captures multi-dimensional patterns across spatial, temporal, and spatio-temporal domains, fundamentally decoupling pattern indexing from pattern utilization to mitigate catastrophic forgetting and alleviate the STOOD problem.
We design an adaptive fusion and learning mechanism that dynamically integrates retrieved historical patterns with current observations, enabling robust and flexible prediction over continuously evolving spatio-temporal data streams.
Experiments on multiple real-world streaming graph datasets demonstrate that STRAP achieves SOTA performance STOOD tasks, showcasing its effectiveness in continual generalization.
2
Related Work
2.1 Continue Learning on STOOD Tasks
Continuous Learning typically maintains long-term and important information while updating model memory using newly arrived instances 452,4,9] Due to continuous learning's s excellent performance in adapting to evolving data and avoiding catastrophic forgetting, a series of methods based on continuous learning have been proposed. Chen [10] introduced historical data replay strategy called TtrefieStream based on the classic replay strategy in continuous learning, which feeds all nodes to update the neural network, thereby achieving balance between historical information and current information. Similarly based on experience replay, Wang et al. [64] proposed PECPM, a continuous spatio-temporal learning framework based pattern matching, which learns to match patterns evolving traffic networks for current data traffic prediction. Miao et al. [48] further emphasized replay-based continuous learning by sampling current spatio-temporal data and fusing it with selected samples from a replay buffer of previously learned observations. Chen et al. [10] proposed a parameter-tuning prediction framework called EAC, which freezes the base STGNN model to prevent knowledge forgetting and adjusts prompt parameter pools to adapt to emerging expanded node data.
2.2 Pattern Retrieval Learning
Pattern Retrieval Learning refers methods of representation learning and reasoning through identifying, extracting, and utilizing key patterns in data [44, 57, 65, 19J. In the context of graph neural networks, pattern retrieval learning typically focuses on how discover stable and predictive patterns from graph structures and node features [3, 27, 17J. In spatio-tempora data, pattern retrieval faces unique challenges as it must simultaneously consider spatial dependencies and temporal evolution patterns [2]. Han et al. [20] proposed RAFT, setrieval-augmentee
time series forecasting method that directly retrieves historical patterns most similar to the input from training data and utilizes their future values alongside the input for prediction, reducing the model's burden of memorizing all complex patterns. Li et [36] proposed a framework focused on extracting seasonal and trend patterns from spatio-temporal data. By representing these patterns in disentangled manner, their method could better handle distribution shifts non-stationary temporal data. In the area of -utto--distribution detection, Zhang et al. [79] proposed an OOD detection method based on Modern Hopfield Energy, which memorizes in didiitiibuttinn data patterns from the training set and then compares unseen samples with stored patterns to detect nat-of-distribution samples,but it's heavy reliance attention mechanisms limits it's stability in complex and highly variable environments.
3 Preliminaries
We first formalize spatio-temporal graph [1, 78] data structures, followed by an introduction OOD learning with focus on spatial and temporal distribution shifts. Based on these foundations, we propose unified prediction framework designed address the challenges of robust modeling in dynamically evolving environments. Notations are provided in in Table 3 in Appendix A.
Definition 1. (Dynamic
Graph) We define a dynamic spatio-temporal graph as sequence of graphs G, (V,,A)) E [1,T], where V, {Ui (2,,02.... u uN is the set of
3

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Nr nodes and A, N is the weighted adjacency matrix at time step t, encoding dynamic pairwise relationships among nodes. Each entry Ar,ij E indicates the strength of the connection between nodes vú and ti at time I, and its size N,, which may vary over time. At each discrete time step I, graph signal X, E RR is observed, with each node is associated with a c-dimensional feature vector. The sequence of graph signals over T time steps is denoted as 1 Xr] T
TxXee
Definition 2. (Spatio-Temporde Out-of-Disttribtiinn Learning) Let the training environment be de- noted as c = -g" ) where g" AV" represents the training graph and D = ( ( } the corresponding dataset consisting of n samples. The objective of OOD learning [62. 79] is to generalize from this training environment to arbitrary test eevironnnttttts ex ~ E, where test distributions may differ significantly from those seen during training, i.e., P(e") * P(c"). This formulation accommodates both classic OOD scenarios: where test environments differ significantly from training due to structural or temporal changes and continual learning scenarios: where distribution shifts emerge progressively new data streams in over time.
In STRAP, we consider three types of distribution shifts: Spatial distribution shifts: Changes in the underlying graph structure, formally denoted as P(G*) PPG"), These shifts may arise from varia- tions in node connectivity, edge weights, or even the addition or removal of nodes. Such changes affect how information flows through the network and can alter the relative importance of nodes and edges. @ Temporal distribution shifts: Changes in temporal dynamics, expressed as P(X (X::) ) P(X++1 x1=)". These shifts reflect evolving temporal patterns, including modifications in periodicity, trend, or correlation structure. They can emerge due to abrupt regime changes or through gradual evolution over time. @ Spatio-temporal distribution shifts: Joint changes across both spatial and temporal dimensions, captured by P(X,-1 |X 1:2 11 * P(X [X
These shifts model the interplay between dynamic graph structures and evolving temporal signals, often arising in real-world settings where the data-gen data-generating process itself is non-stationary and context-dependent.
Definition 3. (Unified STOOD Prediction Framework) STOOD prediction framework addresses the challenge of generalizing across both spatial and temporal distribution shifts by formulating the learning objective as a unified min-max optimization problem [9, 10]:
-e = argmin supE (X)
Where fe : TxXXx T is a neural network parameterized by θ which maps an input sequence of node features to sequence of future predictions. The target output 1=
x represents the ground-truth observations over a prediction horizon of Tp time steps. The loss function L measures the gap between predicted and true values, typically using MSE for regression or Binary Cross Entropy for classification tasks. The conditional distribution P(e) characterizes the data generation in environment while E represents all possible environments, including those with distributions different from the training environment.
4 STRAP Framework
framework addressing streaming spatio-temporal outlier detection by leveraging historical patterns (Figure 1). Our approach first decomposes complex spatio-temporal data into manageable subgraphs, then extracts and stores multi-dimensional patterns in a searchable library. During inference, STRAP retrieves relevant historical patterns and adaptively fuses them with current observations for optimal prediction. For enhanced clarity, the Spatio-Temport Pattern Library Construction is outlined in Algorithm (cf. Appendix B.2) and the Training and Inference with Toy Graphs Retrieval are detailed in Algorithm 2 (cf. Appendix B.2). Theoretical analysis in Appendix B. demonstrates the effectiveness of our pattern extraction and retrieval mechanisms under distribution shift.
We present STRAP, a
4.1 Spatial Temporal Subgraph Chunking
To effectively capture diverse and disentangled spatio-temporal patterns, we decompose the original graph sequence into three types of specialized subgraphs, each designed to emphasize a specific dimension of variability: spatial, temporal, or spatio-temporal

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Spatial Temporal Subgraph Chunking
Pattern Library Construction
Historical Information
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Figure 1: The overall framework of STRAP.
Spatial Subgraphs (9s): These subgraphs {Gs} are constructed by slicing the temporal axis into overlapping windows of fixed time length Tg- For each window + Ts], aggregate both the connectivity and node features to form a window-lever spatial representation:
g== )
( (1,44ss)
Where A |tt+rs] is the time-averaged adjacency matrix, and X [ttt+rs] is the aggregated node feature matrix across the window. These subgraphs emphasize persistent spatial structures that remain stable over short temporal intervals.
Temporal Subgraphs (Gr): To isolate temporal dynamics, we sample a central node v. along with its k-hop spatial neighborhood. (v.) during T, and track their evolution the full time span:
Gr = (fveeNN (va) Aprm (e...A. MG
Where A A1:7llas (x.) and X [1:ry las (1x) are the sequences of adjacency matrices and node features restricted to U. and its neighbors (1())). These subgraphs {Gr} focus on localized temporal.
@ Temporl Subgraphs (GsT): ): To jointly capture spatial and temporal interactions, we first apply spectral clustering [61] to partition the node set into m communities (C,, C,, based on structural coherence. For each community C,, we extract time- subgraphs:
GSr 78) Ica X (1a4tsr)]ee;
Where the adjacency matrices and node features are restricted toC, within the interval [f,++TTT]. These subgraphs (GsT) capture coherent spatio-temporal dynamics among functionally related node groups.
4.2 Multi-dimennsionll Pattern Library Construction
To more effectively capture dynamic opatio-temport patterns, we extend the chunking approach introduced in Section 4.1 by constructing the structured key-value pattern libraries across different dimensions. Each subgraph instance -stitaaaespptial,, temporal, apatio-temporal pair that captures characteristic variations within its respective dimension. The processes for generating pattern keys and values are detailed in Sections 4.2.1 and 4.2.2, respectively. Based on these patterns, we construct three distinct pattern libraries: Spatial Library Bs. @ Temporal I Library Br, and @ Spatio- Spatio-Temporal Library BST.
encoded as key-value
5

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4.2.1 Pattern Key Generation
Retrieval-augmented learning effectiveness depends discriminative pattern keys robust to distributional shifts, for which we design dimension-specific extraction methods.
Spatial Pattern Keys. Spatial shifts often manifest as changes in graph connectivity, community composition, or centrality structure [13]. To capture them, we extract multi-scale topological features:
From the aspect of local structure, we compute neighborhood statistics D(Gs) = (pd, aa, max(d), min(d)] [6], where represents node degrees, and clustering coefficients [56] CL(Gs) (Cis) (2,,,,,...CC. with C. = Alfe,ell (i] Ejk are edges between neighbors of node i, and k; is the degree of node i. @ From the aspect of global connectivity, robustness against changing graph scales, we calculate path-based metrics such as shortest path statistics [45] SP(Gs) = [ sp: diamm (Gs)] where Msp and sp are the mean and standard deviation of shortest path lengths, and diam is the graph diameter. @ From the aspect of geometric properties, We also employ Forman- Ricaci curva- ture [33] capture intrinsic geometric properties that remain stable despite local perturbations. For
des dus .du, + +E,, LE,,EE((s)) Wess"
a node eú, this is computed as: (R( =1 Eu,,N(Ei) 2Weyf
where de, is the
degree of node 2/2 .N;)) is the set of neighboring nodes, Wesy is the edge weight between nodes U; and új and F((;)) is the set of incident edges. This curvature analysis identifies distinet topological structures: negative curvature nodes, zero curvature nodes, and positive curvature nodes.
Finally, we concatenate and normalize these features to form the spatial key:
kg = (C
(S)
Temporal Pattern Keys. Temporal shifts may arise from changes in variance, periodicity, trend, or complexity (47,39, 38, 11]. J. To address this, we extract features that describe the temporal signal multiple scales:
Statistical and spectral descriptors: We compute statistical moments S(X)
[ux, ox, skew(X), kur(X)],, and extract dominant frequency components F(X) =
W1 Wm Em]] where each w; denotes prominent frequency and E, its corresponding energy. @ resolitresolttion analysis: To capture transient and multi-scale phenomena, we apply wavelet X (t) (z=)) where a the scale parameter and 6 the time shift. ① Temporal dependencies and complexity: We compute autocorrelation functions R(X)= = R } to identify periodicity at lag k and entropy H(X) = ( p(r)))oppp(( to
transforms [77]: W(X)= ((X)=(waad (W.
quantify uncertainty and regularity.
Finally, we concatenate and normalize these features to form the temporal key:
kt = (XORMALIZE(S(X))))) XUNAAAAALLL((AAAAAA//AAAAAAAEEEL
(6)
Tentiolleempaall Interaction Keys. To encode joint patterns that emerge from the interaction of structure and dynamics, we define gross-dimensionas interaction keys as:
k ST NORMALIZE(Ks @kr)
Where & denotes an element-wise cross-product. This formulation allows the model to capture coupled dependencies across spatial and temporal dimensions without treating them independently.
4.2.2 Pattern Value Generation
Pattern values the semantic content associated with each key, representing informative subgraph embeddings extracted from the backbone model. For G; in any dimension B. E (B5,Br,BB7 }, we compute the pattern value by applying frozen shared pretrained STGNN backbone parameterized by Op (i.e., STGCN [69], ASTGCN [18]) to the corresponding subgraph and aggregating its pattern as v;:
V (OAAKOPOO.AAAKONEEEEEE (9:)),
(8)
Where MEANPOOL(() denotes mean-pooling to obtain the full G. value. Thus, for each dimension, store each key-value pair (k,,v,) into the pattern library construction.

