Learning with Calibration: Exploring Test-Time Computing of Spatio-Temporal Forecasting
Authors: Wei Chen
Yuxuan Liang
Venue: NeurIPS 2025 spotlight ()
Keywords: Spatio-Temporal Forecasting
Open-World Learning
Primary area: machine_learning_for_sciences
TL;DR: We propose a novel test-time computing paradigm of spatio-temporal forecasting.

Abstract: Spatio-temporal forecasting is crucial in many domains, such as transportation, meteorology, and energy. However, real-world scenarios frequently present challenges such as signal anomalies, noise, and distributional shifts. Existing solutions primarily enhance robustness by modifying network architectures or training procedures. Nevertheless, these approaches are computationally intensive and resource-demanding, especially for large-scale applications. In this paper, we explore a _novel **t**est-**t**ime **c**omputing paradigm, namely learning with calibration, **ST-TTC**_, for **s**patio-**t**emporal forecasting. Through learning with calibration, we aim to capture periodic structural biases arising from non-stationarity during the testing phase and perform real-time bias correction on predictions to improve accuracy. Specifically, we first introduce a spectral-domain calibrator with phase-amplitude modulation to mitigate periodic shift and then propose a flash updating mechanism with a streaming memory queue for efficient test-time computation. _**ST-TTC**_ effectively bypasses complex training-stage techniques, offering an efficient and generalizable paradigm. Extensive experiments on real-world datasets demonstrate the effectiveness, universality, flexibility and efficiency of our proposed method.

Learning with Calibration: Exploring Test- Time Computing of
Forecasting
Wei Chen, Yuxuan Liang'
INTR & DSA Thrust, The Hong Kong University of Science and Technology (Guangzhou)
onedeanxxxx@maill com, yuxliang@out com
Abstract
forecasting is crucial in many domains, such as transportation, meteorology, and energy. However, real-world scenarios frequently present chal- lenges such as signal anomalies, noise, and distributional shifts. Existing solutions primarily enhance robustness by modifying network architectures or training proce- dures. Nevertheless, these approaches are computationally intensive and resource- demanding, especially for large-scale applications. In this paper, we explore novel test-fime computing paradigm, namely learning with calibration, ST-TTC, for spatio-temporal forecasting. Through learning with calibration, we aim to capture periodic structural biases arising from non-stationarity during the testing phase and perform real-time bias correction on predictions to improve accuracy. Specifically, we first introduce spectral -omainn calibrator with stase-amplitdee modulation to mitigate periodic shift and then propose a flash updating mechanism with a streaming memory queue for efficient test-time computation. ST-TTC effectively bypasses complex training-stage techniques, offering an efficient and generalizable paradigm. Extensive experiments on real-world datasets demonstrate the effec- tiveness, universality, flexibility and efficiency of our proposed method. Our code repository is available at https: pestps://githie /ttpt/gttttt/////////e//eeeehhtt cww/ Onwddenn/ST---. SST-TTC.
1 Introduction
Spatio-temporal forecasting (STF) aims to predict the future state of dynamic systems from histori- cal spatio-temporal observations and underpins many real- real-world applications, such as traffic flow forecasting [24], air quality forecasting [51], and energy consumption forecasting [76]. Although pratio-temporal neural networks [32, 33, 61]. which couple spatial neural operators with temporal neural operators. have achieved remarkable progress on these tasks. their deployment in practical environments remains fraught with challenges. These observations, typically collected by sensors, are frequently corrupted by noise, outliers (e.g.. spikes or dropouts due to hardware failure) [85], and more commonly, non-station distribution shifts arising from sensor aging and seasonal patterns [74].
To enhance generalization and performance, prior work has focused primarily on out-of-distribution (OOD) learning for ST data during the training phase: designing architectures that resist pertur- bations [31, 49, 68, 84], augmenting training data with noise or adversarial examples [3, 46, 97], and introducing specialized loss functions or regularizers [43, 98] counteract distribution drift. However, these methods share fundamental limitations: they assume that the training data sufficiently captures all future target domain invariance, a premise that is rarely valid in real-world settings. Concurrently, an emerging paradigm of continual fine-tuning [10, 11, 35, 38, 69, 70, 71] has become popular in spatio-temporal learning by continuously tuning the model adapt to dynamic changes. Though promising, it still divides the target domain into multiple periods of training and testing and relies on period-specifit training data to optimize model, thereby failing in data-scarse scenarios.
Y. Liang is the corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Table Formal comparison of different spatio-temporal learning paradigms for generalization from the perspective of data and learning. denotes the source domain, denotes the target domain, and y denote the samples and labels sampled from X and Y. respectively. OOD learning expects inputs sampled from any environment e" E to be valid, while others are only optimized for the current training or test environment e. In particular, continual fine-tuning divides the target domain into multiple stages and optimizes for specific stage t environment e², X means not involved.
Data Perspective
Learning Perspective
Setting
Example Works
Source
Target
Tran Time
Time
Leaming
STONE [68], CaST [84]
(X.
Pix ((f(()).)) C'
Continual Fino-Turing
EAC EACT1O [lo]. TrafficStraam (11)
(X), V1)
min Reass-nox (A-for (r).
Test Time Training
TTTST [9]
X-
X
uam Aasat-Ppiii [Lf6(())..)
min R Pi (1.
Online Continall Learning
[77]
X
Rexat-ro jol (U
Tes--Time Compuinn
ST-TIC (Our)
X
min Eeews-noo of (Mae(
x
fa(3)
y
g
(F 0)
Loss($*,x')
x²
g f (xx (8))
-
Loss (f5,y))
(a) Test-Time Training
(b) Online Continual Learning
fo
ga
Red represents the parameters that need to be optimized during the test.
x=
g f(x10)
- Peat 0
Pem
Loss
(c) Test-Time Computing
Figure I: Conceptual visualization comparison of different spatio-temporal learning paradigms under test environment. (a) Test- Training requires the of additional pretext tasks in the training and test phases to optimize the self-supervision head or the overall model parameters fe. (b) Online Continual Learning, by optimizing some internal parameters fo(s) of the model, requires additional modifications to the internal architecture of the network. Our (c) Test-Time Computing method only requires lightweight calibrator go. which is seamless and lightweight plug-and and-play module.
Recently, leveraging test-time information has attracted widespread attention for its ability to signifi- cantly improve language model performance on complex reasoning tasks [1. 64]. In computer vision, this concept has already been extensively developed: test-time training (TTT) was first introduced by [66], which defines an auxiliary self-supervised task applied both training and test samples to better balance bias and variance [20]. A similar idea was adapted to apatio-temport forecasting in TTT-ST [9]. Unlike language and vision
where obtaining ground -tuth labels for test samples at inference time is nearly impossible STF benefits from label autocorrelation [14]: each observation strongly depends on its predecessor, and training instances are constructed from sliding windows, which provide access to historical samples and their true labels. Moreover, this property makes STF also require timeliness [60], that is, the additional computing time during inference must be less than the window-stride interval. A recent STF method, DOST [72], explores online continual learning, which initially explored this direction. It uses historical test sample labels to dynamically adapt the modified model architecture. Though promising. these approaches typically involve complex self-supervised tasks or structural adaptations and still fall short of the timeliness demands of STF.
To address this gap, we propose Test-Time Computing of Spatio-Temporal Forecasting (ST-TTC), an attractive complementary paradigm. ST-TTC achieves learning with calibration by iteratively leveraging available test information during inference, enabling seamless integration with diverse models. This adapts the model to evolving spatio-temporal patterns, thereby calibrating predictions. Our principal insight is that performance degradation during test time is primarily driven by non- stationary distributional shifts stemming from progressive periodic biases. Therefore, we propose a spectral domain calibrator. This involves appending lightweight module, operating in the frequency

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domain, subsequent to the backbone network. This module calibrates biases by learning minor, node- specific amplitude and phase correction factors. Furthermore, flash gradient updating mechanism with streaming memory queue, ensures universal, rapid, and resource-efficient test-time computing. Table provides formal comparison of our method against existing learning paradigms, and Figure offers conceptual visualization of learning with test domain. In summary, our contributions are:
We propose a novel test-time computing paradigm of spatio-temporal forecasting, termed ST TTC.
We systematically explore the goals and means achieving this paradigm. Concretely, we introduce spectral domain calibrator with -mppliude modulation to mitigate periodic shift and present flash updating mechanism with a streaming memory queue for efficient test-time computation.
Experimental results on real-world learning paradigms demonstrate the effectiveness and universality of ST-TTC.
datasets in different fields, scenarios, and
2 Related Work
Spatio-Temporey Forecasting. Spatio-temporal sequences can be regarded as spatially extended
multivariate time series. Although one can trivially apply multivariate forecasting methods [5, 7, 52, 96] independently at each location, such decoupling of spatial and temporal dependencies invariably yields suboptimal results [61]. Classical spatio-temporal forecasting method instead relies shallow models or apatio-temporal kernels, including feature- based methods [53, 102], state space models [2, 13, 56], and Gaussian process models [18, 58]. Unfortunately, the overall nonlinearity of these models is limited, and the high complexity of computation and storage further hinders the availability of massive training instances [63]. In recent years, spatio-temporal neural networks [32, 33, 36] have been widely adopted to learn the complex dynamics of such systems. Early work concentrated on devising neural operators to extract spatial or temporal correlation [17, 47, 62, 83, 90] and on designing fusion architectures to integrate them [12, 16, 23, 40, 54]. More recent efforts have explored representation learning [49, 103, 104] and continual model adaptation [10, 11, 89] to better accommodate unseen environmental shifts. However, these methods still depend exclusively on offline training data and thus cannot deliver truly timely and effective adaptation in real settings.
Test-Time Computing. Test-time computation is inspired by the human cognition [34], in which additional computational effort is allocated during inference to improve task performance. This insight has recently driven considerable interest in the nature language process community, fueled by the success of aessoing-auugmenee and adapt internal computations at test time via supervised fine-tuning or reinforcement learning (RL) [99]. While the generalization properties of RL-based adaptation remain debated [95], the notion of supervised learning on unlabeled test data dates back to "transductive learning" [19] in the 1990s and has demonstrated empirical benefits [6, 67]. In the computer vision domain, this idea was formalized as Test-Time Training [66], which attaches an auxiliary self-supervised head to enable online adaptation to each test instance a paradigm subsequently generalized as test-time forecasting has seen limited exploration of such techniques. TTT-ST [9] applies TTT-style auxiliary objectives during training and continues to update at inference, and DOST [72] further incorporates dynamic learning mechanisms within modified model architectures for test-time updates. In addition, some methods [22, 100] are conceptually close to ours, such as CompFormer [100], which proposes test-time compensated representation learning framework, but still requires access to additional training data. Notably, we formalize the test-time computing of spatio-temporde forecasting, and propose a unified that is general, lightweight, efficient, and effective for STF at test-time.
language models (e.g., ol [29] and r1 [21]) that activate
adaptation [30, 44, 73, 77]. However,
frraaer framework
For more related work, we provide a more detailed introduction in Appendix A.
3 Preliminaries
Problem Definition. Let E TxC denote the multivariate time series recorded at each location sensor, capturing the dynamic observations of C' measured features in T consecutive time steps. Stacking these sequences for all N locations yields the spatio-temporal tensor X E N Given historical observations X RNxT*xx (and an optional spatial correlation graph G representing the spatial relationships of N locations), spatio-temporal forecasting aims to learn a mapping fo
3

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(X*,9) + X E RRNTTTi where X² is the signal for the next T time steps. In practice, according to [40, 61], the feature to be predicted usually only the target variable.
Scenario Definition. In deep learning systems, batch-based testing is typically employed to exploit parallelism. In real-world deployment, however, predictions must be produced for each incoming time-step sample-i.e, with batch size / set to 1. At time index t, once the new sliding- winddww input X2 RN XXNTxxC arrives, the true labels for all test samples before time index f T -T' + become available. Thus, test-time computing of spatio-temporal temporal forecasting can leverage this accumulated historical information to enhance the accuracy of the current prediction, while ensuring that any additional computation latency remains below a threshold defined by the sliding-window stride.
Methodology
Our test-time computing framework of spatio-temporal forecasting (ST-TTC) integrates two syner- gistic components: 1) a spectral domain calibrator with phase-amplitude modulation; and 2) flash gradient update mechanism with streaming memory queue. In this section, we introduce these two key components, respectively, from the perspective of what is computed and how it is computed.
4.1 What to Compute? Spectral Domain Calibrator with Phase-Amplitude Modulation
Motivation. Spatio-temporal data, such as traflic flow and air quality, often exhibit periodic patterns (e.g., daily or weekly cycles). However, in real-world deployments, these patterns are not stationary; they are dynamically influenced by various internal and external factors [75]. Such influences lead to non-stationariites manifesting as fluctuations in amplitude (e.g., increased or decreased traffic peaks due to seasonal changes) or phase shifts (e.g., peak hours are advanced or delayed due to traffic congestion). Pre-training models typically fit fixed periodic patterns during training, which makes them vulnerable to performance degradation under such persistent dynamic changes during inference [74]. Therefore, we argue that the goal of test-time computation is: how to design an effective calibrator that can efficiently capture such gradual systematic bias from the pattern to correct the prediction errors caused by non-stationarity, while avoiding overfitting random noise? ?
Key Challenges. While correction in the time domain is possible [22, 100], it often requires extensive parameterization, leading to increased model complexity and limited ability to capture evolving periodic structures. Moreover, the coupled structural and branching modules [9, 72] are prone to evolution. To address this, we propose calibration
overfitting the random noise in the in the spectral domain, where periodic variations are more transparently expressed as changes in the amplitude and phase of specific frequency components. Spectral correction offers a potentially more direct and robust solution. However, this introduces two main challenges: I the degree of non-stationarity varies across spatial nodes; and @ full-spectrum parameterization is computationally expensive. The core problem thus becomes how to design a lightweight, spatial-ave -aware calibrator.
Implementation Details. To this end, we formally introduce the spectral domain calibrator (SD- Calibrator), which a lightweight glug-and-plas module that performs spectral domain calibration on the time domain prediction results of the pre-trained model, aiming to achieve efficient test-time computation for ppatio-temporal forecasting. Specifically, can be divided into three steps:
Spatial-aware Decompoxition. To ensure spatial awareness, we apply a real-to-complex fast Fourier transform (rFFT) along the time dimension of the backbone model's prediction ý E BxNTT separately for each spatial node. This yields the frequency spectrum: Y, = rFFT(ū) E CBBNxM" where M- = T
7 + 1 is the number of unique frequency bins for real-valued signals. Then, we decompose Yj into its amplitude A lYgl E RBBNXM and phase P ZY, E BB
Group-wise Modulation. To ensure lightweight and balanced spectrum expression, we divide the M frequency bins into G contiguous groups of size [M/G]], and learn per-group, per-node amplitude and phase offsets X" Cx X E Gx (Note: Both X and X are initialized to 0 to avoid incorrect calibration of predictions before learning). For each group E {1,..., G}, we apply
A = Ag @ (1 + X3), = Pg + Ag. and reconstruct the spectrum as YJ = U A' o P.)...
Inverse Transform. Finally, the calibrated time-domain signal obtained by Inverser rFFT yea! = irFFT(Y,) BBxNxI along the frequency dimension.