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4.3 Pattern Retrieval and Knowledge Fusion
4.3.1 Pattern Library Retrieval
After constructing and indexing the pattern libraries, we implement similarity-based retrieval process to identify relevant historical patterns for the current observation. For 9i in any dimension B. E " we first compute the similarity between the query key kद (extracted from the current subgraph) and all stored keys kj in the corresponding library B.:
s skg exp(-
|kk -k,1k))))) ky E.
(9)
Similarity scores are then used to retrieve the top-k most relevant key-value pairs from each library:
R4 (k). TopKk kk),k,))
(10)
Where s) denotes the similarity score, kj. is the retrieved pattern key, and vý is its corresponding value. By performing retrieval independently across spatial, temporal, and spatio-temporal libraries, the model obtains multiple sets of complementary patternvaauu pairs. This multi-dimennional retrieval strategy enables the model to incorporate a diverse set of historical ceitexts-structiee patterns from graph topology, temporal dynamics from time series behavior, and integrated patterns from their interaction interaction-thereby improving its ability to make robust predictions under distributional shifts, including both abrupt changes and gradual evolutions.
4.3.2 Knowledge Fusion Mechanism
After retrieving relevant pattern values from each library, we integrate this historical knowledge with the current observation using an Eeformation-thooeeee fusion mechanism designed to maximize the joint representational capacity. For G, in any dimension B. {Bs, Br, ). we first compute similarity-weighted average over the retrieved values: V Lkkg.y..)) SOFTMAX(s))
Next. to capture non-linear cross-dimensional dependencies, we utilize the same architectural backbone, parameterized by Orain (initialized from Op and subsequently fine-tuned), encode the current observation G. Two separate multilayer perceptrons- MLPP for the current observation and MLP₂ for the retrieved values are then applied embed the respective representations. Formally, the transformations are defined as:
Z = MI.P [BACKRONE (G:)), Zz = ML.2 (2 @vT
(11)
Next, the final fused representation is computed convex combination of the transformed current input and the aggregated historical knowledge:
Z 2
(12)
Where y is fusion weight that calibrates the balance between current observations and retrieved historical patterns. The resulting fused embedding Z is then channeled into the decoder for downstream tasks. This deliberate integration mechanism synthesizes complementary information sources, allowing the model to leverage both immediate context and relevant historical knowledge, thereby enhancing predictive performance across varying distribution conditions.
Experiments
In this section, present comprehensive of experiments evaluate the effectiveness of STRAP compared to offte-of-the-ar baselines on three real-world streaming spatio-temporal graph datasets. Our experiments designed answer the following research questions:
RQ1: How does STRAP perform compared to state-of-the-ar methods on STOOD task?
RQ2: What are the contribution of different pattern library and key components to the overall performance?
RQ3: How sensitive is STRAP key hyperparameters? (Results presented in Appendix C.4.)
7

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How robust is STRAP when deployed under significant distribution shifts, including both abrupt and gradual changes?
RQ4:
How does STRAP perform compared to other retrieval- based methods, and how does it perform terms of computational efficiency (Results are presented in Appendix C.6.)?
RQ5:
RQ6: How does STRAP perform compared to baseline methods in few-shot scenarios?
5.1 Experimental Setup
Datasets. We evaluate STRAP on three real-world streaming spatio-temporal graph datasets: AIR-Stream [9], PEMS- Stream [10], and ENERGY-Stream [9]. Detailed dataset statistics, experimental settings and evaluation are provided in Table in Appendix C.3 and C. in Appendix C.
Backbones and Baselines. We consider four versions of our proposed framework STRAP:
STRAP, which utilizes the complete pattern library system; @ STRAP w/o S, which indicates we operate without the spatial pattern library; @ STRAP w/o T, which operates without the temporal pattern library; and 4) STRAP w/o S+T, which functions without the spatio-temporal pattern library. For baselines, we implement: O two standard training paradigms
included: Pretrain and Retrain,
which directly utilize the backbone models; we also compare with state-of-the-ar approaches for graph learning: TrafficStream [10], ST-LoRA [54], STKEC [63], EAC [9], EWC [42], Replay [16], ST-Adapter [49], GraphPro [71], and PECPM [64]. These baselines represent diverse strategies for han- dling strucurrd streaming data, including backbone, architecture- based, regularization-batt based, and replay- replay-based based methods for evolving graph streams. For STRAP AP variants and baselines, we conduct experiments with four different backbone architectures: STGNN [69]. ASTGNN [18], DCRNN [37], and TGCN [80]. A detailed description of baselines and backbones can be referred to in Appendix C.2.
5.2 STRAP Results (RQ1& RQ2)
As illustrated in Table 1, our STRAP framework consistently outperforms baseline methods across different datasets and metrics. We summarize our key findings below. Further details and experiment results are provided in Table 4, 5 and 6 in Appendix C.
SOTA Result Across Categories (RQ1). STRAP achieves the highest average performance with 7.17% % improvement across metries (MAE: 4.88% % RMSE: 9.12%, MAPE: 7.5%). This stems from our multi-level pattern library approach that effectively captures complex streaming spatio-temporal dynamics. Our analysis reveals key advantages over existing categories: backbone-bart methods lack OOD handling mechanisms, leading to catastrophic forgetting [70]; architecture- based and regularization- baaed approaches implement parameter protection but insufficiently utilize historical data; and replay-based methods store knowledge implicitly in model parameters, facing capacity constraints [50]. In contrast, STRAP addresses C1 through explicit pattern libraries and retrieval- fusion, maintaining an interpretable external memory that ensures robust performance across varying distribution conditions.
Ablation Study (RQ2). The ablation studies (w/o S, w/o T, w/o S+T) clearly demonstrate each pattern library's impor- tance, with the spatial component being most critical. The temporal component also significantly contributes to perfor- mance.
$0,61
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4
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850
Specifically, Spatial I and 2 refer to fea-
Figure 2: Impact of different pattern libraries and keys. Left: library. Right: key.
tures from the aspect of local structure and the shortest path statistics feature
from global connectivity, while Spatial 3 represents the Forman forman-Ricci curvature from geometric
properties. In terms of time, Temporal 1, 2. and correspond to Statistical and spectral descriptors, Multi-resolution analysis, and Temporal dependencies and complexity, respectively. From the experi- mental results, in the spatial pattern analysis, Spatial 3 (w/o demonstrates the highest importance with a MAPE of 49.97 %, representing a performance drop of 6.32% when removed. This in- dicates that the Forman- Ricci curvature from geometric properties plays crucial role in capturing

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the intrinsic geometric structure of peatioltempora graphs. Spatial I and 2, while contributing to the model performance, show relatively smaller impacts when removed individually, suggesting that geometric features may be more critical than previously assumed in spatio-tempora, forecasting tasks. In the temporal pattern analysis, Temporal 1 (w/o T1) emerges as the most critical component with a MAPE of 50.61 %, showing the largest performance degradation of 7.96 % when removed. This demonstrates that Statistical and spectral descriptors are fundamental for temporal modeling. In contrast, Temporal 2 MMuli--reoolutio
analysis) shows the smallest impact when removed (MAPE: 14.98%), indicating that while useful, it may be the least critical among the temporal components for this specific forecasting task.
Table I: Comparison of the overall performance of different methods (STGNN backbone).
Dainerts
Atr-Stram
PRAMS- Sewas
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15
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12.00-04
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16 15
11.23+300
5.50
5-43cc 1
5/12aa11
5.45-a
Bemain
RMSE
80.18.199
$4.88
48.80.13
64.42...5
54
23.56.009
22.94.00
25.58um1
23.13
5,00.885
0.742115
2,07
MADE,CC)
24.080011
28.69>
0
35 16
14.75401
26.12m4-
20.00
20.54-2
52.226
52.
55.820005
52.44 20.50
MAE
24
21
12.0
1507
16 5ints
5.50
Tryfi Stews
RMSE
25. 63
38 00103
50.37
35.6
5
5
13
5.630111
MAPE
27.80u
82.8
23.18
40.05.144
61.84163
90.224100
LARA
RMSE
34.19
53.54
20.02016
29:0
5,50
5.50
5.53
5.00oux
(AP
23.04
20.98a231
01.9
28.800333
17.16
18.00
2.
18914330
52.00
55.051145
64.10.135
63.544154
MAB
18. 63
21.25
21
21 52.5
12
16. Shoao
16.24
5.M6c 12
5,55a
STREC
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20.92.u1
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12.00
20/0744-3
23.50uc
20.56.33
55.15
58.241331
55, 55.01o007
basod
RMSE
58.60u0
52.9kam
20
22.13.342
5.46.335
5,58ut
6.72
(A)
25. 42
27.24
32.06m05
21.1
20.30
22. Mbc
56.
57.05500
58. 26.66.11
MAPL
19.1 11
21 91
15 17
21 77777
12:1
15 8b
15 97
15
5.3
5 5.3
5.30
RMSSE
20.14
54.3722
18.80.10
20.5Guns
22.5
26. Slou
5.682886
5.50u
5.02a11
(AFE((5))
25.65
27.2760:00
31.0000s
31
22
17.56044
18
2
51.1763
51.86011
52.80035
GragMPo
MAPE(())
23.06
27
12.05
17.60.11
23.04.135
54.70
58.07.533
05,17.533
64.04
MAE
15. 44
14
21.
21.17a315
12 T0u00
18.85.r0
16.11umts
14.032200
5.40
5.46ut
6.48a312
6.47am0
POCH
KMSSI
26.71-119
3R. 16-mm
S3-35e
20.0
22 70
56. M60
22
5.56
5
MAPE((S)
25.83
27.75
00
12.01um
17.68
19.2..9
22.92
10000::00
50.15.214
58.83100
55,
G4.00.344
Regularitation-
basol
MAPE(S)
RMSE
MAE
28.M0
15.2
21.1
37
39.58
24.0003
21000
53.26ws
17.0003
11.0
14266111
18
28.12a11
92.10
2::7w033
16.7200
14:35311
5.
5.62
02
Rapha-
Raphay
RMSE
25.14aus
42.02
22.5.a00
25.04.03
28.10.30
5.87
MADEL(S))
22 61-
35.91
32 19-10
M6.7740
19.52-111
22.06-07
19 1882-111
52.11
52.0-1
54 31.88-114
10-1
Retrieval- haned
SYRAP
RMSE
MAE
26
15:44
05.06
90
20
57.1.)
23,
35
30
20 30
00.35..144
12.
18.64. G4..5
20 18..2)
18 18.311
10.30 30
23.07.m3
20 40.46.1.
4 4.5
4.83
5.01.115
6. 5.16
4.88
4.8tons
5 5.08ums
MAFE
25
26
300
26.
26.74uc
16.85rss
17.70.0
v
50.57m007
18 02-101
42 18.386..
44.30.115
49. 43.11
5.3
Case Study (RQ4)
Horizon
Horizon
Period
0.0G
[a]
Probabiltty Denrin
0.06
(b)
3.10
1.48
MAPE
1
1.49
Probabilng
Probability
0.04
1.2
0.02
Retrain
EWC
Replay
Graphi
STRAP
Rutrain
RWC Replay GraphPro STRAP
0.00
0.00
25
50
75
-25
2%
50
Pcrod
Vallun
Horizon 12
Horizon Avg.
9.06-
0.00
[c]
Probubility Denstty
0.00
(d0
MAPE
1.8
1.6
166
MAPE
1.6
1.8
150
3.28
Probabitty
0.04
0.04
1.4
9.02
Ratrain SWC
Replay
EAC
PraphPra
STRAP
Ratrain
SWC
Replay
BAC
PraphPro
STRAP
8.00
2.5
30
75
0.80
-25
25
Value
Vallue
Figure 3: Test set distributions for ENERGY-Wind for 4 periods 0 (a). 1 (b), 2 (c), and 3 (d).
Figure 4: Performance analysis (MAPE) of different
horizons across various baselines.
To further investigate the effectiveness of our proposed STRAP AP method under significant distribution shifts, we conduct a detailed case study on the ENERGY- Wind dataset. As illustrated in Figure 3, the distributions of test set values vary considerably across the four periods, with period 3 (Figure 4(d)) exhibiting the most pronounced shift from the initial distribution (Figure 4(a)). This is evidenced by
9

---

the substantial decrease in both mean and median values, representing a reduction of approximately 77% and 76% respectively.
Figure 4 presents the performance comparison across different prediction horizons during period 3 on STGNN backbone (More experiments are presented in C.5 in Appendix C), which experiences the most severe distribution shift. The results demonstrate that STRAP significantly outperforms all baseline models across all prediction horizons, achieving the lowest MAPE of 1.19, 1.22, 1.27, and 1.22 for horizons 3, 6, 12, and on average, respectively. This remarkable performance can be attributed to STRAP's s retrieval- based key-value mechanism, which selectively identifies and extracts the most information-rin pattems from historical knowledge while efficiently integrating them with current observations. thus achieving an optimal balance that enables robust prediction even under extreme distribution shifts.
5.4 Few-shot Learning Performance Evaluation (RQ6)
We evaluate STRAP under data-constrained conditions on the Energy-Wind dataset with 50% and 30% missing data scenarios (Table 2). STRAP consistently outperforms all baseline methods across both settings. Under severe constraints (50% missing data). STRAP achieves 6.29 MAE, outperforming the best baseline EWC by 8.7%. With moderate constraints (30% missing data), STRAP maintains superiority with 5.77 MAE, surpassing Graphpro by 3.4%. The method demonstrates exceptional relative accuracy with MAPE scores of 78.92% and 67. 42% respectively, while maintaining consistent performance across different prediction horizons.
Table 2: Few-shot Performance Comparison on TGCN Backbone (Energy- Strrayy-
Availabiliyy
30% Mossin Date
Mixiing Dasss
Data
Categury
Mellod
Matrie
Ang.
Asg.
Avg.
MAB
7.1616:2
7.
7.15mmn
7.10 7.10-111
6.2 6.23-mm
0.17x
6.3mmrs
5 6.18mmn
5,90m01
8 8M2 1
K.
8.9
Prstaah
RMSE
7:28un1
7.5Lin12
7,57.010
7.82
6.41an.9
6.40unss
6,50uam
8.4.am
9,12.a1e
0.1banas
9,18
0.
Back-
MAPE (9)
'2 4442
50.38.155
94,60.142
93.96.10
25.05.2.5
70.472112
70,77216
11825
319,16553
120.38.335
119.20
119.5.112
MAE
6,91inss
6,50umm
6,86.006
6.89
6.35un25
0.28um04
6,27.0r
6,27.0
5,68.112
0.50un.s
5.48
5,56a009
Rotaii
RMSE
7.0Gunee
7.00ius
7.10.au
3.05
6.55an55
0.32mms
6,6L.0m
3,8
6.72m04
3.90
MAPE (4)
39.05. 65 59
50.91+182
00,90-135
20.00
71.28
72.51a100
71.52.11
53.704..5
65.05
55.1
54.04
MAN
65
5.10-111
0.96mms
6.00m00
5.88-114
5.50mm
5.50mmm
Gupllm
RMSE
7.14
0.20um00
6,54.mre
6.31.mm
3.81.114
5.77anus
25
52
50,501344
02.18.20
24.012300
74.83112
70.341135
74.561134
50.70.332
58.07.3
66.37
54.04
MAE
7,02
7.03
6.26a01
6.22.00
5,47.00
6.37an32
8.86
6.30un0
Architecture-
57-AAuye
RMSE
1:384014
7:30-117
6.47mm
6.61-116
77.6614
51.17400
52.85
MAP
6:38wirs
6:27-mm
RMSE
1.08w011
7.10-1.0
1.05-3:1
0.50mmm
6.61-0m
6.30-m
5.80-110
5.67
35
10100:20
51.78o09
Replay- hosed
Reploy
RMSF
XEAE
1s
7.30u014
7.51-015
7:57-a14
7.1ha313
7:30-a1s
7.48u814
6:11e6
0.27am1
0.21omn
6:33mm
618.20
6:1--w
3.67-1
5.20um
5
6420031
5.77-111
5.67011
MAPE
45
90
38-18
91.65-175
03.90-341
25.06-335
78-47414
90.79a13
75.80.106
50.564150
32.95
51.384174
19
Ratriancal- booel
STRAP
RXSSE
SIAE
6.4440.0
6.
29
0.48ums
6.
6.2000000
0. 0.53.m00
8.28.00
6.47.0m
6.29
3.74
6.10u835
6.024025
5.644004
0.11a004
6.8860m
B.PYam
0.14w00
4.95amm
4.85am17
5.01/8:0
4.648
6.18
4.88m11
MAPE (19)
7% 28-
93-33-111
70.98-110
78-92-1
66
67 02-02-1
is
36.
17
07.
47--42-1
42.18-181
43.02-
30
44.30-1
43. 14
6 Conclusion
We introduced STRAP, novel framework for streaming graph prediction that leverages specialized pattern libraries across spatial, temporal, and spatiotemporal dimensions to capture the complex dynamics of evolving graphs. It encompasses three innovative components: spatial temporal subgraph chunking, multi multi-dimensional pattern library construction, and pattern retrieval and knowledge fusion. Extensive experiments show that STRAP consistently surpasses state-of-the-ar methods across various backbone architectures. However, our approach faces limitations: rising computational demands with larger libraries and reliance robust historical datasets. In the future, we aim to develop adaptive library management techniques, integrate uncertainty measures, and expand STRAP to multi-modal graph scenarios.
7
Acknowledgements
The paper is supported by the Young Scientists Fund Program C of the National Natural Science Foundation of China (Grant No. 62502406) and the Start-up Fund from the City University of Hong Kong (Dongguan).
10

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[81] G. Zheng, S. Zhou, V. Braverman, M. A. Jacobs, and V. Parekh. Selective experience replay compression using coresets for lifelong deep reinforcement learning in medical imaging. In Medical Imdicalmmaging with Deep Learning. pages 1751-1764. PMLR, 2024.
[82] Z. Zhou, Q. Huang, K. Yang. K. Wang. X. Wang. Y. Zhang, Y. Liang, and Y. Wang. Maintaining the status quo: Capturing invariant relations for ood spatiotemporal learning In SIGKDD, pages 3603-3614 14, 2023.
15

---

A Notations
The notations this paper are summarized in Table 3.
Table 3: Notations Tables in STRAP
Notation Ge/Ve A
Definition
The dynamic graph node set adjacency matrix at time The feature matrix time t
Xt
tr le
The training environment test environment
The set of graph communities
N(v)
The neighbors of node v k-hop neighborhood of central node Ve
Nu(ue)
Gs
The spatial subgraph
GT
The temporal subgraph
GST
The spatio-temporal subgraph
Tsl TST
Time length of spatial spatio-temporal windows
8 1T" 1BST
The spatial/ / /ttpr//poorr//pppptttttppppppppp pattern library
1. TK TEST
The seattaalieemmpoal//ppiiii
pattern keys
S 1 1
The spatial / temporal spatio-temporal pattern values
D(Gs)
The neighborhood statistics of graph Gs
CL(Gs)
The clustering coefficients of graph Gs
SP(gs)
The shortest path statistics graph Gs
FR(U.)
The Forman-Rice curvature of node t;
S(X)
The statistical moments of temporal signal X
F(X)
The frequency components temporal signal X
W(X)
The wavelet transform of temporal signal X
R(X)
The autocorrelation functions of temporal signal X
H(X)
The entropy of temporal signal X
s(1 .b))
The similarity between query key ki and stored key hy
R,
The retrieved key-valus pairs for query
2
The moallarit--weighte average of retrieved values
θ pt
trrin
The pretrained/ trainable backbone parameters
Z1 Zz
The current observation / historical pattern embeddings
The balance weight between current and historical information The loss function for prediction
The number of time steps
T
The prediction horizon The number of nodes
The dimension of node features
Flement- cross-product operation
B Further Methods Details
B.1 Theoretical Analysis
Theorem B.1. Let X be the original data. Consider two feature extraction approaches:
Decomposed approach: Features from separate libraries (xx(x)).x(X)))feer
Unified approach: Features from parametric model fo(X)
The mutual information advantage the approac
(13)
Proof. Let denote: 3=1_,
16

---

We need to prove:
(XX:5),5T)-1(x22330
(14)
By definition of mutual information:
((x:
P(X,T,
p ((,,2)log p(X,7)
= E
(X,,,
(15)
((S))(SSI,STT
p(X)p(Z)
S,S,T,TT
X,Z
P(X|S,T,ST)
p(X
Σ X,S.T.ST
PXX.
P(xxZ))og
(16)
p(X)
p(X)
X,Z
We can rewrite the second term by marginalizing over (S,),
z(
ST. ((X
Σ
Σ
(15)
p(X)
p(X)
X,2
X,S,T,ST.Z
p(X
= E
(16)
p(X)
S,T,
This gives us:
(17)
(X|S,TTSTT)
((X|z)
Σ PXX,S.T.ST)log
Σ 7
p(X)
p(X)
X,S.TSTT
X.S.TTT
(18)
STT
Σ Ip(21X,SST,ST)Oog p(X 2)
= Σ (T,ST
log
(19)
P(X)
p(X)
S,S
1opp() [p(2Ix,,,1, p(X
Σ ST,,TT
(20)
p(X)
XTS
Σ S(, ST
(21)
2
Σ
(22)
Since
we have:
(23)
= Σ P(X.S7..57/10g)(((57755
(24)
X.S.T.TT
-Xog
(25)
Σ ((X,S,T,ST)
logr(X1S,T,ST) 110SST/5)T-<22211777755555 Ep(27..57.57)1oppp(V. (XIZ)
(26)
X.S.T.ST
Using Jensen's inequality for the concave function log:
Σ
EpLEIX..77..)JoopXX22223 [p(ZIX.SST.ST)x(X1)
(27)
17

---

Therefore:
([X:S.T.ST))1(x:222
Σ X,S,
(X
(28)
-log Σ ((XXSTTSS))((X
(29)
Due to the Markov chain Z - X - -S,,,STT), we have p - This Markov property holds because all features S, T, .T and Z are deterministic functions of X, making them conditionally independent given X.
Therefore:
([X:STT.ST)-((::222
Σ 8,S,7,8T
(X STT,ST)
(30)
log plzZX)p(XX
(31)
Since fo() is deterministic function, xZ is point mass at Zx xx= fo()), giving:
Σ x pp XX
(32)
Similarly, for the deterministic functions Sx (x= and STx fsr((X):
(33)
By Bayes' theorem:
p(X)
(Xxx) XT
(34)
P(X)
p(X]Zx)= p(Zx)
(35)
For any given X:
(36)
This directly implies:
P(Sx,Tx.STx)=
Σ
p(x)
(37)
Σ M(X'
(38)
=p(Zx)
(39)
Therefore:
p(X) P(X)
xXX|SxIxx xx
=P(XIZx)
(40)
p(Zx)
Taking logarithms:
loga (opp V p(Z(X))(X1Z))
(41)
Substituting back:
(42)
Therefore:
(43)
18

---

B.2 Algorithms
Algorithm presents the Spatio-Temporal Pattern Library Construction process, which forms the foundation of our retrieval-augmented framework. Given dynamic spatio-temporal graph, this algorithm systematically extracts and stores multi-dimensional patterns across spatial, temporal, and spatio-temporal domains. For each snapshot, we decompose the graph into specialized subgraphs using domain-specific chunking methods, then generate discriminative keys and informative values for each pattern type. Keys are extracted using topological properties for spatial patterns, time series characteristics for temporal patterns, and cross tross-dimensione interactions for spatio-tempor patterns, while values are generated by applying a pre-trained backbone to preserve essential features. The algorithm also implements an importance- based sampling strategy to manage historical patterns efficiently, ensuring the libraries maintain the most informative patterns while controlling memory usage.
Algorithm 2 outlines the Retrieval-Augmentt the previously constructed pattern libraries to enhance prediction performance under distribution shifts. When presented with new input features and graph structure, the algorithm first projects the query features into the pattern space and performs multi-dimensional retrieval across spatial, temporal, and spatio-temponn libraries based on similarity scores. For each pattern type, retrieves the top-k most relevant patterns and computes similarity- -weerttd averages of their values. The algorithm then implements an adaptive knowledge fusion mechanism that balances the contributions from current observations (processed by the backbone) and retrieved historical knowledge through a learnable fusion weight, enabling the model to dynamically adjust the influence of historical patterns based on their relevance to the current input. This fused representation is finally passed to decoder to generate the enhanced prediction.
Spatio-Tempony Prediction framework that leverages
C Additional Experiment Details
Table 4: Comparison of the overall performance of different methods (TGCN backbone).
Eavegr-Nives
Maibel
Mosic
12
MAA
18.01
21.
24.50-1177
23:25-013
15.10
15.80
10.85
HMMS:
201.5
33.79
233-30
27 14.4
10.740000
20060
214 Th
Back-
MAPE
28.50 01 3m:10
27
38:51-945
27.29
37.47
85 17
100 G4
170.20
70.300
171 53cc
100-39
120
RMSE
34.12:011
21.40
20.15
5.00100
5,00
MAPE (5)
33.00:834
27.20
38:50 0035
27.31 mm
18.7
10.83
52 26:12
50
12:33.5
54.50 40
55.00
56.00.200 2..04.00
50, 18 18:311
MAL
18.08 6:333
21.0044544
24.37
2085
13/00400
14.026404
16 077
14
0.44 1.
Try
RMSE
28.00 9977
35
15.01.300
38:11-345
31.36-039
21.77
23.63
87 11:211
m1
5.58
5.01 2111
5.00-111
5.622111
MAUI
24.50-mm
21.08-nic
14
16 16:30
14:22
ST.LR
RMSE
28 741855
33.5 38.8119022
38.02
-015
33.36
21.05
22.07:0.1
56 10
13.91:117
5,00:300
5.09.:00
1.00...0
(SP
28.00 18:0
27.001335
31.97 5035
26334.035
18.86mm
20.1312:0
59 14
20 00:
51.552135
54.151503
50. 42
54 14177
STXEC
29.811808
22.04.
6.50
Architectun ture-
(SP
28.7 13TT113 13.9
27.00
32.54.05
0054
27.34
0055
18.94
20.2510:7
59 08
54.15.04)
54.12 (1:31
$5.91
$4, 43422
Busc
MAR:
10 91
21 61
21.89-191
21.47:11
2111
13.51
1
5.97
RMSE
20.74
20.7413344
30.37 1132
93.87-143
21.661011
MAE
18.12
21. 28:8
24.38
13
14.77
16 20
14:5::0
5.50
5.01.50 1::0
5.1
5.33
SY-AAqper
RAISE
28.32 4.23
35.541311
35.54
11.55
25
0.88
MARE
25,00
27.00
31.58
25.92
20.05.000
02.361077
53.18
$4.07
UniptPrr
HMME
28.0-6511
355
35.18
38.
33.25
13.35mm:
22.87
5.80
(SFE
22 58 1::m
26.
2111
31.77:0144
25.78.m1
18 33
10.00 10.95
52
32.30
53.10
54.05.199
MAII
21. 0010
21.8-1111
21.51-010
13.55
14.51
16 02
5
5.52-0m
5.53
MAPE (5))
28.5111.11
27.
12:58
27.38.007
19
20:2510:1
51.15.47:
53.50
50.58
Regutartnaton-
MAA
21.71:2.33
24300-04
21:35
13355mm
11,85
15
besel
LBC
MAPE.
HAMSE:
28
23175
19.19
34,07 4130
27.63:343
38:55.0311
36-77-14
27.54:204
34.15-ma
19.04.mm
20:22
28 11
20 20.0
12
49.50u1.00
5.50
5.00
00:20
51.51:143
01
50
3.00-1.00
Beplo-
MAE
17.97 14:33
20.91
24.22-111
20.71
13.01400
14:00-1.0
10:08
14:00 1300
5.421.00
MABELOS1
02 77
76
32:06-11
30.50-177
90.5
01.58
49.55-197
50.15 25.15
51.60
18.50-7m
Retieral besed
STRAY
RMSSE
MAAE
27.0011.0
18.00 13.001155
30.91 18:0
$1. 07.07 1800
33
$6.11
(12)
31.36
2051
18.51
12.51
20.30
18.21
25
15 18:2811
20
0000000
6.17 cous
4.9% m000
4.07
5.29 1009
5.00
3.84/308
6.281308
4.9 1310
52
30.36-010
16.94-1
20.47-100
42.81-11
43.53-999
C.1 Implementation Details and Evaluation
We establish a data split ratio of rraining/vaiddaiionttt===/ 6/2/2 for all experiments. For fair comparisons, we set the learning rate to either 0.03 or 0.01 based on the specific situation of each dataset and model requirements (Table 7). The parameters of basclines were set based on their original papers and any
19

---

Algorithm 1
Spatio-Temports Pattern Library Construction
Require:
Dynamic spatio-temporal graph G, feature dimension d, pre-trained backbone fe. history ratio 3, retrieval count &
Ensure: Spatio-temporal pattern libraries 8 BT BST
Initialize pattern libraries 8 0, 1TT 0, BST -
2: for each snapshot G- E do
Extract Patterns
3: Spatial Patterns:
4: {G*} SPATAALSUDGGGAPPHCHINNGGGGG
D Via Eq. (2)
5:
for each subgraph GP { do
6:
Extract key k EXTRAACTSPATTLLKEYC))
> Via Eq. (5)
Extract value u. MGAN 8: Store pattern (NF in B
7:
Via Eq. (8)
9: end for
10: Temporal Patterns:
11:
< {G")
b Via Eq. (3)
12:
for each subgraph G. {G") do
13:
Extract key k.- -ETTRACCTTEPPORAAKKYGG]]] Extract value u²? < MEANPOOL((6((())
Via Eq. (6)
14:
b Via Eq. (8)
15:
Store pattern (k? (T)) in B
16:
end for
17:
Spatio-Temporal Patterns: {GST] IRRECTRAACCUSTERRNGGGE TST)
D Via Eq. (4)
19:
for each subgraph G.5T E(GST) do
20:
Extract key k. - 1. Skg
b Via Eq. (7)
21:
Extract value 152 + MEANPOOLLf((
b Via Eq. (8)
22:
Store pattern (R-ST ST)T) in BST
23:
end for
24: Historical Patterns Management:
25:
for each library BE {B _ "BST" do
26:
[ > Boon__hstory_.o size then
27:
Calculate pattern importance I(k:) < Ti
Sample indices WEIGHTEDSSAMLLINGG... I, (.)1))) B ((
29:
30:
end if
31: Build search index for B
32:
end for
33:
end for
34: return Pattern librarics BS, BT, BST
accompanying code. We utilized either their default parameters or the best-reported parameters from their reported publications.
All experiments conducted with the same early stopping mechanism prevent overfitting. To ensure robust results, we repeated each experiment with 3 different random seeds and reported the average performance. All experiments were performed using NVIDIA A100 80G GPUs to ensure consistency in computational resources and reproducibility. For evaluations, we employed three standard evaluation metrics comprehensively assess model performance: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE). Lower values across these metrics indicate better performance.
C.2 Backbone and Baseline Details
Backbone Architectures. We conducted experiments using four different spatio-tempora graph neural network architectures as backbones to evaluate the robustness and versatility of our approach:
STGNN [69]: Spatial-Tempprra Graph Neural Network integrates graph convolution with convolution capture spatial dependencies and temporal dynamics simultancously. It employs
20