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For clarity, we provide a Algorithm workflow 1 and Pytorch-Style Pseudocode 2 in Appendix C.I.
Complexity Analysis. The full-spectrum parameterization learns independent amplitude and phase offsets for each of the M = T/2 + 1 frequency bins and N nodes, totaling 2N M parameters. In contrast, our G-group design learns only 2NG parameters. Since G is constant and M grows linearly with T', G < . is usually the case. For large-scale long-term scenario, this significantly reduces memory footprint and gradient update cost while retaining interpretable per-band calibration.
Theoretical Analysis. We also provide a theoretical approximate bound on the output perturbation induced by the SD- Salaaiibr,,,r, ensuring controlled deviation from the original prediction to prevent overfitting (Please refer to Theorem and the proof in Appendix B).
4.2 How to Compute? Flash Gradient Update with Streaming Memory Queue
Motivation. The SD Da-ibbibrrtoor provides an effective mechanism for output correction. To accommo- date the dynamic nature of spatio-temporal data, its parameters (A", X²) must be continuously updated during inference. Fortunately, as we discussed above, due to the streaming nature of spatio-temporal data, unlike Visual and textual tasks, we have access to the true labels of historical samples. However, simply accumulating all historical data for updates is not feasible due to the increasing computational load and memory usage. Therefore, we argue that the key to test-time computation is: How to design an efficient data selection and learning mechanism that leverages appropriate historical information to tuning the SD- DD-Caaibrrttr without incurring a lot of computational overhead?
Key Challenges. Although retrieving similar sequences from historical training databases can partially compensate for prediction errors [100], this assumption unrealistic, as only test-time information is available in our scenario. Moreover, selectively storing historical test samples via memory bank primarily serves to mitigate catastrophic forgetting in the backbone model [72]. which misaligns with the learning objective of our SD-calibrator. To address this, we propose freezing the backbonn and updating only the calibrator using recent test samples for efficient test-time computing, However, this strategy introduces two critical challenges: ! recent studies [37] have shown that real-time updates may cause information leakage; and @ excessive updates can lead to overfitting of the calibration parameters and increased computational burden. The core problem thus becomes how to design a efficient calibration parameter learning mechanism without information leakage.
Implementation Details. To address these challenges, we introduce the flash gradient update strategy coupled with a streaming memory queue. The process is as follows:
Streaming Memory Queue. We maintain a first-in, first-out (FIFO) queue, denoted as Q, with a maximum size equal to the prediction horizon T For each incoming test instance I, after making prediction, we store the input-label pair (X,, Yi) into Q (Here is for engineering convenience. In real deployment, data points can be merged at each step to form the true label). Once Q is full, for every new test sample (X,, Y,) added, the oldest sample pair (X., Y,) is dequeued. This dequeued sample (X,, Y.) is then used for the gradient update, thus avoiding the information leakage.
Flash Gradient Update. Once we have (Xo, we first obtain the backbone model's prediction for the historical input: Y = fo(X.) (note: the backbone model weights So are frozen). Then, the Dalibbibr 9o processes this prediction: yool = go (Ý.)). The loss function between the calibrated prediction yrcal and the true historical label Y. is calculated, and only single gradient descent step is performed to update the parameters of the SD-Cod Da--Cibbbratr À t V For the next input sample X,, the updated ID-Calibrator is used for prediction. Using this single-sample single-step gradient descent strategy, we achieve lightning- parameter updates.
For clarity, we provide a Algorithm workflow 3 and Pytorch-Styla Pseudocode 4 in Appendix C.2.
Complexity Analysis. The primary focus here is the time complexity. The Streaming Memory Queue itself has an (11) time complexity for enqueue and dequeue operations. The Lightning Gradient Update is performed only once for each incoming test sample. Each update involves: 1). Forward propagation of the backbone and calibrator (dominated by the computational cost (NTloogT) of IFFT and irFFT) 2). Backward propagation of the calibrator (dominated by parameter cost (NG)).
Theoretical Analysis. We also show that this single update step leads to a controlled adjustment, ensuring that the calibrator makes progress on the newest sample it's trained on, without causing erratic behavior, under standard assumptions. (Please refer to Proposition in Appendix B).
5

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5 Experiments
In this section,w we conduct extensive experiments to answer the following research questions (RQs):
RQ1:
Can ST-TTC have consistent improvement various types of models and datasets? Can ST-TTC outperform previous learning methods that leverage test data? (Effectiveness)
RQ2: Can ST-TTC effective in various real-world scenarios, including few-shot learning, long- term forecasting, and large-scale forecasting? (Universality)
RQ3: Can ST-TTC further enhance the performance of existing learning paradigms that utilize training data, such OOD Learning and continual learning? (Flexibility)
RQ4: How does ST-TTC work? Which components strategies crucial? Are these compo- nents or strategies sensitive to parameters or design? (Mechanism & Robustness)
RQ5: What is the time and parameter cost of ST-TTC during test-time computation, and how does it compare other advanced methods? (Efficiency Lightweight)
5.1 Experimental Setup
Datasets. We employ publicly available benchmark datasets widely used in the literature to cover typical caatio-temporal forecasting scenarios in the traffic domain (PEMS-03, PEMS-04 -4,S-04, PEMS-07, PEMS-08 [65]), the meteorological domain (KnowAir [79]), and the energy domain (UrbanEV [39]). In addition, we also leverage the traffic-speed benchmark METR-LA [40], the large-scale spatio- temporal benchmark LargeS7 [48], and dynamic-stream benchmarks (Energy-Streann Air-Stream, PEMS-SIn -StMe-m [10]) assess our methods across varied settings and learning paradigms. Unless otherwise specified, all datasets are chronologically split into training, validation and test sets in a 6
2: ratio. For more detailed description of each dataset, please see the Appendix D.I.
Baseline, For the default evaluation, we cover various widely used spatio-temporal backbones, which can be divided into three categories: (1) teassforrer-bbasee STAEformer [47] and STTN [86]; (2) Graph-based: GWNet [83] and STGCN [90]; (3) MLP- based: STID [62] and ST-Norm [15]. For the baselines that leverage test information, we cover three types: (1) popular test-time adaptation methods in vision: TTT-MAE [20] and TENT [73]; (2) Online time series forecasting methods: OnlineTCN [105], KSNer [57] and OneNet [81]; (3) Comparable online spatio-temporal forecasting methods: CompFormer [100] and DOST [72]. For the baselines on large-scale benchmarks, we use the efficient PatchSTG [17] as the backbone. For the baseline of OOD learning scenarios, we the
advanced STONE [68] as the default method. For the continual learning scenario, we use EAC [10] and STKEC [70] as the default methods. We follow the default parameter settings of the models for all scenarios according to the corresponding literature. For details of each method, see Appendix D.2.
the previous 12 time steps to predict the next 12 steps and their mean- m evaluated with mean absolute error (MAE), root mean square error (RMSH), and mean absolute percentage error (MAPE). For simplicity, all experiments share the same hyperparameters of our ST-TTC: the calibration module learning rate Ir is set to 1e-4, the memory-queue sample count n used for updating is 1, and the number of groups m to 4. To ensure fairness, each experiment is repeated five times, with results reported as mean & standard deviation (denoted in gray +). More protocol details, see Appendix D.3.
Protocol. Following prior benchmarks [61], we employ a 12-to- 12 forecasting
5.2 Effectiveness Study (RQ1)
Consistent Effectiveness. Table 2 presents the results of our method for 12-step future prediction across six models six public datasets. The X column denotes the results of standard testing, while the / column indicates results obtained with our proposed ST-TTC approach. The best results in the X and v columns are highlighted in bold blue and pink fonts, respectively. We also compute the relative improvement, denoted by the A column. Based on these results, we make the following observations: ① The application of our test-time computation method, ST-TTC, consistently yields performance gains across various backbone architectures and dataset combinations. @ From model- centric perspective, our approach can further enhance the performance of even the top-performing methods across different metrics and datasets. @ From a data-centric perspective, UrbanEV shows more significant relative improvement, likely due to its more pronounced distribution shift.

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Table 2: Performance comparison of different models w/ and w/o ST-TTC on common benchmarks.
Medis
Trendernce hocd
Grigh kood
Mi Pool
STM [M]]
GRille PC3
ST30 (02)
27 Neoosl15
MAR
12 17
16
17:00-m0
11:33
11:01
1.39
17:66
17.9kvm
1.00
17:00
1.330
10000
1.87
1.774
27.58013
3.000
3.000
3.24
222
2671e
11.30
MARQUS
1533
15824.4
0.00
18 03
15.01 km
1 12.44
16.70cm
16.00-40
1.00
16300
1.36
17.00
17 17.3809
0.60
17.00
16
1143
MAR
10355m
1.077
3183000
1.0.3
23.5
Bonaan
2136c
1.0.0
MAE
21
1:00
10.04
22
32 00.
10.71
36.
1.99
01 53
0.79
32
22 1
PSAY947
10000
1748
1.20
17.5
0.83
3637
38.0
0.08
35.83
1.77
56
0.66
28.14
37.776m
1.97
MA
0.56
10.0
1..01
10.30
13.0..00
1.80
1400
19.00
MAP
9
10.33
11.27
11,00
1033
1.40
11
11.3
0.00
0.01
11.28
2.36
MAR
1.0.4
[2.36am
1.0.7
(7.Mex
10.5
11/85.m
13.8
0.00
17.0aax
19.35
Axeelo-
3533
1.027
06.3
10.09
36
Mildinn
0.90
0.33
10.33
01/91111
10.77
11:01
1.500
1497
MAP
10.00
1.41
1:34
35
0:33
1.50
283
1.7
1.41
13455
10000
1.0.00
1.15
1:225
1.00
407
3.40
Allac
9.20
1.000
MARQ/S3
3675.m
11.11
3875
28.00.00
11.81
2.16
31 2..
0.00
37.35
1.40
24 20.5
1..91
Competitive Effectiveness. We further compare our method against various advanced approaches that can leverage test-time information. Since the official source code of CompFormer and DOST is not available and uses additional data informa- tion, it leads to an unfair comparison. Nev- ertheless, we still include all reported METR- LA benchmark values (indicated with *) using a unified GWNer backbone, categorized into reg- ular and online settings as presented in Table 3, based on their respective papers. Additionally, we implemented the popular 777-MAE method as surrogate for the unavailable TTT-ST method. Our observations are as follows: For the reg- ular setting, our method achieves competitive re- sults with more stable standard deviations. While
Table 3: Performance comparison of the advanced
method with ST-TTC on METR-LA benchmark. Marker indicates the results are statistically sig- nificant (t-test with p- p-value < 0.01).
Method
MAE
RMSE
Training Set
Moditying
The matning /allidation fest set serippii used below is 70% 10% 109//20% 20%.
TTI-MAE (20g
3,47uns
7,43
TENT 173)
CompFormer" [100]
7.19
ST TTC
3,46-1n
-.21-a30
The iniining vulicloinn / lins api used bnlow is 20% /59//75
OulivrTNN' [105]
4.78ress
8.70
FSNer [57)
5.79
11.06
OneNer'
4.84usss
8,80a00
DOST [2]]
4.38u0z
8,26
7
x
ST-12C
3.77.
7.75uxas
other methods like CompFormer demonstrate similar performance, they often utilize more training in- formation and computational resources. @ In the online setting, our method significantly outperforms existing approaches without requiring more complex model architecture modifications.
5.3 Universality Study (RQ2)
To demonstrate the universality of ST-TTC across diverse real-world scenarios, we explore various forecasting scenarios in the literature, including few-shot [94], long-term [59], and large-scale [25].
Few-Shot Scenario. To simulate limited training data, we retrained models using only the first 10% of existing training sets to investigate a more common and challenging few-shot scenario. Figure/ shows the relative performance gains with ST-ITC (For full results, please refer Table 6 in the Appendix). We observe: ST-TIC provides more significant improvements in the few-shot setting compared to the full-shot case in Table 2, with about half exceeding 2%. @ KnowAir shows the largest gain compared to other datasets, likely because its four-year long period leads to a substantial test distribution shift in the few-shot scenario, where our method adapts well.
PEMS-03
PEMS-04
PEMS-07
PEMS-08
KnowAir
UrbanEV
ST.Nom-
616
0.31
140
0.7
1:2
4.7
1.91
1.57
4:37
31
STOCN-
GWN
8.78
111
2355
134
6:44
824
240
140
0.26
2.41
102
-15
STTN-
171
1.9
0/44
411
6.1
1:0
MAE
HAISE
Mdre
MAE
RMSE
MAPE
MAE
BOiSE
MAPE
MÁE
RAGEE
MADE
MAB
191SE
MAPE
MÀE
MAPE
Figure 2: Relative improvements of different models w/ ST-TTC in the few-shot setting.
Long-Term Scenario. In real-world scenarios, long-term forecasting helps to further plan future decisions. We predicted 24 future steps from 24 past steps to explore more complex temporal changes. As shown in Figure 3, we present the relative performance improvement of the advanced STID model
7