---

Algorithm 2 Retrieval-Augmentte Spatio-Tempora Prediction
Require: Input features X, adjacency matrix A, pattern libraries 8,, BBT,, backbone fe, fusion
weight y, retrieval count k
Ensure: Enhanced prediction Y
1: Pattern Retrieval:
2: Project query features X' < PROJECTFEATURES(X)
3: Multi-dimensional Retrieval:
4: for each pattern type/ E (S, do
5: Calculate similarity scores s <- exp(-IIXX -g 19)))) for all E
6: Retrieve top-k patterns R₂ + [K] 0515)))))) E Tsp (s((ss }
> Via Eq. (10)
7: Compute weighted average of
(kg (fg. Softmax($)) (8))
8: end for
9: Knowledge Fusion:
10: Current representation 2 +- (f
Via Eq. (11)
11: Retrieved knowledge 72 < MLP, (vğ U4 (DUTT)
Via Eq. (11)
12: Fused representation Z 7- + (1 -?) Z2
Via Eq. (12)
13: Prediction:
14: Final prediction y + Decoder(2 Z)
15: return Enhanced prediction Y
Table 5: Comparison of the overall performance of different methods (ASTGNN backbone).
Datnetts
Atr-Steow
PEMS Strea
Enwrgy-Strow
Methed
Metric
MAE
15 68
21 3.:3
24.58.44
11
14:32
15.55
15 70
10 AiGloc
10 10.00 10.67
17
Premats
XMSE
20.Saunca
54 S4.88u231
38, 12.13
S3.58a5-4
22.48
24.80ut16
29,
25.12
10.85a2
10.02a11
11,04a02
10.58un31
Back- boue
MAPF
96 17--04
29 8760
34.37-11 70
20
32.00-011
37.40
170.03-00
171.00-0
173.00
171 16 es
MAB
19:00
21 31
25. 0M000
21 6.68
13.12
34.77:M
14.57:30
5.4
5.88et 15
5.43
Bemain
RMSE
20 88uus
S4.5bu
84.84444
S4.88
21.23
10
72433
5.63
6.
Toafi Sprast
54:21.772
28.5Lo44
53.57
21.07.00
28.51.11
5.07
24 10
28 26266
33, 10-15
00
17.53-007
19.31-005
23.51-01
19.65-34
58.9143
59.5-190
00.8-3111
MAPL
18. 000000
21 11-1--
31 71
21 76.
12.00 12.00
14.19-111
16:00
11 31
5:35
5.3
1441-119
LoRA
RMSE
20.25
46.15u241
38.80u33
53
20,50a
28.17.33
27.
28.41:330
5,500030
6.58
6.72
MARTiCS)
27.2140:1
18.0
18.0
09.11
50.7761
52.8611
509061
20.77
54.75a
21,6
Architecture
MA
24 MM-00
27 77.5mmm
32.55-04
17.00
1035-361
50,09-1
1941
Bused
MAP
10 1:
22 22.0
25. 14
21 37.5
13
14
16 75mcs
14.5 51
5.37
5.4
EAC
RASSE
30002-211
$4.87
38.87
21.18an11
28.25a11
27.
20.860116
5,50
6.8722 80
6.84
MAPK((S)
15.33
284 06-
33.38-10
06-11
75
50.85
50.00mm
55.
50.90
51
Mo
12
(APE(
18.47,077
56.05
67.F
MAE
18. 18.30
21 11.58cc
24 80
21 21.3
12.88a0s
15
16, 58
14. 14.20
5.30
5.3bc
RMSE
20 14100117
30.
38. 08
20.80 20.8
20 23
57 10mm
23 23
5.50
5.50r
771111
1.02a11
MAPE
23 23.10
44
02 Muus
27 56
17.080377
19.35
25.00
$2.80
55.051133
65, 45..1
63.51.134
MAE
21.51a:
24
13.0000s
5.28
PECPM
23
29.47:113
5,40e
(ARE(())
34
Regularization
haned
JWC
MAPE
RMSSI
24.5
36 07-1x
27.
51.75
29.
42.00
40.00-17
26.
L6u
17.50
21.41-09
20.25.19
2400
21.80033
15
19 70.75
12.40
5,55
58.82.116
5.67ec
64 L4.9
5.8
61.66n03
Replin- based
Replay
KMSSE
MAE
15.401
25.65-15
$101+2
21.1.
38-2/
2LS
S3.37a
21
11.02m0
14.0
25
26. Mboii
17.0m01
25
14:02304
6.2km
5.30
4.25
5-45c
MAPE(()
21.0Gu
27
32 Ntui
87 28
17.70
10.38.13
21.42ous
1888::77
40.77:2.
51.96
53.82
Retriccal- basel
STRAP
RMSE
MAB
26
18
28
06-
80
20
74.1.0
9:
35. dhui):
23.00
23.54
30
20
44:1
12:36-00
18.71.us
13:3:
20.48.3.
16.5 11
1843))
13 49:30
20177.111
1.80 34
0.03304
4.90-14
3.1000
1.02uu
8.07
4.0000s
hierarchical structure where graph convolution extracts spatial features while temporal convolution captures sequential patterns, making it effective for traffic forecasting tasks.
ASTGNN [18]: Attention Spatial-Temporal Graph Neural Network enhances STGNN with multi-head attention mechanisms to dynamically capture both spatial and temporal dependencies. It introduces adaptive adjacency matrices that evolve over time, allowing the model to identify i important connections that might change across different time periods.
DCRNN [37]: Diffusion Convolutional Recurrent Neural Network combines diffusion convolution with recurrent neural networks to model spatio-temporal dependencies. It formulates the traffic flow as a diffusion process on directed graph and employs an encoder-decoder architecture with scheduled sampling for sequence prediction tasks.
21

---

Table 6: Comparison of the overall performance of different methods (DCRNN backbone).
Alr-Straa
Entrgy--Sevee
Mathel
Stire
12
MEAF:
26.96612
18 CE
18.00 18
1KD
10
Protein S7
RMSE
36.07.5.1
41.35:545
10.4
26.7inss
28.74005
27.81mn3
10.53
10.55:111
13 11.0L.026
10 10.9kan:1
Back- bone
MAPE:19)
21: 13x.22
30.22.339
36.36.197
36.73433
36.24
36.246135
39.96..15
38.878324
170.18000
177 377.50601254
180.46635-15
178.3366175
MAE
24.26.123
20.7huos
24.17.14
14.0
14.7
16
15.000015
5.00
6.2
MAPE
31.61.50
15.00.330
31.63
23.
24.5-133
27.061135
25.0
06.38.100
50.05.100
30,00.002
53
MAE
21.26001
2100
15
8.2862
8:256211
20
Strvare
RMSE
74
30.0
88
22
28
28.75
2430
5.0
3,51:5
1.
5 5.02
MAPE (9)
25,00000
26.96.00
11.88045
28.9
206
21.00.00
24.00007
22/06003
90.9
61.74:125
55.07.134
61.
MAE
22.17044
16
22
13
18.0500
16.1200s
N.280000
0.25
0.2
20
LARA
RMSE
30.05:111
21.0
20.17
22.07
MAE
10.15
21.84.02
26.5
21 Noons
16.00
5,88.3
5.89.3/4
5. 1.88 uu
STASC
HOMSE
20.05
34.49 34.05
30
25 Heoss
3.66-10
5 Ma
Architectone
MAPE (6)
28.65
27.58.044
32
27.58
184
20.77:01
28.641122
21.08
21.08:155
02.57
50.45:11
34.70:1
58.07
Basod
12
EAC
RMSE
30.31.00
10.2
34.3
28.55
21.500
MAPS
26
27.81-04
32
23.83
18.0
19
20.0
19.57
52.700
54.00-11
25.20
53.00
MAR:
20 17
75.55 53
22 17mm
15 10
15
11 19
13
3.30a 75
5 15
RMSE
30.50u01
80.28,045
40.30025
34.80uss
21.04,033
22.63.02
200070077
22.920255
1.882111
24.00
24.00
26.15
15-15
32.5 3253
25 25.3
20
11:3
35
52,55
53
13
53.911
MAE
18.1
18.0800s
14.25
RMMS
10
75
50
21
17
96
5,00
5.59
-.
MCPPE(55
24.00
41,039
82.82-37
27.8
20 1012
21.25
11.20000
24.02002
21.54ocs
50.23,27
51.71130
MAE
19. 42u03
22006000
26. 1100
21.M0a0s
18.52aus
18. Manu
14.8
6.20.
5.20s
PECPM
RMIS
90
34:00-0m
16
14
26.50
20.00
5,00mm
3.50
3.37-11
5.51 -0os
89.06
base
EWC
MAPE (90
RMSE
20.27.1.34
05
34.22.00
36.00-10
39.42003
11.8
28.87ass
20.00009
21.08-100
25.42.044
24,76-
28.08.055
22.28-105
26.R0a013
09.764.0
5.8821
31.50-
Replay-
based
Rephay
MAPE
IOMSE
KTAE
23.05
15.30
28
15.3
35.75004
21:30.055
11
38
21:00:01
35.2
26.8.m
228
180
24.4
23.22
14102m0
26.00034
23.50m33
16
90.34
K3
50.49-21
4.21211
6.42
41.00:244
4.15.3
8-46a.14
30.01
8-4hou
Retricral
MAE
21.10.00
23.77-04
2099.015
12:00
18.18am
15.12
1838
4.80u
4.90.304
4.92.000
4.00uss
38.76,055
50.74.021
38.77.02
18.13
18.82
31.07.040
19.14,035
43.09.13)
Table Hyperparameter Settings for All Methods Across Different Datasets
AIR-Stream
PEMS-Stream
ENERGY-Stream
Method
LR
BS
LR
BS
LR
BS
Pretrain
0.03
128
0.03
128
0.01
128
Retrain
0.03
128
0.03
128
0.03
128
TrafficStream
0.01
128
0.03
128
0.03
128
ST-LoRA
0.03
128
0.03
128
0,03
128
STKEс
0.01
128
0.01
128
0.03
128
EAC
0.03
128
0.03
128
0.03
128
ST-Adapter
0.03
128
0.03
128
0.03
128
GraphPro
0.03
128
0.03
128
0.03
128
PECPM
0.03
128
0.03
128
0.03
128
EWC
0.01
128
0.03
128
0.03
128
Replay
0.01
128
0.03
128
0.03
128
RAGraph
0.03
128
0.03
128
0.03
128
PRODIGY
0.03
128
0.03
128
0.03
128
STRAP
0.03
128
0.03
128
0.03
128
TGCN [80]: Temporal Graph Convolutional Network integrates graph convolutional networks with gated recurrent units to capture spatial dependencies and temporal dynamics simultancously. It maintains a balance between model complexity and predictive power, making it particularly suitable for traffic prediction tasks with limited computational resources.
We compared our proposed STRAP framework against various state-of-the-art methods spanning multiple categories:
Baseline Methods.
1 Backbone-based Methods.
This approach involves training the backbone model on historical data and directly applying it to new streaming data without any adaptation. serves as a lower bound baseline that illustrates the performance degradation when models fail to adapt to distribution shifts.
Pretrain:
22