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Growd
Sel Meroel
100
140
1m
Tor- Time Skop links
796
rids Sarvik
Figure 3: Left: relative improvement of long-term setting. Right: visualization study of PEMS-08.
with our ST-TTC method, and give a test set prediction visualization case on the PEMS-08 dataset (see Figure 9 in the Appendix for more examples). Our observations include: 1 ST-TTC consistently improves long-term forecasting, even more than short-tern (Table 2), likely due to more learnable information in longer windows. @ As the pink and orange box shows, method learns test-time history, capturing both the global traffic decline and local fluctuations, leading to effective calibration.
Large-Scale Scenario. Beyond current regional datasets, state or national-level spatio-temporal fore- casting can involve tens of thousands of stations and longer time frames. We explore large-scale scenarios using the popular LargeST benchmark (comprising SD, GBA, GLA, and CA subsets). Figure 4 illus- trates the 12-step prediction performance gains of the state-of-the-arr efficient spatio-temporal model PatchSTG [17] with ST-TTC along with com- parison of inference time complexity (For full re- sults, see Table 7 in Appendix). We observe: O Our ST-TTC consistently yields further performance im- provements across all datasets, even surpassing the improvement of the second-best baseline over the PatchSTG on some datasets. The additional inference time is at most 3.82 minutes, which is a clear advantage for the achieved performance gains compared to the training time cost of up to 14 hours.
MAPE (%)
Infereace & Training Time
Sucual Ree Rea ST-TIC
PradSTIO Traniig PradSTIC fefler (nks))
00.90
ATSTTT TC Bndteass
10.63
5--
1.59
6-
0..46
0.34
1.42
0.49
00225
sb
GIM
GlA
0-
GLA
Figure 4: Performance on LargeST.
5.4 Flexibility Study (RQ3)
To illustrate the flexibility of ST-TTC in accommodating existing learning paradigms, we explore its
integration with two training data-levergging paradigms: OOD learning and Continual Learning.
OOD Learning Setting. Following prior work [68]. we use the SD dataset to simulate spatio-temporal shift. For the temporal dimension, we use 1-8/2019, 9-10/2019, and 11-12/2020 for training, validation, and testing, respectively. For the spatial dimension, we randomly mask 10% of nodes consider three proportions of new nodes (10% 15%
All Nodes
New Nodes
MAE
30-
RMSE
Improvemaat (%g
MAPE
20-
the test set and
10-
5-
20%) relative the training node mimic varying degrees of shift. In Figure 5, we present the 12-step average prediction performance gains of the advanced OOD learning model STONE with our ST-TTC, eval- uated on all nodes and new nodes to demonstrate gen- eralizability and scalability (Full results in Table 8). We observe that: The STONE model with ST-TTC consistently achieves performance benefits, significantly outperforming all previous settings, indicating that existing OOD models are still insuf- ficient for true OOD generalization, while our method is highly effective. @ For both all and new nodes, our improvements become more pronounced as the shift increases, further demonstrating our effectiveness in handling both generalizability and scalability in challenging scenarios.
0
10%
15%
20%
10%
15%
20%
Shift Degree
Shift Degree
Figure 5: Relative improvement using our ST-TTC in the OOD learning setting.
Continual Learning Setting. Following prior work [10], we used multi multi-period streaming spatio- temporal data to examine our ST-TTC 's integration with continual learning method. Table 4 shows the improved 1 12-step forecasting of advanced continual learning models EAC and S7KEC with our ST-TTC. We observed: 1 Consistent performance gains for both models across all datasets; STKEC with ST- TTC even achieved comparable performance to best model EAC. (2) Energy-
8

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Table 4: Performance comparison in continual learning setting.
Period
Methols SI-IIC
Atr-Siman
SEMM--mmar
MAR
MARR(S)
MAR
RMSE
MARRRR)) MAR
RMSE MAM9(S)
M1. i 38 u 31, Niee
11.00n 21 1ien 30 Whee 5. Aiboooo 50-35-ras
EAC
<
23.5 is 37. Me 31.05ses
14.7imm
25.81enn
20 Slecs
3.07mm
3.9kam 30 10.66
2.5%
1,9%
11.4%
41.2%
11.4%
4.366%
2.7.8%
21..6%
25, 6duins 10
1633oo
28 3too 5/0ur
5.73mmm
All..
0.26
6:40
STREC
Frequency Energy Rasio
4.00% 2.79
1498
1128
1198
120%
199.55
25.8%
17.8%
Figure 6: Sinrgy-Streamt Shift.
Stream achieves significant improvement over other datasets, as the ST-TTC effectively learns and calibrates temporal changes, as shown by the frequency analysis (drastic shift changes) Figure 6.
5.5
Mechanism & Robustness Study (RQ4)
36,82
STONE (14 80%1 Devietion
$4.70
MAP1550
MAPE,N0 (1)
84
25.1 25 00
34T2
24
SETTC
Time
Amp
Nade
Rand.
162
Learoing Rate
Led
Gropg
Samples
Sim
1e-5
Figure 7: Left: Strategy comparison. Middle: Effect of Ir w.r.t m. Right: Effect of n w.r.f s.
We follow the OOD setup (challenging setting with 20% new nodes) to evaluate ST-TTC.
Strategy Study. We compare different strategies: 1) simple nonlinear time domain calibration (Time), 2) learning only phase or amplitude modulation factors (Pha. / Amp.), 3) node-share modeling (Node), and (4) random selection or retrieval of the most similar samples (Rand. Sim.). shown in Figure 7 left, we observe: 1 Frequency-done domain calibration significantly outperforms time-domain calibration, with amplitude modulation being the primary contributor; @ Sharing nodes leads to performance degradation due to spatial heterogeneity in spatio-temporal data; O Random sample selection reduces performance, and retrieving similar samples offers negligible gains while incurring higher computational cost. Our proposed update strategy is already near-optimal.
Parameter study. We analyze the sensitivity of two parameter groups. As shown in the middle and right of Figure 7: Higher learning rates and fewer groups generally lead to poorer performance, likely due to limited parameter capacity hindering stable learning: @ Increasing the number of samples or update steps has minimal impact on performance (fluctuations < 1 1%), but significantly increases time cost, highlighting the rationale of our flash update mechanism.
5.6 Efficiency & Lightweight Study (RQ5)
METR-LA Beochaadk
Result Analysis. We use GWNer as the backbone and compare ST-TTC with other test-time adaptation methods on METR-LA in terms of total inference time and memory usage. As shown in Figure 8, ST-TTC achieves the best overall efficiency (excluding the GWNer baseline), being 4.64x faster and reducing memory usage by 37.12% com- pared to the least efficient method, which is much smaller than the sliding size (5 min.), meeting the time require- ment.
Thone (MB))
TMVVA 235
TENT
Merees Furiger
FSN
ThelineCNN CORMI 14
DOST SEEMI 47%
DineNa
100
200
400
000
400
50
Ioal inference lime 30
Figure 8: time and memory.
6 Conclusion
In this paper, we investigate the objectives of test-time computation in spatio-temporal forecasting and explore effective approaches for its implementation. We propose ST-TTC, a novel paradigm that uses flash gradient update with streaming memory queue to learning a spectral-domait calibrator via phase-amplitude modulation, effectively addressing non-stationary errors. Extensive experiments confirm its effectiveness, universality, and flexibility. In future work, we aim to explore how to enhance the internal computational capacity of spatio-temporal foundation models during test time.

---

Acknowledgments
The first author would like to thank all the anonymous reviewers for their valuable comments and high recognition. Although he has almost lost his passion for this field and is ready to leave, he hopes that this study can still bring something new to the ST community.
This work is mainly supported by the National Natural Science Foundation of China (No. 62402414). This work is also supported by the Huawei Co., Ltd (No. TC200210230277 the Guangzhou- HKUST(GZZ) Joint Funding Program (No. 2024A03J0620), Guangzhou Municipal Science and Technology Project (No. 2033A03J, 1), the Guangzhou Industrial Information and Intelligent Key Laboratory Project (No. 2024A0310628), and a grant from State Key Laboratory of Resources and En- vironmental Information System, and Guangdong Provincial Key Lab of Integrated Communication, Sensing and Computation for Ubiquitous Internet of Things (No. 2023B121201000)
References
[1] Akyürek, M. Damani, A. Zweiger, L. Qiu, H. Guo, J. Pari, Y. Kim, and J. Andreas. The surprising effectiveness of test-time training for few-shot learning. arXiv preprint arXiv:2411.07279, 2024.
[2] M. T. Bahadori, Q. R. Yu, and Y. Liu. Fast multivariate spatio-temporal analysis via low rank tensor learning, Advances in neural information processing systems, 27, 2014.
[3] S. Bai, Y. Ji, Y. Liu, X. Zhang, X. Zheng, and D. D. Zeng. Alleviating performance disparity in adversarial spatiotemporal graph learning under zero-inflated distribution. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages 1433-11444, 2025.
[4] C. Bergmeir. Fundamental limitations of foundational forecasting models: The need for multimodality and rigorous evaluation. In Proc. NeurIPS Workshop. 2024.
[5] Biller and B. Nelson, Modeling and generating multivariate time-series input processes using vector autoregressive technique. ACM Transactions Modeling and Computer Simulation (TOMACS), 1313)221--377, 2003.
[6] L. Bottou and V. Vapnik. Local learning algorithms. Neural computation, 4(6):888 900, 1992.
[7] G. E. Box and D. A. Pierce. Distribution of residual autocorrelations in autoregressive- integrated moving average time series models. Journal of the American statistical Association, (5(332):150--1526 1970.
[8] L. Brigato, R. Morand, K. Strømmen, M. Panagiotou, M. Schmidt, and S. Mougiakakou. Position: There are no champions in long-term time series forecasting. arXiv preprint arXiv:250.114045, 2025.
[9] C. Chen, Y. Liu, L. Chen, and C. Zhang. Test-time training for temporale forecasting. In Proceedings of the 2024 SIAM International Conference on Data Mining (SDM), pages SIAM, 2024.
[10] W. Chen and Y. Liang. Expand and compress: Exploring tuning principles for continual spatio-temporal graph forecasting. In The Thirteenth International Conference on Learning Representations, 2025.
[11] X. Chen, J. Wang, and K. Xie. Traffiestream: A streaming traffic flow forecasting framework based on graph neural networks and continual learning. In IJCAI, 2021.
[12] A. Cini, I. Marisca, D. Zambon, and C. Alippi. Taming local effects in graph-based spatiotem- poral forecasting. Advances in Neural Information Processing Systems, 36:55375-55393, 2023.
[13] A. Cliff and J. K. Ord. Space-time modelling with an application regional forecasting. Transactions of the Institute of British Geographers, pages 119-128, 1975.
[14] N. Cressie and C. K. Wikle. Statistics for spatio-temporal data. John Wiley & Sons, 2011.
10

---

[15] J. Deng, X. Chen, R. Jiang, X. Song, and 1. W. Tsang. St-norm: Spatial and temporal normalization for multi-variate time series forecasting. In Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining, pages 269-278, 2021.
[16] J. Deng, X. Chen, R. Jiang, D. Yin, Y. Yang, X. Song, and I. W. Tsang. Disentangling structured components: Towards adaptive, interpretable and scalable time series forecasting. IEEE Transactions Knowledge and Data Engineering. 2024.
[17] Y. Fang, Y. Liang, B. Hui, Z. Shao, L. Deng, X. Liu, X. Jiang, and K. Zheng. Efficient large-scale traffic forecasting with transformers: A spatial data management perspective. In Proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining, 2025.
[18] S. R. Flaxman. Machine learning in space and time. PhD thesis, Ph. D. thesis, Carnegie Mellon University, 2015.
[19] A. Gammerman, V. Vovk, and V. Vapnik. Learning by transduction. Proceedings of the Fourteenth Conference Uncertainty in Artificial Intelligence, UAI988, page 148-155, 1998.
[20] Y. Gandelsman, Y. Sun, X. Chen, and A. Efros. Test-time training with masked autoencoders. Advances in Neural Information Processing Systems, 35:29374-29385, 2022.
[21] D. Guo, D. Yang, H. Zhang, J. Song, R. Zhang, R. Xu, Q. Zhu, S. Ma, P. Wang. X. Bi, et al. Deepseck-rl: Incentivizing reasoning capability in Ilms via reinforcement learning. arXiv preprint arXiv:2501.1294: 2025.
[22] P. Guo, P. Jin, Z. Li, L. Bai, and Y. Zhang. Online test-time adaptation of spatial-temporal traffic flow forecasting. arXiv preprint arXiv:2401.04 00/448 148, 2024.
[23] S. Guo, Y. Lin, N. Feng. C. Song, and H. Wan. Attention based spatial-temporal graph convolutional networks for traffic flow forecasting. In Proceedings of the AAAI conference artificial intelligence, volume 33, pages 922-929, 2019.
[24] S. Guo, Y. Lin, H. Wan, X. Li, and G. Cong. Learning dynamics and heterogeneity of spatial-temporal graph data for traffic forecasting. IEEE Transactions on Knowledge and Data Engineering, 34(11):54 (4(1))541555422
2021.
[25] J. Han, W. Zhang, H. Liu, T. Tao, N. Tan, and H. Xiong. Bigst: Linear complexity spatio- temporal graph neural network for traffic forecasting on large-scale road networks. Proceedings of the VLDB Endowment, 17(5): 1080-, 2024.
[26] M. Hardt and Y. Sun. Test-time training nearest neighbors for large language models. In The Twelfth International Conference on Learning Representations, 2024.
[27] P. Hu, R. Wang, X. Zheng, T. Zhang, H. Feng, R. Feng, L. Wei, Y. Wang, Z.-M. Ma, and T. Wu. Wavelet diffusion neural operator. 2025.
[28] S. Huang, Z. Zhao, C. Li, and L. Bai. Timekan: Kan-based frequency decomposition learning architecture for long-term time series forecasting. 2025.
[29] A. Jaech, A. Kalai, A. Lerer, A. Richardson, A. El-Kishky, A. Low, A. Helyar, A. Madry,
A. Beutel, A. Carney, et al. Openai ol system card. arXiv preprint 221.226222.6100 2024.
[30] M. Jang, S.-Y. Chung, and H. W. Chung. Test-time adaptation via self-training with nearest neighbor information. In The Eleventh International Conference on Learning Representations, 2023.
[31] J. Ji. W. Zhang, J. Wang, and C. Huang. Seeing the unseen: Learning basis confounder repre- sentations for robust traffic prediction. In Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V. 1, pages 577-588, 2025.
[32] G. Jin, Y. Liang, Y. Fang, Z. Shao, J. Huang. J. Zhang, and Y. Zheng. Spatio-temporal graph neural networks for predictive learning in urban computing: A survey. IEEE Transactions on Knowledge and Data Engineering, 36 (6(100)5388-555 2023.

---

[33] M. Jin, H. Y. Koh, Q. Wen, D. Zambon, C. Alippi, G. I. Webb, I. King, and S. Pan. A survey on graph neural networks for time series: Forecasting, classification, imputation, and anomaly detection. IEEE Transactions Pattern Analysis and Machine Intelligence, 2024.
[34] Kahneman. Thinking, fast and slow. maemillan, 2011.
[35] D. Kieu, T. Kieu, P. Han, B. Yang, C. S. Jensen, and B. Le. Team: Topological evolution-aware framework for traffic forecasting. Proceedings of the VLDB Endowment, 18(2):265-278, 2024.
[36] R. Kumar, M. Bhanu, J. Mendes-Moreira, and J. Chandra. Spatio-temporal predictive modeling techniques for different domains: a survey. ACM Computing Surveys, 57(2): 2024.
[37] Y-y. A. Lau, Z. Shao, and D.-Y. Yeung. Fast and slow streams for online time series forecast- ing without information leakage. In The Thirteenth International Conference on Learning Representations, 2025.
[38] S. Lee and C. Park. Continual traffic forecasting via mixture of experts. arXiv preprint arXiv:2406.031 444.0340,, 2024.
[39] H. Li, H. Qu, X. Tan, L. You, R. Zhu, and W. Fan. Urbanev: An open benchmark dataset for urban electric vehicle charging demand prediction. Scientific Data, page 523, 2025.
[40] Y. Li, R. Yu, C. Shahabi, and Y. Liu. Diffusion convolutional recurrent neural network: Data-driven traffic forecasting. In International Conference on Learning Representations. 2018.
[41] Z. Li, L. Xia, L. Shi. Xu, D. Yin, and C. Huang. Opencity: Open spatio-temporal foundation models for traffic prediction. arXiv preprint arXiv:2408. 10269, 2024.
[42] Z. Li, L. Xia, Tang, Xu, I.. Shi, I. Xia, Yin, and C. Huang. Urbangpt: Spatio-temporal large language models. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 5351-5362, 2024.
[43] Z. Li, L. Xia, Y. Xu, and C. Huang. Flashst: A simple and universal prompt-tuning framework for traffic prediction. In Proceedings of the 41st International Conference on Machine Learning, pages 28978-28988 2024.
[44] J. Liang, R. He, and T. Tan. A comprehensive survey on test-time adaptation under distribution shifts. International Journal of Computer Vision, 133(1):31-64 2025.
[45] J. Liang, D. Hu, and J. Feng. Do we really need to access the source data? source hypothesis transfer for unsupervised domain adaptation. In International conference machine learning, pages 6028-6039. PMLR, 2020.
[46] F. Liu, H. Liu, and W. Jiang. Practical adversarial attacks on spatiotemporal traffic forecasting models. Advances in Neural Information Processing Systems, 35:19035-19047, 2022.
[47] H. Liu, Z. Dong, R. Jiang, J. Deng, J. Deng, Q. Chen, and X. Song. Spatio-temporal adaptive embedding makes vanilla transformer sota for traffic forecasting. In Proceedings of the 32nd ACM international conference on information and knowledge management, pages 4125-4129, 2023.
[48] Liu, Xia, Y. Liang, J. Hu, Wang, L. Bai, C. Huang, Z. Liu, B. Hooi, and R. Zimmer- mann. Largest: A benchmark dataset for large-scale traffic forecasting. In Advances in Neural Information Processing Systems, 2023.
[49] J. Ma, P. Wang, B. Wang, Z. Zhou, X. Wang, Y. Zhang. D. Qian, and Y. Wang- Stop! a out-of-distributtio processor with robust spatiotemporal interaction. 2024.
[50] Y. Nesterov. Introductory lectures on convex optimization: busic course, volume 87. Springer Science & Business Media, 2013.
12

---

[51] T. Nguyen, J. Brandstetter, A. Kapoor, J. K. Gupta, and A. Grover. Climax: A foundation model for weather and climate. In International Conference on Machine Learning, pages 25904-25933 PMLR, 2023.
[52] Y. Nie, N. H. Nguyen, P. Sinthong, and J. Kalagnanam. A time series is worth 64 words: Long- term forecasting with transformers. In The Eleventh International Conference on Learning Representations, 2023.
[53] O. Ohashi and L. Torgo. Wind speed forecasting using spatio-temporal indicators. In ECAI 2012, pages 975-980. IOS Press, 2012.
[54] B. N. Oreshkin, A. Amini, L. Coyle, and M. Coates. Fe-gaga: Fully connected gated graph architecture for spatio-temporal traffic forecasting. In Proceedings of the AAAI conference artificial intelligence, volume 35, pages 9233-9241 0241,9921,10 2021.
[55] M.-A. Parseval. Mémoire sur les séries et sur l'intégration complète d' l'une équation aux différences partielles linéaires du second ordre. à coefficients constants. Mém. prés. par divers savants, Acad. des Sciences, Paris, 16638-64 1(638-648):42 1806.
[56] P. E. Pfeifer and S. J. Deutsch. A starima model-building building procedure with application to description and regional forecasting. Transactions of the Instiuute of British Geographers, pages 330-349, 1980.
[57] Q. Pham, C. Liu, D. Sahoo, and S. Hoi. Learning fast and slow for online time series forecasting. The Eleventh International Conference on Learning Representations, 2023.
[58] R. Senanayake, S. O'callaghan, and F. Ramos. Predicting spatio-temporal propagation of seasonal influenza using variational gaussian process regression. In Proceedings of the AAAI conference on artificial intelligence, volume 30, 2016.
[59] W. Shao, Z. Jin, S. Wang, Y. Kang, X. Xiao, H. Menouar, Z. Zhang, J. Zhang, and Salim. Long-term spatio-temporal forecasting via dynamic multiple-graph attention. In 31st Interna- tional Joint Conference on Artificial Intelligence, IJCAI 2022, pages 2225-2233 International Joint Conferences Artificial Intelligence, 2022.
[60] W. Shao, Y. Kang, Peng, X. Xiao, L. Wang, Y. Yang. and D. Salim. Stemo: Early spatio-temporal forecasting with multi-objective reinforcement learning. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 2618-2627, 2024.
[61] Z. Shao, F. Wang, Y. Xu, W. Wei, C. Yu, Z. Zhang, D. Yao, T. Sun, G. Jin, X. Cao, et al. Exploring progress in multivariate time series forecasting: Comprehensive benchmarking and heterogeneity analysis. IEEE Transactions on Knowledge and Data Engineering, 2024.
[62] 7. Shao, 7.. Zhang, F. Wang, W. Wei, and Y. Xu. Spatial-temporal identity: A simple yet effective baseline for multivariate time series forecasting. In Proceedings of the 31st ACM international conference on information & knowledge management, pages 4454-4458, 2022.
[63] X. Shi and D.-Y. Yeung. Machine learning for spatiotemporal sequence forecasting: A survey. arXiv preprint arXiv: wwX.vv/808.000 06865, 2018
[64] C. V. Snell, J. Lee, K. Xu, and A. Kumar. Scaling I1m test-time compute optimally can be more effective than scaling parameters for reasoning. In The Thirleenth International Conference on Learning Representations, volume 2, page 7, 2025.
[65] C. Song, Y. Lin, S. Guo, and H. Wan. Spatial-tempont synchronous graph convolutional networks: A new framework for spatial-temporal network data forecasting. In Proceedings of the AAAI conference on artificial intelligence, volume 34, pages 914 921, 2020.
[66] Y. Sun, X. Wang, Z. Liu, J. Miller, A. Efros, and M. Hardt. Test-time training with self- supervision for generalization under distribution shifts. In International conference on machine learning, pages
PMLR, 2020.
[67] V. Vapnik. The nature of statistical learning theory. Springer science & business media, 1999.
13

---

[68] B. Wang, J. Ma, P. Wang, X. Wang, Y. Zhang, Z. Zhou, and Y. Wang. Stone: A spatio-temporal ood learning framework kills both spatial and temporal shifts. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 2948 2959, 2024.
[69] B. Wang, P. Wang, Y. Zhang, X. Wang, Z. Zhou, L. Bai, and Y. Wang. Towards dynamic spatial- temporal graph learning: A decoupled perspective. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 9089-9097, 2024.
[70] B. Wang, Y. Zhang, Shi, P. Wang. X. Wang. L. Bai, and Y. Wang. Knowledge expansion and consolidation for continual traffic prediction with expanding graphs. IEEE Transactions Intelligent Transportation Systems, 24(7):710--2211 2023.
[71] B. Wang, Y. Zhang, X. Wang, P. Wang, Z. Zhou, L. Bai, and Y. Wang. Pattern expansion and consolidation on evolving graphs for continual traffic prediction. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 2223-2232, 2023.
[72] C. Wang. G. Tan, S. B. Roy, and B. C. Ooi. Distribution-aware online continual learning for urban spatio-temporal forecasting. arXiv preprint arXiv:2411.1589) 2024.
[73] D. Wang, E. Shelhamer, S. Liu, B. Olshausen, and T. Darrell. Tent: Fully test-time adaptation by entropy minimization. In The Ninth International Conference on Leurning Representations, 2021.
[74] H. Wang. J. Chen, T. Pan, Z. Dong, L. Zhang, R. Jiang, and X. Song. Evaluating the general- ization ability of spatiotemporal model in urban scenario. arXiv preprint arXiv:2410.04740, 2024.
[75] H. Wang, J. Chen, T. Pan, Z. Dong. L. Zhang. R. Jiang, and X. Song. Robust traffic forecasting against spatial shift over years. arXiv preprint arXiv:2410.00373, 2024.
[76] H. Wang, Z. Lei, X. Zhang, B. Zhou, and J. Peng. A review of deep learning for renewable energy forecasting. Energy Conversion and Management, 198:1 18::111700 1199, 2019.
[77] Q. Wang, O. Fink, L. Van Gool, and D. Dai. Continual test-time domain adaptation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7201-7211, 2022.
[78] R. Wang. Y. Sun, A. Tandon, Y. Gandelsman, X. Chen, A. A. Efros, and X. Wang. Test-time training on video streams. Journal of Machine Learning Research, 26(9):1-29, 2025.
[79] S. Wang, Y. Li, J. Zhang, Q. Meng, L. Meng, and F. Gao. Pm2. 5 5-gmn: A domain knowledge enhanced graph neural network for pm2. 5 forecasting. In Proceedings of the 28th international conference on advances in geographic information systems, pages (66.166,7 2020.
[80] Y. Wang, H. WU, Y. Ma, Y. Fang. 7. Zhang, Y. Liu, S. Wang, 7. Ye, Y. Xiang, J. Wang, et al. Accuracy law for the future of deep time series forecasting, arXiv preprint arXiv:2510002729, 2025.
[81] Q. Wen, W. Chen, L. Sun, Z. Zhang, L. Wang, R. Jin, T. Tan, et al. Onenet: time series forecasting models under concept drift by online ensembling. Advances in Neural Information Processing Systems, 36:69949-69988 2023.
Enhancing
[82] H. Wu, F. Xu, C. Chen, X.-S. Hua, X. Luo. and H. Wang. Pastnet: Introducing physical inductive biases for patio-temppraa video prediction. In Proceedings of the 32nd ACM International Conference on Multimedia, pages 2917-2926, 2024.
[83] 7. Wu, S. Pan, G. Long, J. Jiang, and C. Zhang. Graph wavenet for deep spatial-temporal graph modeling. arXiv preprint 190.0001,000 2019.
[84] Y. Xia, Y. Liang, H. Wen, X. Liu, K. Wang, Z. Zhou, and R. Zimmermann. Deciphering spatio- temporal graph forecasting: A causal lens and treatment. Advances Neural Information Processing Systems, 16:37766-377083 2023.
14