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This method completely retrains the backbone model from scratch whenever new data arrives. While it can adapt to new distributions, suffers from catastrophic forgetting of previously learned patterns and incurs substantial computational costs.
Retrain:
Architecture-based Methods.
TrafficStream [10]: A streaming traffic flow forecasting framework based on continual learning principles. It maintains a memory buffer of historical samples and employs experience replay to mitigate catastrophic forgetting while adapting to evolving traffic patterns.
ST-LoRA [54]: Spatio-Temporal Low-Rank Adaptation introduces parameter-efficient fine-tuning for spatio-temporal models by inserting lightweight, trainable low-rank matrices while keeping most pretrained parameters frozen, enabling efficient adaptation to new distributions with minimal computational overhead.
STKEC [63]: designed for continual traffic prediction with expanding graphs. It maintains knowledge from historical graphs while accommodating new nodes and edges through specialized knowledge transfer mechanisms.
Knowledge Expansion and Consolidation framework specifically
EAC [9]: Expand and Compress introduces parameter-tuning framework for continual spatio- temporal graph forecasting that freezes the base model to preserve prior knowledge while adapting to new data through prompt parameter pools, effectively balancing stability and plasticity.
ST-Adapter [49]: Originally designed for image-to to-deoo transfer learning. this approach adapts pretrained models to temporal dynamics while preserving spatial representations from the pretrained model.
tasks by inserting lightweight adapter modules that capture
GraphPro [71]: A graph pre-tra traininiingg and prompt learning framework that utilizes task-specific prompts adapt pretrained graph neural networks downstream tasks, achieving efficient knowl- edge transfer with minimal parameter updates.
3 eegularization-basee Methods. EWC [42]: Elastic Weight Consolidation selectively constrains important parameters for previously learned tasks while allowing flexibility in less critical parameters. It utilizes Fisher information matrices to estimate parameter importance and applies regularization accordingly, preventing catastrophic forgetting during continual learning.
4 Replay-based Methods. Replay [16]: This approach maintains memory buffer of representative samples from historical data distributions and periodically replays them during training on new data. It explicilly preserves knowledge of previous distributions, though at the cost of increased memory requirements and potentially inefficient knowledge consolidation.
Methods. PECPM [64]: Pattern Expansion and Consolidation on evolving graphs for continual traffic prediction leverages pattern matching techniques to identify relevant historical patterns, constructs a pattern memory module that stores and retrieves patterns based on spatio-temporal similarity, enabling adaptation evolving graph structures.
6 Pattern Matching-
C.3 Datasets Statistics
Our experiments real-world natural streaming datasets, and detailed statistics for each dataset shown in Table 8 below:
Table 8: Dataset Details
Dataset
Domain
Time Range
Period
Node Evolution
Frequency Frames
1087 1115 1154
Air-Stream
Weather 01/01/2016 12/31/2019
4
hour 34,065
+ 1193 + 1202
655 - 713 786
PEMS-Stream
Traffic
7
+ 822 - 834 + 850
5 min 61,992
- 871
103 + 113
Energy-Strre Stream Energy
Unknown (245 days)
10 min
34.560
122 -+ 134
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We use three real-world streaming graph datasets for our analysis. First. the PEMS-Strean dataset serves benchmark for traffic flow prediction, where the goal predict future traffic flow based on historical observations from directed sensor graph. Second, we utilize the A/R- Streammm dataset for meteorological domain analysis, which focuses on predicting future air quality index (AQI) flow based on observations from various environmental monitoring stations located in China. We segment the data into four periods, corresponding to four years. Third, the ENERGY-Stream dataset examines wind power in the energy domain, where the objective is to predict future indicators based on the generation metrics of a wind farm operated by a specific company (using temperature inside the turbine nacelle substitute for active power flow observations). This dataset is also divided into four periods, corresponding to four years, according to the appropriate sub-period dataset size.
For all datasets, we follow conventional practices [37] to define the graph topology. Specifically, we compute the adjacency matrix A for each year using a thresholded Gaussian kernel, defined follows:
exp 0
if exe otherwise
-2 -z 2r and i
Anp
(44)
where dy represents the distance between sensors and j. a is the standard deviation of all distances, and is the threshold. Empirically, we select values of 0.5 and 0.99 for the air quality and wind power datasets, respectively.
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C.4 Hyper-parameter Study (RQ3)
Fusion Ratio. Figure presents the ef- fect of varying fusion ratios on different backbone architectures, revealing distinct optimal balancing points between histor- ical knowledge and current observations. For ASTGNN, we observe clear perfor- mance improvement as the fusion ratio increases to 0.9, with MAPE decreasing from43.695 to 40.7% on average, suggest- ing this attention- architecture bene- fits significantly from prioritizing current observations. In contrast, STGNN shows optimal performance at moderate fusion ratio of 0.7, with performance degrading at both extremes.
ASTGNN
STGNN
Step -
Step
Step =
Step
MAPE (%)
Step 12
MAPE (%)
Stop 12
Average
22
40
41
0.1
0.3
0.5
0.7
0.9
0.1
0.3
0.5
0.7
0.9
Ratio
Ratio
MAPE (%)
69
Step 12
Step
MAPE (16
Step 12
Step 6
Average
+2
Average
45
36
0.1
0.3
0.5
0.7
0.9
0.1
0.3
0.5
0.7
0.9
Fusion Ratio
Fusion Ratio
DCRNN and TGCN display markedly dif- ferent patterns. DCRNN performs best at fusion ratios of 0.3 and 0.7-0.9, indi- cating its dual-phase nature benefits from
Figure 5: Performance analysis of different backbone various fusion ratios 7
either stronger historical knowledge incorporation current observation emphasis, but struggles with equal weighting. Most notably, TGCN demonstrates the most pronounced sensitivity to the fusion ratio, achieving its optimal performance at preciscly 0.5, with substantial performance degradation at other ratios. This suggests TGCN's temporal gating mechanisms particularly benefit from balanced integration of historical patterns and current data.
Dropout Ratio. Figure demonstrates the impact of pattern library dropout rate on model performance across AST- GNN and DCRNN backbones. The con- sistently increasing MAPE with higher dropout rates provides compelling evi- dence for the effectiveness of our pat- tern library construction methodology. This clear degradation trend confirms that each pattern stored in our library con- tributes valuable information for accurate forecasting, with minimal redundancy noise. The near-linear performance de- cline with increasing dropout suggests our pattern selection and extraction mechanisms effectively capture essential centio-temmpral dynamics while filtering out irrelevant information. The particularly steep performance drop in DCRNN further emphasizes the high information density of our constructed library, where even moderate pattern removal significantly impacts predictive capability.
ASTGNN
DCRNN
Step =
Step =3
46
Step =
MAPE (%)
MAPE (%)
83
8
39
0.05
0.3
0.5
D.7
0.9
0.05
0.3
0.5
0.7
0.9
Dropout Rate
Dropout Rate
Figure 6: Performance analysis (MAPE) of different pattern library dropout ratios.
Retrieval Count. Figure examines how the number of retrieved patterns (k) from our pattern library affects pre- diction performance across STGNN and
STGNN
DCRNN
52
MAPE (%)
48
Average
MAPE (%)
50
Average
DCRNN backbones, revealing an opti- mal retrieval range that balances suffi- cient historical knowledge representation with minimal noise introduction. The re- sults demonstrate clear U-shaped rela- tionship between retrieval count and pre- diction error, where both insufficient re- trieval (k: 5) and excessive retrieval (k= 70) lead suboptimal performance,
86
40
30
30
50
70
510
30
5.0
70
Retrieval Count
Retrieval Count
Figure 7: Performance analysis of different retrieval counts.
25

---

while moderate retrieval counts (10 for STGNN and 30-50 for DCRNN) achieve the lowest MAPE. This pattern suggests that retrieving too few patterns fails to capture sufficient historical knowledge for accurate predictions, while excessive retrieval introduces noise and potentially irrelevant patterns that dilute the quality of predictions. Notably, the optimal retrieval count differs between architectures, with the more complex DCRNN benefiting from larger pattern set (30-50) compared to STGNN (10).
C.5
Case Study (RQ4)
Horizon
Horizon
Horizon 3
Horizon
2.38
1.8
1.48
1.8
2.0
MAPE
1.6
1.53
S.M
MAPE
1.6
1.6
1.5
1.
140
1.4
144
Lo4
Retrain
BWC
Replay
Graphero
STRAP
Retrain
EWC Replay
EAC GraphPro
STRAP
Retrain
BWC Replay
EAC Graphera
STRAP
Retrain
BWC
Replay
GraphPro STRAP
Horizon
Horizon Avg.
Horizon 12
Horizon Avg.
10
2.0
MAPE
MAPE
1.M
1.66
1:5
1.63
1.6
1.4
14
1.36
Rotrain
EWC Roplay
Graphpro STRAP
BAC
Retrain
EWC
Raplas
BAC
Graphpro
SYRAP
Ratrain
EWC
Replay
BAC Graphpro SYrAP
Rntrain in
EWC
Raplay
GraphPro
STRAP
(a) Performance analysis (MAPE) of different horizons on ASTGNN backbone.
Performance analysis (MAPE) of different horizons
on TGCN backbone.
Horizon
1.6
1.6
MAPE
2.47
MAPE
1.4
131
1.39
3.53
Retrain
EWC Raplay
EAC GraphPre
STRAP
Retmin
EWC
Replay
FAC
Pro
STRAP
Horizon
Horizon Aug.
2,41
1.66
2.53
2.58
150
MAPE
MAPE
140
122
Retrain
1.2
EWC Replay
GraphPro
STRAP
Retrain
EWC
Replay
Graphpro
EAC
STRAP
(c) Performance analysis (MAPE) of different horizons on DCRNN backbone.
Figure 8: Performance analysis (MAPE) of different horizons on different backbones.
As illustrated in Figure 8, we conducted a comprehensive analysis of model performance across differ- ent prediction horizons (3, 6, 12, and average) three backbone architectures: ASTGNN, TGCN, and DCRNN. The results demonstrate that while baseline methods exhibit considerable performance variations across different backbone architectures, our STRAP consistently maintains superior perfor- mance regardless of the underlying backbone. This remarkable consistency can be attributed to two key factors: First, our approach decouples pattern extraction and retrieval from the specific neural network architecture, enabling a more robust knowledge representation that transcends the limitations of any particular backbone. Second, our multi-level pattern library framework operates as aldg-and enhancement that seamlessly integrates with various graph neural network foundations without requir- ing architecture-see specifcc modifications. On ASTGNN. STRAP achieves average MAPE reductions of 19%, 22%. and 24% compared to the best baseline for horizons 3, 6, and 12, respectively. Similarly significant improvements are observed on TGCN and DCRNN. These consistent gains across different architectures underscore the versatility and robustness of our approach, which effectively enhances prediction performance without being constrained by backbone design choices or implementation details.
26

---

C.6 Retrieval-based Methods and Computational Efficiency (RQ5)
C.6.1 Retrieval-basee Methods
We extended our experimental evaluation to incorporate two state-of-the-art methods, RAGraph [26] and PRODIGY [24], across all four backbone architectures (STGNN, ASTGNN, DCRNN, TGCN) on the -Stremm dataset (Figure 9). The comprehensive results demonstrate that while these advanced methods indeed provide substantial improvements over conventional baseline approaches, our proposed STRAP framework consistently achieves superior performance across all evaluation metrics and backbone architectures, further validating its effectiveness and generalizability.
TGCN Backbone
STGNN Backbona
PEOSICT ENGINT
PR00 HART
CHAW
MAPE 150
MAPE PND
2-102
Inttap
Prediction Harizon
22-tap
Areaage
2-40p
Prediction Horbson
Acarage
DCRNN Backbone Results
ASTGNN dièone
SPAR
PREST HAMP
STAPPINOR
REAS CHAPP
PROD HARP
PARE EN
3-110
S-ttpp
Prediction 124tpp
Amariaa
J-10ap
C-110 12-092
Anraag
Prediction Hortron
Figure 9: Performance comparison of STRAP, PRODIGY, and RAGraph across different backbone architectures. The figure shows MAE (bar charts) and MAPE (line charts) metrics for 3-step, 6-step, 12-step predictions and their averages. STRAP consistently outperforms both baseline methods across all backbone networks (TGCN, STGNN, DCRNN, ASTGNN).
C.6.2 Computational Efficiency
As demonstrated in our experimental evaluation, STRAP achieves a favorable balance between computational efficiency and prediction performance. The computational cost analysis presented in Figure 10 reveals that STRAP's training time (measured in seconds per epoch) falls within a moderate range compared to existing methods. Specifically, using ASTGNN as the backbone architecture the ENERGY--Sreet Stream dataset, our approach requires moderately higher computational resources than lightweight methods such EAC, EWC, and GraphPro. but significantly less computational overhead than the most intensive baseline PECPM.
The inherent computational requirements of our retrieval- augmented framework stem from two primary components: pattern library maintenance and dynamic retrieval operations during training and inference. While this introduces unavoidable computational overhead compared to non-retrieval methods, the trade-off yields substantial benefits in prediction accuracy and enhanced robustness to distribution shifts critical advantages in real-worle traffic forecasting scenarios.
27

---

3-step Prediction Horizon
6-step Prediction Horizon
Prediction
Phice
MAPE (N4 6-ttep Predicatio
oTher
23.0
$0.0
43.0
0.2
25
04
6.
06
0.7
25
0.
2.0
Computational Efficiency (Uiseconds per spech)
Computational Erficiency (3/seconds per apach)
12-step Prediction Horizon
Prediction Horizon
2100
Seats
MAPE (N) Prediction
60.0
MAPE 1No Average prediction
67.5
$5.0-
12.5
13.5
$3.0
67.5
425
25 04
25
2.0
Computational Efficiency (Liseconds apech)
Computational Erfciency (alseconds per apech
Figure 10: MAPE vs Computational Efficiency Analysis across Different Prediction Horizons. The bubble chart shows the relationship between computational efficiency (x-axis) and MAPE performance (y-axis) for all methods across 3-step, 6-step. 12-step, and average predictions on the ENERGY- Stream dataset. Bubble size represents computational efficiency, with larger bubbles indicating higher efficiency. STRAP consistently achieves the best MAPE performance across all prediction horizons while maintaining reasonable computational efficiency.
Despite the moderate computational cost increase, argue that the performance gains justify this trade-off, particularly in applications where prediction accuracy under evolving traffic patterns is paramount. The computational overhead remains reasonable and scales efficiently with dataset size. Future research directions include exploring efficiency improvements through optimized pattern library indexing strategies and adaptive retrieval mechanisms further optimize the aefformancc-efffciinn balance.
D Broader Impacts
Our work builds on the widespread application of retreeval-augmmeeee methods in machine learning and aims extend this paradigm spatio-temporal graph data streaming environments, This approach allows models to maintain consistent performance across distribution shifts without catastrophic forgetting, avoiding potential performance degradation common in streaming learning settings. Our strreval-bbsed framework is particularly effective in domains with continuous data streams and evolving patterns, such as traffic flow prediction, air quality monitoring, renewable energy forecasting. and intelligent transportation systems. Additionally, our multi-level pattern library establishes an excellent paradigm by explicitly storing and leveraging historical spatio-temporal patterns, significantly enhancing the model's adaptability to changing conditions. By combining retrieval mechanisms with spatio-temporal graph neural networks, our work provides valuable insights and serves as a reference for future streaming graph learning models in dynamic real-world applications.
28

---

E Data Ethics Statement
To evaluate the efficacy of this work, we conducted experiments using only publicly available datasets, namely, PEMS- FEMS-Stream, AIR- AIR-Stream, and ANERGY--Steall datasets that contain traffic sensor data, air quality monitoring data, and wind power generation metrics, respectively. All datasets were used in accordance with their usage terms and conditions. We further declare that no personally identifiable information was used in these datasets. The traffic flow and air quality data were collected from public monitoring stations, while the energy data uses temperature measurements from wind turbines operated by an anonymized company with all identifying information removed. No human or animal subject was involved in this research, and all results reported reflect aggregated statistical measures without any privacy implications.
29

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Reviews:
[{"review_id": "KSoF1yCq7r", "reviewer": "Reviewer_WWVH", "summary": "This paper addresses the challenge of spatio-temporal out-of-distribution (STOOD) generalization, where the distribution of test data diverges significantly from that of the training set. Rather than relying solely on model parameter adaptation or overwriting with patterns learned from past data, this paper proposes an explicit memory mechanism by constructing a three-dimensional pattern library. This library stores essential patterns extracted from historical data, including spatial subgraphs, temporal dynamics, and spatio-temporal motifs.\nWhen processing new data, this paper introduces a similarity-based retrieval strategy that identifies and retrieves the most relevant historical patterns from the library according to their similarity to current graph features. These retrieved patterns are then explicitly fused with the current observations through a similarity-weighted aggregation. By integrating both retrieved historical knowledge and current observations, this approach enhances model robustness to distribution shifts and significantly improves performance in spatio-temporal OOD scenarios.", "questions": "1.\tThe paper should clearly differentiate between spatio-temporal OOD generalization and continual spatio-temporal learning, and explicitly clarify which problem is being addressed in the experiments and method design.\n\n2.\tProvide efficiency analysis (in Spatio-Temporal Pattern Library construction and pattern retrieval). \n\n3.\tAdditional baselines using replay-based methods should be included for a more comprehensive comparison.\n\n4.\tFigure 3 should be revised to provide evidence of the model’s robustness to distribution shifts between the training and testing data across all periods, rather than only illustrating the dataset’s distribution shift.\n\n5.\tOn lines 335–336, “Figure 4” should be corrected to “Figure 3.”\n\n6.\tIt would be helpful to clarify in the paper that the values 3, 6, and 12 in Table 1 represent the prediction horizon, as this may be confusing for readers who are not familiar with this area.", "limitations": "yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Significance Strengths：The paper provides a clear comparison with existing methods, including architecture-based, replay-based, and regularization-based approaches. The proposed retrieval-based method demonstrates notable originality and represents a meaningful advance beyond prior work. By positioning the new approach alongside established baselines, the paper effectively highlights its unique contribution and potential impact on the field.\n\nOriginality Strength: The use of a pattern library to store historical patterns and mitigate the forgetting problem by retrieving relevant historical patterns is a novel idea. This approach offers a fresh perspective for handling real-world streaming spatio-temporal data in both OOD and continual learning scenarios. The explicit memory mechanism distinguishes this work from prior methods that rely solely on parameter adaptation or data replay.\n\nWeakness1: While the Preliminaries section (around line 145) and the subsequent discussion of distribution shifts clearly describe an OOD setting, where the test distribution differs from the training distribution.There is a mismatch between this description and the actual setting of the paper. Specifically, Definition 3, the learning objective, and the experimental setup all focus on distribution shifts across different time periods, which is characteristic of continual learning rather than classical OOD settings. \n\nWeakness2:  If the paper is operating under an OOD setting, it should emphasize that the training and testing data come from different time periods, for example, training on X_t and testing on X_{t+1}.  According to Definition 3, it may be more appropriate for the paper to highlight the distribution shift between the current graph signal signal X_T nd the target output over a prediction horizon, [X_T,\\ldots X_{T+p}]. The paper should clearly differentiate between spatio-temporal OOD generalization and continual spatio-temporal learning, and explicitly clarify which problem is being addressed in the experiments and method design.\n\nWeakness3: \tThe paper does not discuss efficiency, as it lacks any analysis of the time complexity involved in Spatio-Temporal Pattern Library construction and pattern retrieval, as well as the storage requirements associated with maintaining the pattern library. Given that the performance improvement is not particularly significant, providing such analyses would be valuable for helping readers assess the practical feasibility, scalability, and the overall significance of the contribution.\n\nWeakness4:   Figure 3 demonstrates that the distributions of test set values vary considerably across the four periods. However, the paper claims to focus on Spatio-Temporal Out-of-Distribution (OOD) Learning, where the test distributions should differ significantly from those seen during training.  In this part, the paper should provide evidence of the model’s robustness to distribution shifts between the training and testing data across all periods, rather than only illustrating the dataset’s distribution shift. Clear experimental results reflecting performance under these OOD conditions are needed to support the main claim.\n\n\nWeakness5: There is no evaluation metric reported for mitigating forgetting, even though the abstract (line 15) states that the proposed STRAP approach is able to “mitigate catastrophic forgetting.” The paper should provide appropriate metrics and results to support this claim.\n\n\nWeakness 6: The discussion of related work on replay-based methods should be updated. The paper currently only references one method which is published in 2017, but most recent approaches primarily rely on data replay strategies. The comparison with other retrieval-based methods also needs to be strengthened.\n\nWeakness7: The paper lacks a clear description of the main task being addressed. And the learning objective is not clearly defined, which may make it difficult for readers to fully understand the focus and contributions of the work. Additionally, there are some minor typographical and writing errors throughout the manuscript.", "was_revised": true, "final_justification": "Regarding the efficiency test, I am concerned about the efficiency of this method. Compared to the baseline, it takes almost twice as much time, while the performance improvement is limited. In STGNN problems, people often deal with highly dynamic and large-scale datasets, where efficiency and effectiveness metrics are equally important.\n\nCatastrophic forgetting is actually the key scenario for evaluating continual learning, and it requires dedicated testing scenarios, such as Forgetting Measure,  Backward Transfer, etc.. Indirect testing through standard evaluation metrics (MAE, RMSE, MAPE) does not address my concern. \n\nThere are also typos and inconsistencies in the current version of the paper, as I posted in my review, which suggests it may not yet be ready for publication at a top-tier conference.\n\nBased on the above considerations, I maintain my score, borderline reject, and recommend further improvements to the paper regarding key issues in efficiency, catastrophic forgetting, and presentation.", "rebuttal": "Thank you for your insightful comments. We address your concerns and answer your questions below.\n\n**W1+Q1+W2**\n\nWe appreciate the reviewer's concerns about the distinction between Continual Learning (CL) and Out-of-Distribution (OOD) generalization in our work. We would like to clarify the scope of our work as follows.\n\nContinual Learning (CL) refers to the ability of a model to learn from a continuous stream of data over time, adapting to new patterns while retaining knowledge from previous experiences. In traditional CL paradigms, models are often retrained at fixed intervals to incorporate new information.  Out-of-Distribution (OOD) Generalization concerns a model's ability to perform well on test data whose distribution differs from the distribution of the training data. \n\nOur work addresses a more nuanced challenge at the intersection of the above two domains. While we operate within a CL framework where models learn from streaming data across different time periods, our focus is on the distribution shifts that occur within each time period between training and testing sets. Specifically, for each time period, we divide the data into training set and testing set. The distributions of the training data and the testing data are different, which is actually the classical OOD setting.\n\nAs demonstrated in our revised Figure 3, there are substantial distribution shifts between training and testing data within each individual period. Rather than simply preventing catastrophic forgetting (the typical goal of CL) or broadly generalizing to unseen distributions (the typical goal of OOD methods), STRAP learns and leverages specific patterns from historical data that provide the most informative signal for current predictions under shifted distribution.\n\n**Q2+W3**\n\nWe appreciate the reviewer's question regarding computational efficiency. \n\nAs reported in our experimental logs, STRAP's computational efficiency (seconds/epoch) is slightly lower than some lightweight methods but significantly higher than other more computationally intensive baselines. Specifically, using ASTGNN as the backbone with ENERGY-Stream, our approach requires moderately higher computational resources than some lightweight methods but significantly less than the most computationally intensive baselines.\n\nOur retrieval-augmented framework inherently requires additional computational resources due to the pattern library maintenance and retrieval operations. In future work, we plan to explore efficiency improvements through techniques such as optimized pattern library indexing and adaptive retrieval mechanisms.\n\n| Method | Period 0 | Period 1 | Period 2 | Period 3 |\n|--------|----------|----------|----------|----------|\n| EAC | 1.02 | 1.03 | 1.04 | 1.06 |\n| EWC | 1.00 | 1.54 | 1.58 | 1.60 |\n| GraphPro | 1.00 | 1.00 | 1.04 | 1.05 |\n| PECPM | 3.79 | 4.03 | 4.28 | 4.64 |\n| STRAP | 2.27 | 1.83 | 1.88 | 2.10 |\n| STKEC | 1.01 | 1.21 | 1.24 | 1.22 |\n| ST-LoRA | 1.07 | 1.16 | 1.16 | 1.16 |\n| TrafficStream | 1.01 | 1.60 | 1.66 | 1.64 |\n| RAGraph | 1.27 | 1.21 | 1.20 | 1.20 |\n\n**Q4+W4+Q5**\n\nWe appreciate the reviewer's feedback regarding the evidence of distribution shifts between training and testing data. \n\nIn response to this concern, we revised Figure 3 to include both training and testing data distributions across all time periods (we will revise and add this figure to the final version). The updated figure demonstrates significant distribution shifts not only among different time periods but also between training and testing data in the same time period. \n\n**W5**\n\nWe appreciate the reviewer's thoughtful comments regarding evaluation metrics for catastrophic forgetting. This is an insightful observation that deserves clarification.\n\nWe acknowledge that our approach does not address catastrophic forgetting in the traditional sense, as we are not concerned with performance on past data but rather focus exclusively on future prediction performance in our application scenarios. The primary objective of our work is accurate spatio-temporal prediction under distribution shifts, where historical pattern retrieval serves an auxiliary role in enhancing prediction robustness. Similarly, previous research focusing on catastrophic forgetting primarily examines whether preserved historical information effectively contributes to future predictions under distribution shifts [1][2]. The ultimate measure of whether a model has \"forgotten\" useful patterns is reflected directly in its prediction accuracy on current data that resembles historical distributions. When our model encounters patterns similar to those seen historically, it maintains strong performance because our model's architecture naturally stores and leverages useful historical data without explicit forgetting prevention mechanisms.\n\nThe standard evaluation metrics (MAE, RMSE, MAPE) in our experiments indirectly but comprehensively capture forgetting effects. When the model encounters a traffic pattern similar to one it has seen before, poor performance would indicate catastrophic forgetting of that pattern.\n\n[1] Chen W, Liang Y. Expand and compress: Exploring tuning principles for continual spatio-temporal graph forecasting. arXiv preprint arXiv:2410.12593, 2024.\n\n[2] Wang B, et al. Stone: A spatio-temporal ood learning framework kills both spatial and temporal shifts. ACM SIGKDD. 2024: 2948-2959.\n\n**W6**\n\nWe appreciate the reviewer's suggestion to update our discussion on replay-based methods and strengthen our comparison with retrieval-based approaches.\n\nWe would like to clarify that experience replay is a general strategy commonly employed as a component within many continual learning models. For instance, both STKEC and TrafficStream incorporate replay mechanisms, but these are presented as standard components rather than their novel contributions. Their primary innovations lie elsewhere—in knowledge extraction techniques and streaming architectures, respectively. Thus, we did not categorize them as replay-based methods.\n\nRegarding retrieval-based methods, we strengthened our comparative analysis by including additional experimental results for RAGraph [1] and PRODIGY [2] on the ENERGY-Stream dataset (STGNN backbone). While RAGraph and PRODIGY perform reasonably well on this dataset, our STRAP method still achieves superior performance across all prediction horizons. These results further validate our approach's effectiveness compared to state-of-the-art retrieval-based methods. (Due to character limitations, we only show the STGNN backbone here. The rest will be shown in the appendix.)\n\n| Method   | Metric    | ENERGY-Stream (3) | ENERGY-Stream (6) | ENERGY-Stream (12) | Average    |\n|----------|-----------|-------------------|-------------------|---------------------|------------|\n| PRODIGY  | MAE       | 5.16±0.06         | 5.15±0.07         | 5.16±0.09           | 5.15±0.07  |\n|          | RMSE      | 5.26±0.07         | 5.30±0.07         | 5.40±0.09           | 5.31±0.07  |\n|          | MAPE(%)   | 46.05±2.04        | 46.48±1.92        | 47.52±1.85          | 46.57±1.88 |\n| RAGraph  | MAE       | 5.16±0.05         | 5.14±0.08         | 5.16±0.11           | 5.14±0.08  |\n|          | RMSE      | 5.27±0.04         | 5.31±0.06         | 5.42±0.09           | 5.32±0.07  |\n|          | MAPE(%)   | 45.20±0.71        | 45.84±0.75        | 47.20±0.85          | 45.95±0.76 |\n| STRAP    | MAE       | 4.83±0.17         | 4.84±0.18         | 4.88±0.17           | 4.85±0.18  |\n|          | RMSE      | 4.95±0.18         | 5.01±0.19         | 5.15±0.17           | 5.03±0.18  |\n|          | MAPE(%)   | 42.18±1.64        | 43.02±1.77        | 44.30±1.55          | 43.11±1.72 |\n\n[1] Jiang X et al. Ragraph: A general retrieval-augmented graph learning framework. NIPS 2024, 37: 29948-29985.\n\n[2] Huang Q et al. Prodigy: Enabling in-context learning over graphs. NIPS 2023, 36: 16302-16317.\n\n**W7**\n\nWe appreciate the reviewer's concern regarding the clarity of our task definition. Our manuscript addresses a specific spatiotemporal prediction problem:\n\nIn Section 3.1 of our manuscript, we provided a comprehensive definition of our task. Specifically, we formulated the problem as predicting future values at multiple locations at time t+h given historical observations from time steps t-n to t, while explicitly addressing the challenge that testing data distributions differ substantially from those encountered during training.\n\nTo further clarify, our work focused on streaming data scenarios, as detailed in Appendix C.3, where data arrived continuously over time in sequential periods. This streaming nature introduced unique challenges, as the model had to adapt to evolving patterns and distribution shifts without complete knowledge of future data characteristics.\n\nOur training approach reflected this streaming paradigm: rather than batch training on the entire dataset, the model updated sequentially as new data became available in each period. Specifically, at each time step, the model trained on the most recent available data while leveraging its pattern library to maintain robustness to distribution shifts between training and testing sets within each period.