---

[85] C. Xu, Q. Wang. W. Zhang, and C. Sun. Spatiotemporal ego ego-graph domain adaptation for traffic prediction with data missing. IEEE Transactions on Intelligent Transportation Systems, 2024.
[86] M. Xu, W. Dai, C. Liu, X. Gao, W. Lin, G.-J Qi, and H. Xiong. Spatial-temporal transformer networks for traffic flow forecasting. arXiv preprint WxXv:2001.02900. 2020.
[87] Z. Xu, A. Zeng, and Q. Xu. Fits: Modeling time series with 10k parameters. In The Twelfth International Conference on Learning Representations, 2024.
[88] K. Yi, Q. Zhang, W. Fan, H. He, L. Hu, P. Wang, N. An, L. Cao, and Z. Niu. Fouriergnn: Rethinking multivariate time series forecasting from a pure graph perspective. Advances in neural information processing systems, 36:69638 1266638-69660, 2023.
[89] Z. Yi, Z. Zhou, Q. Huang. Y. Chen, L. Yu, X. Wang, and Y. Wang. Get rid of isolation: A continuous multi-task spatio-temporal learning framework. In The Thirty-eighth Annual Conference on Neural Information P Processing Systems, 2024.
[90] B. Yu, H. Yin, and Z. Zhu. Spatio-temporal graph convolutional networks: a deep learning framework for traffic forecasting. In Proceedings of the 27th International Joint Conference on Artificial Intelligence, pages 3634-3640, 2018.
[91] X. Yu, J. Wang. Y. Yang, Q. Huang, and K. Qu Bigcity: A universal spatiotemporal model for unified trajectory and traffic state data analysis. arXiv preprint arXiv:2412.00955. 2024.
[92] Y. Yuan, Ding. Feng, D. Jin, and Li. Unist: urban spatio-temporal prediction. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 4095-4106, 2024.
universal model for
[93] Y. Yuan, C. Han, J. Ding, D. Jin, and Y. Li. Urbandit: A foundation model for open-world urban spatio-temporal learning, arXiv preprint arXi::2411.12164 2024.
[94] Y. Yuan, C. Shao, J. Ding, D. Jin, and Y. Li. Spatio-temporal few-shot learning via dif- fusive neural network generation. In The Twelfth International Conference on Learning Representations, 2024.
[95] Yue, Z. Chen, R. Lu, A. Zhao, Z. Wang, S. Song, and G. Huang. Does reinforcement learning really incentivize reasoning capacity in Ilms beyond the base model? arXiv preprint arXiv:2504. 13837, 2025.
[96] A. Zeng. M. Chen, L. Zhang, and Q. Xu. Are transformers effective for time series forecasting? In Proceedings of the AAAl conference on artificial intelligence, volume 37, pages 11121- 1 128, 2023.
[97] Q. Zhang, C. Huang, L. Xia, Z. Wang, Z. Li, and S. Yiu. Automated spatio-temporal graph contrastive learning. In Proceedings of the ACM Web Conference 2023, pages 295-305, 2023.
[98] Q. Zhang, C. Huang, Xia, Z. Wang, S. M. Yiu, and R. Han. Spatial-temports graph learning with adversarial contrastive adaptation. In International Conference on Machine Learning, pages 41151-41161 PMLR, 2023.
[99] Q. Zhang, F. Lyu, Z. Sun, L. Wang, W. Zhang, Z. Guo, Y. Wang, King, X. Liu, and C. Ma. What, how, where, and how well? survey test-time scaling in large language models. arXiv preprint arXiv:2503.24235, 2025.
[100] Z. Zhang, W. Zhang, Y. Huang, and K. Chen. Test-time compensated representation learning for extreme traffic forecasting. arXiv preprint arXiv:2309.09074, 20233.
[101] V. Z. Zheng,, S. Choi, and L. Sun. Probabilistic traffic forecasting with dynamic regression. Transportation Science, 2025.
[102] Y. Zheng, X. Yi, M. Li, R. Li, Z. Shan, E. Chang, and T. Li. Forecasting fine-grained air quality based on big data. In Proceedings of the 21th ACM SIGKDD international conference knowledge discovery and data mining, pages 2267-2276 2015.
15

---

[103] Z. Zhou, Q. Huang, B. Wang, J. Hou, K. Yang, Y. Liang, and Y. Wang. Coms2t: A comple- mentary spatiotemporal learning system for adta-adee model evolution. arXiv preprint arXiv:2403.01738, 2024.
[104] 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. Proceedings of the 29th ACM SIGKDD conference on knowledge discovery and data mining, pages 3603-3614, 2023.
[105] M. Zinkevich. Online convex programming and generalized infinitesimal gradient ascent. In Proceedings of the 20th international conference on machine learning (icml-03), pages 928-936, 2003.
16

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SUPPLEMENTARY MATERIAL
LEARNING WITH CALIBRATION: EXPLORING
TEST- TIME COMPUTING OF SPATIO- SERTO-TEMOORAL FORECASTING
TABLE OF CONTENTS
A More Related Work
18
A.1 Spectral Domain Learning.
18
A.2 Online Learning for Forecasting.
18
A.3 Test-Time Adaptation.
18
Theoretical Analysis
19
B.1 Approximate Bound on Output Perturbation
19
B.2 Controlled Descent on Streaming Memory Queues
19
C Method Details
20
C.1 Spectral Domain Calibrator
20
C.2 Lightning Gradient Update
21
D Experimental Details
21
D.I Datasets Details
21
D.2 Baseline Details
24
D.3 Protocol Details
26
E More Results
26
E.1 Complete Results Table
26
E.2
Visualization Case
26
F More Discussion
26
F1
Distinction between Spatio-Temporal Forecasting and Long-Tern -erg-Term Time Series
26
F2
Limitation
28
F3
Future Work
29
Broader Impacts
29
17

---

A More Related Work
A.1 Spectral Domain Learning.
Many recent forecasting models leverage spectral (Fourier or wavelet) representations to capture periodic or multiscale patterns in spatio-temporal data. For example, PastNer [82] integrates a Fourier- domain convolutional operator to embed physical inductive biases, achieving state-of-the of-the-an art results in weather and traffic prediction, FourierGNN [88] builds a learnable Fourier-graph operator that conducts graph convolutions in the frequency domain, reducing convolutional complexity from (nn)) to (n). Wavelet- based methods like WDNO [27] perform diffusion modeling in the wavelet domain to capture abrupt spatio-temporal changes and multi-resooution features. In the pure time-series setting, approaches such as FITS [87] interpolate in the complex Fourier domain and discard negligible high- frequency components to maintain accuracy with very few parameters, and TimeKAN [28] explicitly decomposes multivariate series into multiple frequency bands using Kolmogorov-Amme
networks. These works demonstrate how frequency domain learning can improve forecasting efficiency and accuracy by isolating dominant spectral components. Different from these methods, our method combines spectral domain feature extraction with culibration-aware lest-time compulation to achieve reliable and calibrated forecasts even under changing conditions.
A.2 Online Learning for Forecasting,
Traditional online forecasting methods include adaptive filters like Kalman filters and recursive least squares that update linear models on streaming data. Recently, deep-learning approaches have been proposed to handle nonstationarity in an online fashion. For instance, FSNer [57] implements a complementary "fast and slow" learning system: a fast-adapting component for sudden pattern changes and a slow memory component for repeating trends. OneNet [81] runs two parallel neural forecasters (one modeling temporal dependencies, one modeling cross- variable dependencies) and uses reinforcement learning to dynamically weight their predictions under concept drift. These methods continuously update model parameters or ensemble weights as new data arrive. A recent study [37] pointed out the information leakage problem of previous online time series prediction methods, where the model makes predictions and then evaluates them based on the historical time steps that have been pook-propagated for parameter updates. By redefining the setting to focus on predicting unknown future steps and evaluating unobserved data points, they propose a two- stream framework for online prediction, DSOF, which is conceptually similar to previous methods, generating predictions in a coarse-to- fine manner through teacher-studed model. Compared with these methods, we focus on the more difficult network architecture design. Instead, we propose a calibration aware framework that focuses on adjusting predictions online instead of learning predictions.
predictions while not requiring complex
A.3 Test-Time Adaptation.
Recent test-time adaptation techniques can be grouped by their adaptation strategy. Entropy mini- mization methods adjust a trained model to increase prediction confidence on unlabeled test data. For example, [73] propose TENT, which adapts model parameters by minimizing the entropy of its predictions on each test batch and updating batch-normalizzttion layers online. Feature alignment methods recalibrate feature distributions using test inputs; for instance, adaptive natch-normalization techniques re-estimate BN statistics on the target data to align feature distributions without labels. Self- sele--uueeei adaptation uses auxiliary tasks on the test data refine the model. Test-Time Train- ing [20, 26, 66, 78] converts each test input into a self self-supervised learning problem (e.g. predicting image rotations) and updates model parameters before making prediction. Similarly, SHOT [45] freezes the source classifier and updates the feature extractor on unlabeled target data using pseudo- labeling and information maximization. Each of these paradigms improves generalization under distribution shift without access to target labels. In contrast, unlike these methods that exploit self- supervisory information, our spatio-temporal prediction setting can use labels from historical test information, enabling explicit optimization of the objective at test time, ensuring real-time adaptivity.
18

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B Theoretical Analysis
B.1 Approximate Bound on Output Perturbation
Theorem 1 (Approximate Bound on Output Perturbation). Let Y E CBXNXM be the original frequency-domate representation of the backbone's prediction y BBXNTT and y E BBBNN* be the calibrated output. Suppose the amplitude and phase modulation parameters satisfy 1>g1 S ca and (xg for all groups g {l...., G}. Then, the 22-norm of the calibration ervor satisfies:
11 vl12 S (ea + +0)]|\|12,
where || is the Ez-norm Y.
Proof. Let AY = Y -Y denote the frequency-domain perturbation. For each group the calibrated spectrum is g A, (f +*%) Expanding Y around x 0, Xy 0, we approximate:
Y ~ Y (1 + X +
where higher-order terms (e.g., Xg x are neglected under small cor Cd- Thus, the perturbation is:
AY, Yg + )
The f--orm of AY is bounded by:
|
AY 1 S
2 +
E
|r (Ea + 1r
I /EGroup 9 g=1
SEGroup
By Parseval's theorem [55], 1l - y11 = | hence:
ll ul12 s V +
E 12l2 S (Ea e
Remark This theorem guarantees that the cdlibration-iduucel perturbation is sub-linearly bounded by the modulation parameters Cas Eg. By constraining these parameters (e.g.. via regular- ization during test-tine test-time adaptation). SD-Calibrator ensures the calibrated output does not deviate excessively from the original prediction, thereby avoiding overfitting transient noise. The group- wise parameterization further reduces the effective degrees of freedom (from O to O(N)), inherently limiting the risk of aver-parameterizatton
B.2 Controlled Descent on Streaming Memory Queues
Assumption 1 (Lipschitz Continuous Gradient of the Loss). The loss function L₂(A) ((o k is differentiable with respect to X, and its gradient VxLx(A) is Lipschitz continuous with constant Le > O. That is. for any da, db:
(V>L((>)) VALa(No)l2 LollAa dell2
According the descent Lemma [50], this implies:
Le(Aa)) < (e(Aa) + (VALe(Aa), >a) + Le 2
-a
Assumption 2 (Bounded Gradient). The norm of the gradient of the loss function with respect to the calibrator parameters X is bounded for any sample (x! ,Y(k)) x_()))from from the queue and any reasonable parameter set Ax:
||VLL(>W)l S Gmazz
for some constant Gmax 0.
This is common assumption, especially if the output of the calibrator and the true labels are within certain range, and the calibrator 9λ is well-behaved
19

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Proposition 2 (Controlled Descent on Streaming Memory Queues), Let the above assumptions hold.
For the k-th update step using the dequeued sample pair (Xo²) (k) Yo if the learning rate d satisfies 0 < < 2, decrease in the loss function for that specific sample:
Tee then the single gradient descent step on the SD-Calibrator parameters X ensures
(1-2 (--L-)) Lell (V
L2(x+1) S Lx()
Furthermore, the change in the calibrator parameters bounded:
|
A S 1/Gmaa
be the loss for the k-th dequeued sample. The parameter update rule is Ak+1 dE V/ La (Aa).
Proof. Let (A) ((gx(Jo(X;)) ( )) Yyuk)
From Assumption 1, we have:
(x S Lx(Ax) + (VALL(A)): Ae) L 1111441 - Ax
Le
Substitute Akt1 d Lx
Le -
[e(A++)) S (x(AE) + (VALa(Ae), - -VLA + 2
(x(A++) S (b()a) - VALL0 + Lan
||VALa(>)11
2
Factor out (AR)
La(Ax+1) & Lx(As) - (1 (1112)
Lo'1
(
2
For the loss to decrease (or stay the same if gradient is zero), require the term (1- Lall - (V+))())) 2 O. Since 0 and \ 2 0, we need (1- - > 0.
This implies 1 Lay 2 2 The n. Thus, if n R. the loss Lx(A++1) on the sample (X(*), x) strictly reduced if VALu(AR) #
For the bound on parameter change:
| Aell2 || - v/ (Ne)ll La
Using Assumption (ALa(Ae)l1 Gmazi
| Axll2 S n/Gmar
This completes the proof.
Remark 2. The proposition demonstrates that each single-step update is not arbitrary but moves the SD-Calibrator's 's parameters in a direction that reduces the prediction error on the specific historical sample (x(²)) k) used for the update, provided the learning rate 1j is chosen appropriately (i.e., small enough, specifically n < Lc). The condition 1j ensures that the update step does not overshoot. The second part, [| - Aull2 S 1TG shows that the magnitude of change in the parameters during each update is bounded. This is crucial for preventing the calibrator from experiencing excessively large or erratic parameter shifts from one step to the next, which could lead instability or overfitting noisy individual samples.
C
Method Details
C.1 Spectral Domain Calibrator
Algorithm Workflow. We summarize the algorithm workflow of Section 4.1 Algorithm 1.
Algorithm Pseudo-code. We further present Algorithm the form of pytorch pseudo code in Algorithm 2 for easy understanding.
20

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Algorithm Spectral Domain Calibrator
Require: Pre-trained backbone Sa. Test input x. Horizon length T,, Number of nodes N, Groups G
Ensure: Calibrated output gral
1: Get the backbone predictions: ÿ fo(x) E RXT
2: Compute M + 2 +
D I: Spatial-aware Decomposition
3: Apply real-to-complex FFT along time dimension for each node: Y < rFFT(() E CNXM
4: Decompose: + 1, 2
>> II: Group-wise Modulation
5: for g I.....G do
M MgLM/G]
g= G otherwise
6: Get group index: start (0- -g--1)|M/G] +1, end
7: Get learnable offsets: Xg E 1RN1, XØ E R
8: Modulate group 'luup-siic:AA + A(:, stort: end @ (1+
Pg + Plt start: endl 2
9: Reconstruct slice: Yjl: start end] t A o P
10: end for
> III: Inverse Transform
11: Inverse FFT: grall + irFFT(Y)) e RNXT
return geal
C.2 Lightning Gradient Update
Algorithm Pseudo-code. We summarize the algorithm workflow of Section 4.2 in Algorithm 3.
Algorithm Workflow. We further present Algorithm the form of pytorch pseudo code in Algorithm 4 for easy understanding.
D Experimental Details
D.1 Datasets Details
Our experiments are carried out on 14 real-world datasets from diffrent domain. The statistics of these spatio-temporal datasets are shown in Table 5.
We follow the conventional practice [40] to define the graph topology for all spatio-temporal datasets except Know-Air. Specifically, we construct the adjacency matrix A for each dataset using threshold Gaussian kernel, defined as follows:
exp -
if exp otherwise
d' (- and i $
Abyl
where dij represents the distance between sensors i and j.
standard deviation all distances, and is the threshold. We follow the recommended parameter settings in all corresponding papers.
For the KnowAir dataset, we follow the original paper [79] and calculate the correlation between nodes to construct the adjacency matrix. Intuitively, most acrosol pollutants are distributed within certain range above the ground. addition, the mountains along the two cities will hinder the transmission of pollutants to the PM2.s direction. Based on these intuitions, we constrain the weights the adjacency matrix by the following formula:
Apj) H -di) H(mo - mi;). where
di = =1pp: -yll.
my = sup (h(Ap: + A)p;) ((x(M 1c(0.1)
where P; is the location (latitude, longitude) of node i, h((p) is the height of location A, and || is the 1.2-norm of the vector. H--) is the Heaviside step function, where H(x)) if and only if a > 0. do and mg are the distance and altitude thresholds, respectively. Specifically, we also set the distance threshold de 300 km and the altitude threshold me = 1200 meters.
21

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Algorithm 2 -yyorch-style pseudocode: SD-Calibrator Class
class SD_ _D_Calibrator :
#**
Spectral Domain Calibrator with Phase Phase-Ampl Amplitude Modulation вн*
def
init__sell num nodes, bins, groups=4)
Args:
num_nodes: number of spatial nodes (M)
freq_bins: number frequency bins (M T // 1)
groups: number of frequency groups (G)
"**
super in self.groups groups
self.group_size freq bins // groups
# Learnable offsets for amplitude and phase: (G, N, 1)
self. un.Parameter( forch.zerooe (groups, num_nodes, 1)
self.lambda_ph Paramettr torch. zeros (groups, num_nodes, 1)
def forward y_pred)
Args:
y_pred: prediction from backbone, shape (B, 1, N, T
B defaults to 1, because only one sample can tested
Returns:
calibrated prediction, shape (B, 1, N, T)
B, N, T y_pred. shape
y y-pred 0]
# (B, N, T)
Yf torch fft rfft (y, dim=-1) A torch. (YF)
(B, N, M)
P torch. (Yf)
Yf corr torch. zeros licoossslkeeee_e
for in range (self.groups).
start g self.group_size
if == self folf.groups end T // 2
else
end (g 1) self. gelf.group_stie size
lam_a a self lambda_amgaaaa amp [g] unsquezee (0)
# (1, N, 1)
1am = self lambda__phiiii [g] unsqueeze (0)
A_g Ali, start:end] (1 lam a)
P_g Pl; " start:end] + lam_p
yf_corr [ ; start:end] A_g torch.exp (1j P_g)
y_time torch. fft. fft.irfft (YE_,oIE, n-T, dim=-1) return y_time. unsqueeze (1)
# (B, 1, M, F)
22

---

Algorithm 3 Flash Gradient Update Mechanism
Require: Test spatio-temporal sample stream {2z ) Pre-trained backbone fo. Streaming memory queue Q, Queue size T (equal to horizon length)
Ensure: Spectral domain calibrator ge, Prediction collection of test samples (1taa) Jt=1
1: Initialize Calibrator module Ge = (A*,A%)
X²), empty queue Q
2: for each timestep t 1,2,... do
3: Receive zt, compute default prediction Ōr fo(x))
D- Streaming Memory Queue
4: Use Algorithm I to obtain the calibration results: 0g go (fraat ; A)
5: Record ground truth: Y/ (collected by the value of 24, available T time steps in the future)
6:
Q.enqueue (xtt) y1))
t- II: Flash Gradient Update
7: if Ten( Q T then
8:
(No: Mo) Q.dequeue()
9: Use Algorithm to obtain the calibration results: 1aat = fo (x))
10: Update: +- V L 9
11: end if
12: end for
13: return 9e. (ffal }
Algorithm 4 PyTorch-style pseudocode: Flash Gradient Update Function
def
st st_ttc_test (self, test_loades node_num, T, groups)
Flash Gradient Update with Streaming Memory Queue
SDC SD _D_Calibrator (node_num, T//2+1, groups) to optimizer torch. optim. Adam (SDC. parameters (), 1r=le-4) loss_ fn self._ ()
SMO, preds Queue (maxsize=T), []
for x, y in teat_loader:
x, x.to (self. (self.device), y. (self. with torch.no torch.no_grad mafff.modlll. (x)
y-pred
Y_corr SDC (y_pred)
Use yocorr for inference
y_corr self. inverse tttsssserranooormmmm (y_ c_corr) preds. appendapppdddccc append (y_corr. detach () numpy ())
put ((x, y))
if SMQ. fuil()) ():
x_old, y_old get
with torch.no_grad n)
y-pred_old self model (x_old)
SDC. (rain)
y_corr_old old SDC [y [ty_pree__ole old)
y_corr_old self.scaler.
loss = loss fn (y_corr_old, y_old) loss. backwardd optimizer.stepl
SDC.eval ()
return preds
23

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Table 5: Summary of datasets used for our experiments. Degree; the average degree of each node. Data Points: multiplication of nodes and frames. M: million (10%).
Source
Dataset
Nodes
Time Range
Frames
Sampling Rate Data Points
PEMS03
358
09/01/2018 1/30/2018 26,208
minutes
9.38M
PEMS04
307
01/01/2018 02/28/2018 16,992
5 minutes
5.22M
[65]
PEMS07
883
05/01/2017 08/06/2017
28,224
minutes
24.92M
PEMS08
170
07/01/2016 08/31/2016
17,856
5 minutes
3.04M
[39]
UrbanEV
275
09/01/2022 02/28/2023
4344
1.19M
[79]
Know-Air
184
01/01/2015 12/31/2018
11688
3 hours
2.15M
[40]
METR-LA
03/01/2012 06/27/2012
34,272
minutes
7.09M
CA
8,600
01/01/2019 12/31/2019 35,040
15 minutes
30.13M
GLAA
3,834
01/01/2019 12/31/2019 35,040
15 minutes
13.43M
LargeST [48]
GBA
2,352
01/01/2019 12/31/2019 35,040
15 minutes
8.87M
716
01/01/2019 12/31/2020 70,080
15 minutes
5.02M
1087
1154
Air-Stream
01/01/2016 12/31/2019 34065
hour
15.79M
1193 + 1202
[10]
655 715 786
TEMS-Streamt
822
834 850 00900001-0000//00117 61,992
5 minutes
34.30M
- 871
103 113
Einegg--Stream
Unknown (245 days)
34,560
10 minutes
1.63M
122 + 134
D.2
Baseline Details
our paper, we cover various spatio-temporal forecasting methods under various learning paradigms. The following is a classification and brief introduction of these advanced methods:
Classical Learning Methods for Spatio-Tempore Forecasting.
STAEformer [47]: STAEformer is a spatial-temporal adaptive embedding transformer that makes vanilla transformer state-of-the-ard for apatio-temporal forecasting. It introduces novel archi- tecture to effectively capture the dynamic spatial and temporal dependencies in spatio-temporal data. https::////........ /g/ wwi.thtu..c..oooo com/ XDZhe leeeehheee im/
ST7N [86]: ST7N is spatial-temporal transformer network designed for traffic flow fore- casting. It leverages dynamic directed spatial dependencies and long-range temporal depen- dencies to enhance the accuracy of long-term traffic predictions. https:/ /ttp://gttttt com/ xumingxings jtUSSTNN
GWNer [83]: GWNer is graph wavenet model for deep spatial-temporal graph modeling. It effectively captures the complex spatial and temporal patterns in spatio-temporal data using combination of graph convolutional networks and dilated causal convolutions. https:// github. com/ wnnnnnnnnnna Graphh WaveNet
STGCN [90]: STGCN is spatio-temporal graph convolutional network framework for traffic forecasting. It integrates graph convolutional networks with temporal convolutional networks to model the spatial and temporal dependencies traffic data. https: //g thub. com/ hazdzz/ stgcn
STID [62]: STID a simple yet effective baseline for spatio-temporal forecasting. It addresses the indistinguihaability of samples in spatial and temporal dimensions by attaching spatial and temporal identity information, achieving competitive performance with concise and efficient models. https:/ /tl:://giitinn /github. com/ Gestalt Com/GestaltCooTTee
STID
ST-Norm [15]: ST-Norm is a method that applies spatial and temporal normalization for multi-
variate time series forecasting. It enhances the performance of forecasting models by normalizing the spatial and temporal features of the data. https: / http//tttttt github. com/JLDeng ST-NNrrn

---

Efficient Learning Methods for Large-Scale
Forecasting.
PatchSTG [17]: PatchTTG is attention-based dynamic spatial modeling method that irreg- ular spatial patching for efficient large-scale spatio-temporal forecasting. It reduces computational complexity by segmenting large-scale inputs into balanced and non-overlapped patches, captur- ing local and global spatial dependencies effectively. ht /github. com/ 1mi ssher/ patchste
OOD Learning Methods for
Forecasting.
STONE [68]: STONE is state-of oatee-of-the ff-the-art art apatio-temporal OOD learning framework that effec- tively models spatial heterogeneity and generates temporal and spatial semantic graphs, It intro- duces graph perturbation mechanism to enhance the model's 's environmental modeling capability for better generalization. https: /gi thub. com/ PoorOtterBob/ STTNEE-KDD---E-
Continual Learning Methods for
Forecasting.
EAC [10]: EAC is state-of-the-art method for exploring the rapid adaptation of models in the face of dynamic spatio-temporal graph changes during supervised finetuning. follows the principles of expand and compress to address the challenges of retraining models over data and catastrophic forgetting. https: / //github. com/ Onedean/ /EAC
STKEC [70]: STKEC is a continual learning framework for traffic flow prediction on expand- ing traffic networks. It introduces a pattern bank to store representative network patterns and employs a pattern expansion mechanism to incorporate new patterns from evolving networks with- out requiring historical graph data. https: / //gitttthu.u//. com./ waangbinwuu3116111 STKEC
In addition to these advanced spatio-temporal forecasting models, we also cover various competitive baselines that learn with test information, mainly the following three categories:
Popular test-time training methods
TTT-MAE [20]: TTT-MAE is test-time training method that masked autoencoders to adjust the model during inference. helps improve the performance of the model on unseen data by effectively utilizing test-time information. We adapt it to the backbone model of the spatiotemporal network, which is divided into a feature extractor and a prediction head as well as self-supervisory head. https: : /ggttub..../g.////g com/ Rima- ag / TTT MAE
TENT [73]: TENT a method for adjusting the model test time by normalizing the activation function to reduce the offset between the training distribution and the test distribution. It enhances the generalization ability of the model without retraining on labeled test data. Although it is theoretically designed mainly for the cross entropy loss function, that is, classification tasks, we can still directly apply it to our prediction scenarios. https: / tiuhh.u.... com/ DequanWang/tent:
Classical online time series forecasting methods
OCN [105]: OnlineTCN an online learning method based on a time convolutional network. It can adapt new data sequentially and is very suitable for real-time prediction applications where data arrives continuously. https: pestps:/ggitee /github. com/ www//occssleicccoocoooooccc locuslab/ 1ab//TN /TN
FSNer [57]: FSNet proposes fast and slow learning network for online time series prediction that can handle both sudden changes and repeated patterns. particular, FSNet improves on a slowly learning backbone by dynamically balancing fast adaptation to recent changes and retrieval of similar old knowledge. FSNer implements this mechanism through the interaction between two complementary components of the adapter to monitor each layer's contribution to missing events, and an associative memory that supports remembering, updating, and recalling repeated events. https: : ////t/gttb/////// com/
/fsnet
OneNer [81]: OneNer dynamically updates and combines two models, one focusing on modeling dependencies across time dimensions and the other focusing on cross-variable dependencies. The approach integrates reinforcement learning-base based methods into traditional online convex programming framework, allowing the two models to be linearly combined with dynamically adjusted weights, thereby addressing the main drawback of classical online prediction methods that are slow to adapt to concept drift. https: // / thub. com/ f aazzaagll
Maaaanll44 114 Oneeeet
25