\n\nThank you for pointing out the typos. We carefully corrected the typos throughout the manuscript to ensure clarity and consistency in our presentation.\n\n**Q6**\n\nWe appreciate the reviewer's suggestion regarding the clarification of prediction horizons in Table 1. We agree that this detail is important for readers who may be unfamiliar with the field.\n\nIn our revised manuscript, we modified Table 1 to properly clarify the prediction horizons by:\n\nAdding a clear column header that reads \"Prediction Horizon\" followed by the specific time units for each dataset (Table 6):\n  - For PEMS-Stream: \"(15 min, 30 min, 60 min)\"\n  - For Air-Stream: \"(3 hours, 6 hours, 12 hours)\"\n  - For Energy-Stream: \"(30 min, 1 hour, 2 hours)\""}, {"review_id": "9o3RG7T1Ut", "reviewer": "Reviewer_kmFw", "summary": "This paper presents STRAP, a novel retrieval-augmented framework for spatio-temporal graph learning designed to address out-of-distribution (OOD) challenges. The authors propose a three-component approach that: (1) decomposes complex spatio-temporal data into specialized subgraphs, (2) constructs multi-dimensional pattern libraries (spatial, temporal, and spatio-temporal), and (3) implements a knowledge fusion mechanism that adaptively integrates retrieved historical patterns with current observations. Extensive experiments across three real-world streaming datasets demonstrate consistent performance improvements over state-of-the-art methods.", "questions": "1.For completeness, could you show the specific hyperparameter values (learning rates, batch sizes, etc.) used for each dataset and backbone? \\\n2.Your approach constructs three separate pattern libraries (spatial, temporal, and spatio-temporal). Have you conducted experiments to evaluate whether a single comprehensive spatio-temporal pattern library could achieve comparable performance? Could you provide empirical evidence justifying the necessity of maintaining these separate libraries?\\\n3.Pattern key generation combines multiple feature extractors. Have you conducted experiments to determine the relative importance of these different components? Understanding which topological features contribute most to effective retrieval could lead to more efficient key designs and potentially reveal fundamental aspects of spatio-temporal similarity.\\\n4.Your work falls within the retrieval-augmented learning paradigm, which has seen growing interest in graph learning. How does STRAP compare to other retrieval-based graph learning methods such as RAGraph or similar approaches? \\\n5.How does STRAP perform in few-shot adaptation scenarios where only a small amount of data from a new distribution is available?", "limitations": "See weaknesses.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths:\n1.  The authors address an important problem in spatio-temporal graph learning with a novel retrieval-augmented approach.\n2. The pattern library construction is well-designed, with clear methodological distinctions between spatial, temporal, and spatio-temporal pattern extraction.\n3. The experimental evaluation is comprehensive.\n\nWeaknesses:\n1. The paper proposes three separate pattern libraries (spatial, temporal, and spatio-temporal) without adequately demonstrating why this complexity is necessary. While intuitive that different pattern types might capture complementary information, there is no empirical evidence showing that a single unified spatio-temporal library would be insufficient. This raises questions about the potential redundancy and computational overhead introduced by maintaining three separate libraries.\n2. Despite positioning itself within the retrieval-augmented learning paradigm, the paper does not compare STRAP against other retrieval-based graph learning methods (i.e. RAGraph as you mentioned in your introduction).", "was_revised": true, "final_justification": "This paper proposes an interesting retrieval-augmented framework for spatio-temporal graph learning aimed at tackling OOD challenges, making a valuable contribution to the field. The authors have addressed my concerns during the rebuttal phase; therefore, I hold a positive view of this work.", "rebuttal": "Thank you for your insightful comments. We address your concerns and answer your questions below.\n\n**W1+Q2**\n\nWe appreciate the reviewer's concern regarding our design choice of maintaining three separate pattern libraries (spatial, temporal, and spatio-temporal) instead of a single unified library. We would like to address this concern by referencing both our theoretical analysis in the appendix and our ablation study results.\n\nAs demonstrated in our appendix, the three types of patterns capture fundamentally different aspects of the data distribution. Spatial patterns capture location-specific correlations that remain relatively stable over time but vary across space. Temporal patterns capture time-dependent evolution that is consistent across spatial locations. Spatio-temporal patterns capture complex interactions where spatial correlations evolve differently over time. Our theoretical analysis (Appendix B.1) proves that these three pattern types span different subspaces of the overall distribution space. These subspaces are orthogonal to each other, meaning they capture non-overlapping aspects of the data. A single unified library would require significantly more patterns to approximate the same distribution space, as it would need to independently learn combinations of these fundamentally different pattern types.\n\nIn addition, our ablation study results also address the concern about potential redundancy. When we remove any single pattern library (spatial, temporal, or spatio-temporal), we observe significant performance degradation across all metrics. This confirms that each library captures unique and necessary information that the others cannot compensate for. Most importantly, we explicitly compared our approach with a unified library variant that uses the same total number of patterns. This unified approach performed substantially worse despite having the same pattern capacity. This demonstrates that the separation into specialized libraries is not just a design choice but a necessary architectural component for effective pattern learning and utilization.\n\n**W2**\n\nWe thank the reviewer for this valuable feedback regarding the comparison with retrieval-based graph learning methods. We addressed this concern by including comprehensive comparisons with RAGraph[1] and PRODIGY[2], two state-of-the-art retrieval-based graph learning methods mentioned in our introduction.\n\nWe extended our experimental evaluation to include RAGraph and PRODIGY across all four backbone architectures (STGNN, ASTGNN, DCRNN, TGCN) on ENERGY-Stream. The updated results demonstrate that while they indeed provide improvements over baseline methods, our STRAP approach consistently outperforms it across all metrics and backbone architectures. (Due to character limitations, we only show the STGNN backbone here. The rest will be shown in the appendix.)\n\n| Method   | Metric    | ENERGY-Stream (3) | ENERGY-Stream (6) | ENERGY-Stream (12) | Average    |\n|----------|-----------|-------------------|-------------------|---------------------|------------|\n| PRODIGY  | MAE       | 5.16±0.06         | 5.15±0.07         | 5.16±0.09           | 5.15±0.07  |\n|          | RMSE      | 5.26±0.07         | 5.30±0.07         | 5.40±0.09           | 5.31±0.07  |\n|          | MAPE(%)   | 46.05±2.04        | 46.48±1.92        | 47.52±1.85          | 46.57±1.88 |\n| RAGraph  | MAE       | 5.16±0.05         | 5.14±0.08         | 5.16±0.11           | 5.14±0.08  |\n|          | RMSE      | 5.27±0.04         | 5.31±0.06         | 5.42±0.09           | 5.32±0.07  |\n|          | MAPE(%)   | 45.20±0.71        | 45.84±0.75        | 47.20±0.85          | 45.95±0.76 |\n| STRAP    | MAE       | 4.83±0.17         | 4.84±0.18         | 4.88±0.17           | 4.85±0.18  |\n|          | RMSE      | 4.95±0.18         | 5.01±0.19         | 5.15±0.17           | 5.03±0.18  |\n|          | MAPE(%)   | 42.18±1.64        | 43.02±1.77        | 44.30±1.55          | 43.11±1.72 |\n\n[1] Jiang X, Qiu R, Xu Y, et al. Ragraph: A general retrieval-augmented graph learning framework[J]. Advances in Neural Information Processing Systems, 2024, 37: 29948-29985.\n\n[2] Huang Q, Ren H, Chen P, et al. Prodigy: Enabling in-context learning over graphs[J]. Advances in Neural Information Processing Systems, 2023, 36: 16302-16317.\n\n**Q1**\n\nIn response to your request for hyperparameter details, we provide the complete configuration used in our experiments. For fair comparison, we maintained consistent hyperparameter settings across all methods whenever possible, only adjusting when necessary to achieve optimal performance for each approach. The learning rates and batch sizes for all methods across the three datasets are summarized in the table below. For all backbone architectures, we used the same hyperparameter values within each dataset to ensure fair comparison: (We will add these experimental settings to the appendix later.)\n\n\n**Q3**\n\nWe sincerely thankful for your thoughtful consideration of the relative importance of the feature extraction components. In our study, we conducted a series of ablation experiments to evaluate the contributions of various features in the spatial and temporal pattern keys to effective retrieval. Below is an overall analysis of the experimental results and a discussion of the key features.\n\nSpecifically, Spatial 1 and 2 refer to features from the aspect of local structure and the shortest path statistics feature from global connectivity, while Spatial 3 represents the Forman-Ricci curvature from geometric properties. In terms of time, Temporal 1, 2, and 3 correspond to Statistical and spectral descriptors, Multi-resolution analysis, and Temporal dependencies and complexity, respectively. \n\n| w/o Features | MAPE(%) |\n|--------------|---------|\n| Spatial 1    | 47.00±4.93 |\n| Spatial 2    | 48.92±3.89 |\n| Spatial 3    | 49.97±0.87 |\n| Temporal 1   | 50.61±2.87 |\n| Temporal 2   | 44.98±2.32 |\n| Temporal 3   | 49.76±0.98 |\n| Ours         | 43.65±3.73 |\n\nThe experimental results with the TGCN backbone demonstrate that Spatial pattern 1 and Spatial pattern 2 each contribute to the  effect of local structure and global connectivity features, significantly enhancing the model's understanding of dynamic graph changes, while the multi-resolution analysis feature (Temporal pattern 2) performs best with a MAPE of 44.98±2.32%, its sensitivity to short-term trends effectively capturing signal transients and complexity, thus better adapting to dynamic spatio-temporal environments.\n\nInspired by your comments, we also plan to integrate more spatial and temporal features in future work to explore their interactions and gain a more comprehensive understanding of the complexities in spatio-temporal data.\n\n**Q4**\n\nThank you for highlighting the connection between our work and the broader retrieval-augmented learning paradigm. STRAP builds upon this emerging direction while introducing several key innovations specifically designed for spatio-temporal graph data under distribution shifts.\n\nSTRAP's superior performance stems from several important distinctions:\n\n1. While previous methods typically maintain a single pattern repository, STRAP's separate spatial, temporal, and spatio-temporal libraries enable more precise matching along different dimensions of variation. This is crucial for streaming data where distribution shifts can occur independently in different dimensions.\n2. STRAP employs domain-specific topological and temporal feature extractors designed to capture the unique characteristics of spatio-temporal graphs. In contrast, general retrieval-based methods often rely on generic graph embeddings that may not adequately capture complex spatial-temporal dependencies.\n3. Our framework incorporates a learnable fusion weight that dynamically balances the contribution of retrieved patterns and current observations. This adaptability is particularly valuable in streaming settings where the relevance of historical patterns can vary substantially.\n4. As shown in our theoretical analysis (Theorem B.1), our decomposed approach provides higher mutual information with the underlying data distribution compared to unified representation approaches used in previous methods.\n\nIn addition, we supplemented the RAGraph experiment, as detailed in W2.\n\n**Q5**\n\nWe appreciate this important question about STRAP's performance in few-shot adaptation scenarios. To address this, we conducted additional experiments using the ENERGY dataset as a representative benchmark, as it exhibits complex spatio-temporal dependencies and significant distribution shifts.\n\nWe tested STRAP against several strong baselines under data-limited conditions, specifically when only 70% (30% missing) and 50% (50% missing) of the target distribution data is available for adaptation. The results, summarized in the table below, demonstrate STRAP's superior robustness in few-shot scenarios: (Due to character limitations, only the 30% missing scenario is presented here, with the 50% missing scenario supplemented later in the appendix.)\n\n| Method | Metric | Energy-Stream 3 | Energy-Stream 6 | Energy-Stream 12 | Energy-Stream Avg. |\n|--------|--------|----------------|----------------|-----------------|-------------------|\n| Graphpro | MAE | 6.07 | 5.96 | 6.00 | 5.97 |\n|  | RMSE | 6.28 | 6.20 | 6.34 | 6.23 |\n|  | MAPE(%) | 74.31 | 74.73 | 76.14 | 74.86 |\n| ST-Adapter | MAE | 6.19 | 6.16 | 6.22 | 6.16 |\n|  | RMSE | 6.48 | 6.47 | 6.61 | 6.48 |\n|  | MAPE(%) | 76.15 | 76.64 | 77.96 | 76.74 |\n| Replay | MAE | 6.23 | 6.17 | 6.21 | 6.18 |\n|  | RMSE | 6.41 | 6.40 | 6.53 | 6.41 |\n|  | MAPE(%) | 75.08 | 75.47 | 76.77 | 75.60 |\n| EWC | MAE | 6.35 | 6.28 | 6.27 | 6.27 |\n|  | RMSE | 6.55 | 6.52 | 6.61 | 6.53 |\n|  | MAPE(%) | 70.70 | 71.28 | 72.51 | 71.32 |\n| STRAP | MAE | 5.74 | 5.64 | 5.66 | 5.77 |\n|  | RMSE | 6.10 | 6.01 | 6.11 | 6.14 |\n|  | MAPE(%) | 66.53 | 67.02 | 68.36 | 67.42 |"}, {"review_id": "jdXws3p7m2", "reviewer": "Reviewer_Pbep", "summary": "This paper introduces a novel framework STRAP to improve the generalization of STGNNs under STOOD scenarios, where both spatial structures and temporal dynamics deviate from training distributions. At the heart of STRAP lies a multi-dimensional key-value pattern library that stores representative spatial, temporal, and spatio-temporal patterns, thereby capturing rich historical, structural, and semantic information. During training, STRAP decomposes spatio-temporal graphs into specialized subgraphs using domain-specific chunking strategies, enabling the extraction of discriminative keys and informative values. At inference time, relevant patterns are retrieved through similarity matching, and an adaptive fusion mechanism integrates them with current observations to effectively balance historical knowledge and new inputs. Extensive experiments on multiple real-world datasets demonstrate that STRAP consistently outperforms over ten state-of-the-art baselines across various STGNN backbones.", "questions": "Please address the questions in the Weaknesses.", "limitations": "Yes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 4, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n- STRAP tackles the important and longstanding challenge of STOOD generalization in STGNNs by introducing a novel retrieval-augmented learning paradigm that explicitly incorporates historical patterns to enhance adaptability.\n- The design of a three-dimensional key-value pattern library allows STRAP to systematically capture diverse and representative patterns.\n- The use of domain-specific graph decomposition enhances pattern discriminability by breaking down complex spatio-temporal structures into specialized subgraphs.\n- Comprehensive experiments on three real-world datasets using four different STGNN backbones show consistent and substantial gains over 10+ competitive baselines.\n\n**Weaknesses:**\n- The motivation for defining the spatio-temporal library as the product of separate spatial and temporal libraries rather than directly using them independently is unclear. A deeper justification or ablation analysis would be helpful.\n- While the framework is claimed to be effective in streaming scenarios, the paper lacks a time complexity or efficiency analysis, which is essential for evaluating real-time applicability.