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Advanced spatio-temporal forecasting methods using test information.
CompFormer [100]: CompFormer proposes test-time compensated representation learning framework, including spatiotemporal decomposed datahase and a multi-head spatial transformer model. The former component explicitly separates all training data along the time dimension according to periodic features, while the latter component establishes connections between recent observations and historical sequences in the database through spatial attention matrix. This enables it to transfer robust features to overcome abnormal events
DOST [72]: DOST proposes a novel online continuous learning framework tailored to the characteristics of spatiotemporal data. DOSTadopts an adaptive spatiotemporal network equipped with variable independent adapters to dynamically address the unique distribution changes of each urban location. addition, to adapt to the gradual nature of these transformations, wake-sleep learning strategy is used, which intermittently fine-tunes the adapters during the online stage to reduce computational overhead.
D.3 Protocol Details
Metrics Detail. We use different metrics such as MAE, RMSE, and MAPE. Formally, these metrics formulated following:
MAE
9sh.
RMSE
1 (ys 0.)3.. MAPE 100% y:
Ui
Y2
y/
where n represents the indices of all observed samples, y! denotes the i-th actual sample, and y is the corresponding prediction.
Parameter Detail. For the
settings of all baseline methods, follow the parameter settings recommended by the corresponding references. For our paper, except for the robustness study section, all other experimental hyper-parameteers are uniformly: the learning rate Ir le-4, and the number of groups m is set to 4. All experiments are conducted on a Linux server equipped with AMD EPYC 7763 128-Core Processor CPU (256GB memory) and 4 NVIDIA RTX A6000 (48GB memory) GPUs. To carry out benchmark testing experiments, all baselines are set to run for duration of 100~ 150 epochs by default (depends on the corresponding paper), with specific timings contingent upon the method with early stop mechanism. The number of early stopping steps set to 10.
E
More Results
E.1
Complete Results Table
We provide complete information of the experimental tables in the main text as Table 6, 7,8
E.2
Visualization Case
We provide more visualization examples test set predictions to illustrate the effectiveness of our calibration, as shown in Figure 9
F
More Discussion
F.1
Distinction between
Forecasting and Long-Term Time Series
As stated in the paper, our work adheres to the common settings of previous short-term and long-term spatio-temporal forecasting studies (e.g., 12 + 12, 24 + 24) [59, 61]. However, we are fully aware of the 96 - 96 720 settings prevalent in current long-term time series forecasting. We wish to share our insights regarding this:
There has been long-standing debate concerning the long-term predictability of time series [4, 8). which we not intend to overly critique here. Nevertheless, important to note that in spatio- temporal forecasting, specifically in traffic flow theory research, previous studies [101] utilizing
26

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Table 6: Performance comparison of different models w/ and w/o ST-TTC in the few-shot scenario.
Tranforme-baodd
Graph-hased
Models
SZAE [47]
STIN [36]
GWNNer
STGCN [o]]
STID [62]
ST-Now [1:5]
ST-120
X
MAE
20.57au
22.96.a:0
21.32aa0
21.15
21.70am
21,43
21.
21.28
21,81un3s
21.57
21. Saik:
20.74
PEMS-02
KMSE
37.90.2-1
37.10
19.1
34.52
34.28
34.82.300
$4,08
35,58und)
35.1
J3 78
3307.035
MAPR(S)
21 10
21.23
21.
21:30
19.70
.1.59
21.27
22.57-11
22.04
MAB
35.10
34.57.08
20.76
30.22
32.87.15
29.49
30.65
30.5
PEMS-N4
KMSB
30.94
50.25
44. 17
45.99
3000
49.73
45. M0
45.47
64.8
48.62
45. 00
45,83
MAPE(S)
25 23.55+
22.97+
30.72
22.70
21. 75400
MAB
30.45o
29.70
31. 31..0
31.22
32.17:00
32.82
32
5188
50, 12.4
30,91
31 14.00
30.
67
RMSR
17.80k
16.57 46.8
45.96-10
10.85
49.90 96
88 65
47.50
46.71
47 27
46.54 -4.4
M)
18:87a
14.58
15.04
16.07
15.03
14.00aa0
14.18
MAB
36.98
38.47
24. 17
2588
26
94
M5 M7-175
28.7
24 34.3t
24.06-047
PEMS 08
KMSB
34.61:1044
$2.45
16 40
40.51.111
28, 53
57 80.000
37,00 37.0220077
37.36
37. 17.4
37. .7.30
MAPR(S3
27.38
26.19
10c
17:00
16.82.100
17.84
15.00
14.43
18.28
14,99
MAB
18.48at
18.16
20.47.03
19,85
19:02.003
19,04,02
20.0
30.09.
22,08.123
21.73
21. 21.52:159
20, 20.92.035
KxowAlr
RMSB
27:20 m
26.97
75 10000
mas
17.70
-7.58
250 03
30.20 en
29.0
28.86
MAPE((S)
72.37am1
70L14.10
85.30
81.21
80.40os.o
78.49
81. 41.00zaa
82.13
95.69..m
95.24
91.11.12
MAb
0.3Men
4.05
3.8
4:21
4.10.03
3.30
3.24
4.8000
4.7
UrNNEEV
RMSE
0.15
6,88 on
0.8
6.71
0.64e in
6.59
6.7
6.61-177
5.51
5.42 m
8 8.5tec
8:36-11
MAPE
11.60am
31.33a.
08.41a00
37.32
35.78
34.95.1.1
40.03a144
39.57.132
$1,42w0
30.75
43.20
42.36.122
Table 7: PatchSTG with ST-TTC in LargeST Benchmark.
Methoos
Hoeizon
Herizon
Horizon
Average
MAF
RMSR
MAPP(S)
MAF
RMSF
MAPP(S)
RMSE
MAPF(S)
MAR
MAPR(S)
PT
25.34
9.22
16.86
25.63
11:31
20.66
36.27
14:72
16.90
11.23
T72
14.44
24.07
8.70
16.66
28.18
20.37
35.68
14:27
16.72
28.83
11:11
10.8%
11.1%
1.666
11.2%
11.6%
11.6%
11.4%
1 .1.8%
3.15
11.1%
11.5%
1 11.1%
PTtcSTTG
1681
28.71
12.25
19.68
33.09
14.51
23.49
39.23
18.93
19.50
33.16
14.64
GBA
w/ 51 172
16.65
28.31
12.12
19.30
32.40
14.35
22.96
35.33
18.30
19.16
$2.49
14.48
11.0%
1.4%
1.19
11.9%
12.1%
11.1%
12.3%
4.3.5%
33.3%
11.7%
1.2.0%
0 11.1%
PathSTGG
15.84
26.34
9.27
19.06
31.85
11:30
23.30
39.64
14:60
18.96
32.33
11.44
GLA
w/ S1-170
15.78
26.08
9.15
18.76
31.29
11.21
22,86
38.89
14:35
15.09
31.78
11.36
50.4%
11.0%
1.39%
11.6%%
11.8%
00.8%
12009
11.9%
1.77%
11.4%
1.77%
1 0.77%
PatcSTGG
14.69
24.82
10.51
17.41
29.43
12.83
21.20
36.13
16.00
17.35
29.79
12.79
CA
w/ SI-ITC
14.59
24.61
10.40
17.14
28.97
12.51
20.76
35.38
15.54
17.10
29.31
12.53
1.88%
1100%
1.668
12.5%
1.2.1%
2.11%
2.0%
1..4%
11,6%
residual analysis have indicated that, after minimizing periodicity, the correlation between traffic
data beyond one hour and the past hour's observations is significantly limited for most sensors. Furthermore, typical traffic sensor data collection frequency is approximately 5 minutes. Therefore, for practical traffic forecasting and decision decision-making scenarios, which usually focus on the next 1-2 hours (i.e., max 24 steps), our settings are more aligned with real-world applications.
Given that temporll forecasting can be considered a complex extension of time series forecasting, the additional dimension of sensor count (up to hundreds or thousands) results in an order of magnitude higher data training cost. This is a secondary reason why existing spatio-temporal forecasting often considers 12-step settings.
@ Another notable finding is that a recent study on the accuracy law of deep time series forecast- ing [80], emerging subsequent to this paper, identifies a significant exponential relationship between the minimum prediction error of current deep forecasting models and the complexity of window series patterns. Adopting a Spectral-domain perspective similar to that of this paper, it defines the complexity of series patterns as the total variance of the amplitude spectrum distribution, thereby characterizing the intrinsic heterogeneity of series variations within each relevant window. This ap- proach aligns with ours and provides a novel perspective explain the learnability and effectiveness of the single-step gradient descent in our calibrator. While the study focuses solely on univariate time series forecasting, this limitation does not inherently undermine its relevance. It worth noting that the study concludes that mainstream time series models have not yet reached saturation on traffic scenario-based benchmarks. However, we hold a different view, arguing that this conclusion primarily stems from the study's exclusive use of time series forecasting models, while neglecting mainstream
27

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4601
Grand
150
Pred wio TTC Meas
Value (Nodl 56)
wio TEC 10-30% knorved
Frod Moon
1:0
506
1003
1500
2000
2500
>300
3520
Test Time Step Index
300
Ground
Value (Node RSS)
250
wib TTC
Fiod TTC Mon
200
TTC (0000)
1900 Test Time Stop Index
2000
Lamond Urith
Pred TTC Monn
Valie (Node 22)
TTC ars braavod
10-
992
Step
Prod We TTC Moon
Válise (Node (03)
wis TTT In Witt tranal
Prad ITC Mezz
30m
Tost Time Step Index
Figure show case.
spatio-temporal dependency modeling models. For further in-depth discussions, we suggest that future research should address this aspect.
F.2 Limitation
In this paper, propose novel paradigm for spatio-temporal forecasting: test-time computing. Although there are still many potential areas for improvement, given the superiority and generality of our ST-TTC, we believe this provides pathway for future exploration of larger-scale and more effective test-time computation. While we have taken a small step in this direction, several limitations warrant attention:
Our current study does involve testing on spatio-temporal foundation models. The fundamental reason behind this is our belief that true spatio-temporal foundation models do not yet exist. Although some preliminary exploratory work has been done [92, 93, 42, 41, 91], they are far from achieving true zero-shot generalization. However, considering their future inevitability, we believe that further improving the paradigm of test-time computation, especially how to activate and scale the internal ca- pabilities of spatio-temporal foundation models during testing, goes beyond the design philosophy of our proposed learning with calibration. Nevertheless, our experiments still provide some preliminary guidance and insights.
28