\n- The method's sensitivity to hyperparameters is not discussed, which limits understanding of its robustness and practical deployment considerations.", "was_revised": true, "final_justification": "As I mentioned in the strength part, STRAP tackles the important and longstanding challenge of STOOD generalization in STGNNs by introducing a novel retrieval-augmented learning paradigm that explicitly incorporates historical patterns to enhance adaptability. The design of a three-dimensional key-value pattern library and the use of domain-specific graph decomposition are novel and technically sound. Through the authors' rebuttal, my concerns about the approach's time complexity and sensitivity to hyperparameters have been well addressed. Therefore, I maintain my recommendation.", "rebuttal": "Thank you for your insightful comments. We address your concerns and answer your questions below.\n\n**W1**\n\nWe appreciate the reviewer's comment regarding our spatio-temporal library construction approach. We would like to clarify that our motivation for defining the spatio-temporal library as a product of separate spatial and temporal libraries is both theoretically sound and empirically validated in our work.\n\nFrom a theoretical perspective, as we discussed in Section 4.2.1, the tensor product (cross-product) operation allows us to capture the complex interactions between spatial and temporal patterns simultaneously rather than treating them as independent factors. This approach enables our model to learn comprehensive representations where temporal dynamics can vary across different spatial regions and spatial relationships can evolve over time - a critical characteristic of traffic forecasting problems.\n\nFurthermore, we conducted extensive ablation studies (Figure 2) that explicitly compare our cross-product approach against alternatives. These ablation studies provide strong empirical evidence supporting our design choice, showing that the multiplicative interaction between spatial and temporal components creates a more expressive representation space that better captures the complex interdependencies in traffic data. This approach also offers computational efficiency advantages, as it allows us to maintain a compact representation of both dimensions while still modeling their joint distribution effectively.\n\n**W2**\n\nWe thank the reviewer for this important observation regarding efficiency analysis. We acknowledge that our framework, being a retrieval-augmented approach, is computationally more intensive than lightweight streaming models: (ENERGY-Stream dataset on ASTGNN)\n\n| Method | Period 0 | Period 1 | Period 2 | Period 3 |\n|--------|----------|----------|----------|----------|\n| EAC | 1.02 | 1.03 | 1.04 | 1.06 |\n| EWC | 1.00 | 1.54 | 1.58 | 1.60 |\n| GraphPro | 1.00 | 1.00 | 1.04 | 1.05 |\n| PECPM | 3.79 | 4.03 | 4.28 | 4.64 |\n| STRAP | 2.27 | 1.83 | 1.88 | 2.10 |\n| STKEC | 1.01 | 1.21 | 1.24 | 1.22 |\n| ST-LoRA | 1.07 | 1.16 | 1.16 | 1.16 |\n| TrafficStream | 1.01 | 1.60 | 1.66 | 1.64 |\n| RAGraph | 1.27 | 1.21 | 1.20 | 1.20 |\n\nOur method embraces the inherent trade-off of retrieval-augmented generation (RAG) systems: higher computational cost for significantly improved prediction accuracy. Similar to how RAG approaches have transformed NLP by sacrificing some computational efficiency for dramatically better performance, our work demonstrates that traffic prediction can benefit from the same paradigm.\n\nWe believe this represents a worthy trade-off, particularly for critical applications where prediction accuracy significantly impacts downstream decision-making. Many traffic management systems prioritize prediction quality over minimal latency, especially for longer-term forecasting horizons.\n\nTo time complexity, STRAP's time complexity can be analyzed across its main components: (1) Spatio-Temporal Subgraph Chunking with complexity $O(|V|\\cdot|E|\\cdot\\tau_S)$ for spatial subgraphs, $O(|V|\\cdot k \\cdot T)$ for temporal subgraphs, and $O(|V|^3)$ for spectral clustering; (2) Pattern Library Construction with $O(|V|^2)$ for spatial keys, $O(T\\log T)$ for temporal keys, and $O(B_{STGNN})$ for pattern value generation; (3) Pattern Retrieval and Fusion requiring $O(|B|\\cdot d)$ for similarity computation and $O(|B|\\log k)$ for top-k retrieval. The overall time complexity is $\\mathbf{O(|V|^3 + |B|\\log k + B_{backbone})}$, where $|V|$ is the number of nodes, $|E|$ is the number of edges, $\\tau_S$ is the time window length, $T$ is the time sequence length, $|B|$ is the pattern library size, $d$ is the feature dimension, $k$ is the number of retrieved patterns, and $B_{backbone}$ is the backbone complexity.\n\n**W3**\n\nWe appreciate the reviewer's valid concern regarding hyperparameter sensitivity analysis, which is indeed crucial for understanding model robustness and deployment considerations.\n\nWe would like to clarify that we conducted extensive hyperparameter sensitivity studies, which are presented in Appendix C.4. Due to space constraints in the main paper, we had to place these detailed analyses in the supplementary materials. This appendix includes comprehensive experiments examining the model's sensitivity to key hyperparameters, including fusion ratio, dropout ratio and retrieval count. Our findings demonstrate that while certain hyperparameters (particularly library size and retrieval depth) do impact performance, the model maintains robust performance across reasonable parameter ranges. \n\nWe acknowledge that placing this important analysis in the appendix may make it less accessible during review. In the revised version, we will restructure the paper to incorporate the most critical aspects of this hyperparameter analysis into the main text, particularly highlighting the stability regions for key parameters that are most relevant for practical deployment scenarios."}, {"review_id": "VVx2O5MWZH", "reviewer": "Reviewer_MEgx", "summary": "This paper introduces STRAP, a novel retrieval-augmented framework designed to address generalization challenges for spatio-temporal graph neural networks (STGNNs) in spatio-temporal out-of-distribution (STOOD) scenarios. The authors propose a comprehensive approach centered on constructing a multi-dimensional pattern vector library containing spatial, temporal, and spatio-temporal information. During inference, STRAP retrieves similar patterns from the library based on current inputs and injects them into the model through a plug-and-play mechanism to enhance representation capabilities and mitigate catastrophic forgetting. Experimental results on multiple real-world dynamic graph datasets demonstrate that STRAP significantly outperforms current state-of-the-art baseline models on STOOD tasks.", "questions": "In Section 4.2.1, the notation $\\mathbf{D}(\\mathcal{G_S}) = [\\mu_d, \\sigma_d, \\max(d), \\min(d)]$ introduces $\\mu_d$ and $\\sigma_d$ without proper definition.", "limitations": "Yes. The authors have discussed the limitations and  potential negative societal impact of their work.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n\nS1. The retrieval-augmented learning framework proposed represents a meaningful innovation specifically targeting STGNN generalization under STOOD scenarios - a problem of genuine practical importance. The integration of retrieval mechanisms with continual learning brings fresh insights to this domain.\nS2. The architectural design exhibits strong logical coherence, particularly in the decomposition strategy that separates complex spatio-temporal data into specialized spatial, temporal, and hybrid spatio-temporal subgraphs with corresponding pattern libraries. This decomposition appears both systematic and theoretically motivated.\nS3. Nice and easy-understanding method figure.\n\n** Weaknesses:**\n\nW1. The pattern key generation mechanism relies heavily on manually crafted feature combinations including degree distributions, curvature measures, and spectral descriptors. This hand-engineered approach, while empirically effective, raises concerns about generalizability to diverse spatio-temporal data types and sensitivity to feature selection decisions. The methodology would benefit from either learnable key generation approaches or principled guidelines for feature selection.\n\nW2. Although computational overhead is acknowledged as a limitation in the conclusions, the main text provides insufficient analysis of this critical issue. The continuous growth of pattern libraries as historical data accumulates presents a potential scalability bottleneck. While importance-based sampling strategies are mentioned for library management, their effectiveness and performance implications remain experimentally unvalidated.", "was_revised": true, "final_justification": "I would like to recommend acceptance for this paper. The authors' rebuttal has effectively clarified the generality of the designed features in spatio-temporal sequence problems, and explored which features play a key role in the results under this mechanism through expanded studies. The authors also provided the time complexity analysis demonstrating practical trade-offs, thereby strengthening the framework's feasibility for deployment in streaming application.", "rebuttal": "Thank you for your insightful comments. We address your concerns and answer your questions below.\n\n**W1**\n\nWe greatly value the reviewer’s insightful concerns regarding the generalizability across various spatio-temporal data types and sensitivity in feature selection.\n\nWe acknowledge that the performance results of our methodology indeed depend on feature selection. However, existing research demonstrates that different types of spatio-temporal data exhibit common statistical properties and structural patterns in specific dimensions, such as periodicity and local spatial autocorrelation as universal characteristics (Chen et al., NeurIPS 2024; Trirat et al., 2024). These shared structural properties enable spatio-temporal pattern keys adapted to one task to capture cross-domain statistical invariances and structural regularities, thus naturally containing understanding capabilities for other similar spatio-temporal sequence tasks and possessing generalization potential for different spatio-temporal data types.\n\nTo better assist future research in feature selection and explore the impact of different features on experimental results, we conducted ablation experiments on features in both spatial and temporal dimensions. Spatial 1, 2 refers to the combination of features from the aspect of local structure and the shortest path statistics feature from global connectivity, while Spatial 3 represents the Forman-Ricci curvature from geometric properties. In terms of time, Temporal 1, 2, and 3 correspond to Statistical and spectral descriptors, Multi-resolution analysis, and Temporal dependencies and complexity, respectively: \n\n| w/o Features | MAPE(%) |\n|--------------|---------|\n| Spatial 1    | 47.00±4.93 |\n| Spatial 2    | 48.92±3.89 |\n| Spatial 3    | 49.97±0.87 |\n| Temporal 1   | 50.61±2.87 |\n| Temporal 2   | 44.98±2.32 |\n| Temporal 3   | 49.76±0.98 |\n| Ours         | 43.65±3.73 |\n\nThrough in-depth analysis of the results, we believe that in feature selection: \n1. We should prioritize complementary feature combinations with cross-domain transferability. The Spatial 1,2 demonstrate detailed understanding of community structures through local features (such as node degree and clustering coefficients), while global features (such as shortest path statistics) help reveal the overall graph structure. This local-global complementarity shows strong generalization across different spatio-temporal data types. \n2. Feature selection needs to consider signal variation trends and complexity, prioritizing features that can reflect transient changes, periodicity, and temporal dependencies, as these features better capture the essential statistical properties of spatio-temporal data.\nIn future work, we plan to explore more suitable adaptive feature selection methods, incorporating meta-learning frameworks to reduce dependence on manual feature construction.\n\n[1] Chen W, Hao X, Wu Y, et al. Terra: A multimodal spatio-temporal dataset spanning the earth[J]. Advances in Neural Information Processing Systems, 2024, 37: 66329-66356.\n\n[2] Yi Z, Zhou Z, Huang Q, et al. Get rid of isolation: A continuous multi-task spatio-temporal learning framework[J]. Advances in Neural Information Processing Systems, 2024, 37: 136701-136726.\n\n**W2**\n\nWe thank the reviewer for raising this important question about computational efficiency, which is indeed a critical consideration for streaming applications.\n\nAs reported in our experimental logs, STRAP does incur moderate computational costs compared to some lightweight methods, which is an inherent characteristic of retrieval-augmented approaches:\n\n| Method | Period 0 | Period 1 | Period 2 | Period 3 |\n|--------|----------|----------|----------|----------|\n| EAC | 1.02 | 1.03 | 1.04 | 1.06 |\n| EWC | 1.00 | 1.54 | 1.58 | 1.60 |\n| GraphPro | 1.00 | 1.00 | 1.04 | 1.05 |\n| PECPM | 3.79 | 4.03 | 4.28 | 4.64 |\n| STRAP | 2.27 | 1.83 | 1.88 | 2.10 |\n| STKEC | 1.01 | 1.21 | 1.24 | 1.22 |\n| ST-LoRA | 1.07 | 1.16 | 1.16 | 1.16 |\n| TrafficStream | 1.01 | 1.60 | 1.66 | 1.64 |\n| RAGraph | 1.27 | 1.21 | 1.20 | 1.20 |\n\nThis computational overhead stems from three main factors: (1) maintaining the pattern library, (2) performing similarity-based retrieval operations, and (3) integrating retrieved patterns with current observations. However, we find this trade-off justified as it prioritizes prediction accuracy and robustness to distribution shifts over computational efficiency - similar to how retrieval-augmented approaches have transformed other domains by accepting reasonable computational costs for substantially improved performance.\n\n**Q1**\n\nWe sincerely thank the reviewer for pointing out this oversight in our notation. We apologize for the lack of clear definitions for $\\mu_{d}$ and $\\sigma_{d}$ in the expression which introduces $\\mu_{d}$ and $\\sigma_{d}$ in Section 4.2.1.\n\nTo clarify, $\\mu_{d}$ represents the mean node degree in the graph $G_S$, while $\\sigma_{d}$  denotes the standard deviation of node degrees. Together with $\\max(d)$ and $\\min(d)$, these four statistical measures provide a comprehensive description of the degree distribution in the spatial graph, capturing both central tendency and variability characteristics.\n\nWe will ensure these definitions are explicitly included in the revised manuscript to improve clarity.\n\nTo clarify, $\\mu_{d}$ represents the mean value of the degree distribution across all nodes in the graph $G_S$, and $\\sigma_{d}$ represents the standard deviation of the degree distribution. \n\nThese statistical measures, along with the maximum and minimum degree values, provide a comprehensive characterization of the graph's connectivity patterns, which is essential for accurate pattern matching in our retrieval mechanism.\n\nWe commit to adding these explicit definitions in the revised manuscript to ensure clarity. Additionally, we will conduct a thorough review of all notation throughout the paper to ensure all symbols are properly defined before use. Thank you again for helping us improve the precision and readability of our work."}]

Author rebuttal:

Meta-review: This paper aims to address the challenge of out-of-distribution generalization of Spatio-Temporal Graph Neural Networks (STGNNs), where the distribution of test data diverges significantly from that of the training set. Extensive experiments across three real-world streaming datasets demonstrate consistent performance improvements over state-of-the-art methods.

Reviewers agreed that this paper address an important and longstanding challenge in spatio-temporal graph learning by presenting a novel retrieval-augmented approach. The core idea of this paper is well motivated and clearly explained, and the architectural design exhibits strong logical coherence. Experimental evaluation is comprehensive and convincing. 

Meanwhile, reviewers raised some concerns regarding technical details, design choices, baselines, efficiency, generalizability, etc. The authors have provided detailed responses that have addressed most of the concerns from reviewers. The authors are strongly encouraged to incorporate the new results and discussions to the final version.
Decision: Accept (poster)