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Table 8: Performance of spatio- temporal shift dataset SD-ratio(%)) all nodes and unknown nodes at different spatio-temporal shift levels.
All Node
New Node
Dataset
Horizon
Methods
MAE
RMSE
MAPE(S)
MAE
RMSE
MAPE(S)
STONE
40.74.421
58.4333.67
45.82.9.0
46 46.25.7.02
66.97
47.57.8.02
12
w/ ST-TTC
39.41=382
57.44
38.02a5.19
44.65.6.99
65.06
41.8525.87
A
3.3%
1.7%
1. 17.0%
3.55
J 2.9%
J 12.0%
SD-10%
STONE
30.18-1.19
42.83a1.3
39.44=3.0
32.79
46.68a387
40.12
Avg.
w/ TTC
28.29-1004
41.50=1.16
28.66-1.8
30.66-2.68
44.44=3332
30.80a1.5
6.3%
3.1%%
27.3%
6.5%
4.8%
23.2%
STONE
35
52.87+0.57
34.05-1.7
43.65 13.65
66.07-1.8
30.47
12
w/ ST TTCC
34.86-0
52.25x0.54
29.80.0.7
41.93:0.62
63. 19.0.9
27.70
1.3%
4 1.2%
4 12.5%
4. 3.9%
4 4.4%
4 1.91%%
SD-15%
STONE
28.45_005
41 30an.2
36.02.2.9
33.20a0.69
49.19s097
29.77.3.00
Avg.
w/ ST TTC A
26.59
39.90.0.0
24.96-100
30.65.0.29
46.24=0.52
22.50 3.
6.5%
3.4%
3.307%%
4.7.%
4 6.0%
4 24.4%
STONE
76
53.87+0.44
34.19-1.8
41.64ei.23
63.19 633119-2.11
37.38-3.29
12
w/ ST-TTC A
35.08
52.37an.7
30.55
40.10at.41
60.77
33.20.2.7
2.9%
2.8%
4 10.6%
1 3.7%
J. 3.8%
4. 1.98%
SD-20%
STONE
28.86-0.13
41.72+t.14
34.89-1.15
31.46-995
46.06-1.4 60
36.35
Avg.
w/ ST-TTC TTC
26.67-029
39.71-8.08
24.92-081
28.94-0.99
43.29
26.60+2.49
4 7.6%
4 4.8.%
J. 28.6%%
4. 8.0%
4. 6.0%
4 26.8%
is undoubtedly encouraging that our current calibration mechanism more effective in large-scate and -ut-of-distribution scenarios. However, for commonly used small spatio-temporal benchmark datasets, the performance improvement is not yet significant. Therefore, how to effectively improve the performance of test-time computation small-scale spatio-temporal datasets still requires exploration, and we reserve further improvement efforts for future research.
We observed in experiments that utilizing larger amount of test information that is more similar to the current test sample does not significantly affect the results. This certainly beneficial for real-time efficiency requirements. However, considering our current efficiency is already sufficiently good, further exploration is needed on how to potentially slow down the test-time computing process to make it more scalable and improve forecasting effectiveness.
E33 Future Work
Building upon the research direction presented in this paper, we envision future work encompassing two main aspects:
Exploring how integrate serieval--uugeentee techniques filter more effective learning samples from arbitrary external scenarios, thereby combining them with our test-time computation framework to optimize performance on small-scale datasets.
Investigating the construction of real spatio-temporal foundation models that encapsulate internal compressed knowledge, and exploring how to activate this internal capability during test time.
G Broader Impacts
This paper aims to promote the real-world usability of spatio-temporal forecasting models. We propose novel paradigm, namely test-time computing of spatio-temporal forecasting. This paradigm shows significant generalization, universality across multiple scenarios, multiple tasks, multiple learning paradigms, and scalability to improve performance, providing valuable insights for future research and application value for practitioners. This paper focuses mainly on scientific research and has no obvious negative impact on society.
29

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Reviews:
[{"review_id": "SMzVFyRehf", "reviewer": "Reviewer_eeBu", "summary": "Addressing distribution shift in spatio-temporal data requires some form of adaptation at test time since we rarely see all possible changes during training stages. The work thus proposes ST-TTC, which calibrates the model output in the frequency space through a learned parameter-parsimonious transformation. The adaptation module is continuously updated during inference. The experiments confirm the method's effectiveness and efficiency.", "questions": "Q1: Regarding l. 351, \"fewer groups generally lead to poorer performance\": Fig. 7 (middle) shows rather constant behaviour for varying $m$, much like $n$ in Fig. 7 (right). How was the cited statement derived from those figures?", "limitations": "Nothing is provided in the main text, which is unfortunate. However, Appendix F.1 discusses limitations in great detail.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 2, "strengths_and_weaknesses": "**Strengths:**\n- The writing is of very high quality and clarity, with exceptional Sections 4 & 5.\n- The problem is significant, and the solution is not very original, yet possibly novel.\n- The method is conceptually simple.\n- While I am not sufficiently familiar with the field to judge the overall novelty or the completeness of datasets and baselines, their volume appears rather comprehensive.\n\n**Opportunities for improvement (weaknesses):**\n- It is unclear how the offsets $\\lambda^\\alpha$ and $\\lambda^\\phi$ are initialized and learned before inference time from the main text. Pages 21-22 clarify this, but it should be stated more clearly that there is no training stage in the main paper.\n- Regarding ll. 287ff: The long-term setting is set up for only 24-to-24 time steps. However, recently, long-term time series forecasting often looks at hundreds-to-hundreds (see, e.g., Wu et al. (2022) and many more recent works). Possibly, this is substantially different in spatio-temporal forecasting.\n- Regarding Thm. 1 in App. B.1: The theorem claims an exact upper bound, but the proof relies on a first-order Taylor expansion, which only provides an approximate result. To be rigorous, the theorem should either state that the bound is approximate or the proof should account for the higher-order terms.\n- Checklist item 7 is answered with \"yes\", yet the work only provides variance measurements and no statistical tests.\n\n**Minor Comments:**\n- Fig. 3 (left): Why are the lines connected across datasets? This suggests a connection that is not there. A bar plot might be more appropriate.\n- L. 366: \"noval\" -> \"novel\"\n- Ll. 874-886 are a summary of the entire work and are misplaced there. They should get deleted.\n- Regarding Thm. 1 in App. B.1: The result gets weakened in the very last step (last \"$\\leq$\") of the proof, making the bounds less tight than possible. In fact, regarding Remark 1, the bounds are actually sub-linear in the modulation parameters.\n\n**References:**\n- Wu, H., Xu, J., Wang, J., & Long, M. (2022). Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting. arXiv. https://doi.org/10.48550/arXiv.2106.13008", "was_revised": true, "final_justification": "The rebuttal was very convincing. I keep my \"5: Accept\".\n\nThe statistical significance testing is still missing. The AC should verify that them being present in the camera-ready version as promised by the authors.", "rebuttal": "Dear Reviewer eeBu,\n\nWe sincerely appreciate the time and effort you dedicated to providing insightful feedback on our manuscript. We are honored that you recognized our hard work. We have carefully considered each of your comments and addressed them point by point, categorized by different type.\n\n---\n\n> ### A. Method-related\n\n- **`A.1: Initialization of Offset Parameter:`**\n    - We acknowledge the lack of explicit detail regarding the initialization of the offset parameter in the main text. As you correctly pointed out, in Algorithm on page 21, both $\\lambda_\\alpha$ and $\\lambda_\\phi$ are clearly initialized to 0. The underlying motivation for this is to unify the code design of Algorithm 3, thereby preventing erroneous calibration of predictions before the calibration parameters are learned (i.e., during a very short warm-up period before acquiring the first sample-label pair). We apologize for any potential confusion and will incorporate these details into the main text.\n- **`A.2: Distinction between Long-Term Time Series and Spatio-Temporal Forecasting`**\n    - As stated in the paper, our work adheres to the common settings of previous short-term and long-term spatio-temporal forecasting studies (e.g., 12 → 12, 24 → 24) [1, 2]. However, we are fully aware of the 96 → 96~720 settings prevalent in current long-term time series forecasting. We wish to share our insights regarding this:\n        - There has been a long-standing debate concerning the long-term predictability of time series [3], which we do not intend to overly critique here. Nevertheless, it is important to note that in spatio-temporal forecasting, specifically in traffic flow theory research, previous studies [4] utilizing residual analysis have indicated that, after minimizing periodicity, the correlation between traffic data beyond one hour and the past hour's observations is significantly limited for most sensors. Furthermore, typical traffic sensor data collection frequency is approximately 5 minutes. Therefore, for practical traffic forecasting and decision-making scenarios, which usually focus on the next 1-2 hours (i.e., max 24 steps), our settings are more aligned with real-world applications.\n        - Given that spatio-temporal forecasting can be considered a complex extension of time series forecasting, the additional dimension of sensor count (up to hundreds or thousands) results in an order of magnitude higher data training cost. This is a secondary reason why existing spatio-temporal forecasting often considers 12-step settings.\n        - Despite this, we have included an experimental performance comparison for 96 → 96 prediction on the PeMS08 dataset, using STID as the backbone network, as shown below:\n        - The results show that our approach can also achieve certain performance improvements in long-term forecasting. We sincerely hope that these insights can help you better correct misunderstandings.\n\n| Model | MAE | RMSE | MAPE(%) |\n| --- | --- | --- | -- |\n| w/o ST-TTC| 16.84 | 26.80 | 11.59 |\n| w/ ST-TTC | 16.68 | 26.52 | 11.50 |\n\n---\n\n> ### B. Presentation-related\n\n- **`B.1: Figure 3 (Left) Visualization:`**\n    - You are correct that a bar chart is more appropriate for Figure 3 (Left). We apologize for this oversight; the revised version will feature a bar chart.\n- **`B.2: Discussion of Limitations in main text:`**\n    - We will adopt your suggestion and briefly outline potential limitations in the conclusion section.\n- **`B.3: Typo Errors in Line 336 and Figure 1b:`**\n    - Thank you for your meticulous review. We will conduct a thorough check for all potential typo errors, and rectify them accordingly.\n\n---\n\n> ### C. Experiments-related\n\n- **`C.1: The statement \"fewer groups generally lead to poorer performance\" on line 351 caused confusion. Figure 7 (middle) has a constant behavior similar to Figure 7 (right).`**\n    - We apologize for the confusion caused. This visual discrepancy is due to the differing metric scales between Figure 7 (Middle) and Figure 7 (Right). In actuality, the significant changes in learning rate overshadowed the impact of varying group numbers. However, performance indeed deteriorates as the number of groups decreases. Below we provide a specific example with a learning rate of 1e-3. We will avoid the above misunderstandings in the revised version.\n\n| #Groups | MAPE(%) |\n| --- | --- |\n| 1 | 24.93 |\n| 2 | 24.92 |\n| 4 | 24.85 |\n| 7 | 24.85 |\n\n- **`C.2: Statistical Significance Testing`**\n    - Thank you for your rigorousness. We plan to include statistical significance test results in the revised version.\n\n---\n\n> ### D. Theoretical-related\n\n- **`D.1: Theorem 1 should be stated as an approximate result and is, strictly speaking, sub-linear.`**\n    - We appreciate your precision. We will add more detailed supplements and discussions in the revised version.\n\n---\n\n**References:**\n\n[1] Zezhi Shao, et al. Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis. TKDE, 2024.\n\n[2] Wei Shao, et al. Long-term spatio-temporal forecasting via dynamic multiple-graph attention. IJCAI, 2022.\n\n[3] Christoph Bergmeir. Fundamental limitations of foundational forecasting models. NeurIPS Workshop InvTalk, 2024.\n\n[4] Lorenzo Brigato, et al. Position: There are no Champions in Long-Term Time Series Forecasting. arXiv, 2025.\n\n[5] Vincent Zhihao Zheng, et al. Probabilistic Traffic Forecasting with Dynamic Regression. Transportation Science, 2025.\n\n---\n\nThank you for your invaluable feedback. We will appropriately incorporate these detailed discussions into the final revised version. Once again, we are grateful for your insightful guidance!\n\nBest regards,\n\nAuthors."}, {"review_id": "Cw04jWnTbZ", "reviewer": "Reviewer_N98K", "summary": "The paper proposed a novel test-time computing paradigm for spatio-temporal forecasting, ST-TTC, where a plug-in calibration module is added between the base-model prediction and the final predictions. This calibration module improves performance at sporadic non-stationary spatio-temporal behavior of the data without expensive training. The method is evaluated on traffic, meteorological, and energy datasets. ST-TTC shows promising improvement in performance by efficiently using the computing resources.", "questions": "None", "limitations": "1) Lack of testing on spatio-temporal foundation models\n2) Does not significantly improve performance on small spatio-temporal benchmarks", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1) The codebase is available and documented for review.\n2) The introduction motivates the problem very well.\n3) Figure 1 clearly depicts the difference between test-time training and online continual learning.\n4) Related work is well placed.\n5) The paper explains motivation, key challenges, implementation details with mathematical details, complexity, and theoretical analysis for the methodical design choices.\n6) Tested on six publicly available datasets with Transformer-based, Graph-based, and MLP-based base models. Also outperforms the baselines in most scenarios.\n7) The evaluation shows improvement (%) for different base-model architectures.\n8) ST-TTC is efficient and robust, as shown in the results\n9) Clearly mentioned the observed limitations and future directions.\n\nWeakness:\n1) Missing an Overview diagram for the methodology. I suggest including a pictorial representation of the methodology.", "was_revised": false, "final_justification": "", "rebuttal": ""}, {"review_id": "UwLmplhcoI", "reviewer": "Reviewer_xiA6", "summary": "This paper introduces Spatio-Temporal Test-Time Computing (ST-TTC), a novel and lightweight calibration framework for spatio-temporal forecasting that addresses challenges such as non-stationarity and distribution shifts without modifying the backbone model or requiring additional training data. The proposed method incorporates a Spectral Domain Calibrator, which mitigates periodic biases in the frequency domain through phase-amplitude modulation, alongside a Flash Gradient Update mechanism utilizing a Streaming Memory Queue to efficiently adapt calibration parameters during inference. Extensive experiments across diverse benchmarks consistently demonstrate that ST-TTC enhances forecasting accuracy over strong baselines while incurring minimal computational overhead.", "questions": "The experimental evaluation is comprehensive. However, my main concern lies in the performance under OOD conditions. Since the extent of distribution shifts in the datasets is not quantified, it remains unclear how effectively the proposed method can handle truly OOD scenarios. In particular, spatio-temporal distribution shifts can manifest at both structural and temporal levels. While Figure 5 offers some insight into this, the degree of shift introduced by new nodes is not explicitly presented. It would be very helpful for the authors to clarify the following points:\n\n1. To what extent do temporal feature distribution shifts exist in the datasets used? It would be beneficial to quantify the degree of such shifts using appropriate metrics or visualizations.\n\n2. Does the current framework adapt to structural shifts such as changes in node homophily or the overall graph topology?\n\n3. Does the proposed framework support dynamic graphs with evolving structures over time?", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths 1.\tThe paper addresses an important and practical problem in spatio-temporal modeling. Non-stationary data is prevalent and challenging, and proposing a generalizable framework to leverage test-time data is a promising direction.\n2.\tThe use of spectral domain calibration with phase-amplitude modulation is theoretically grounded, interpretable, and empirically shown to effectively mitigate non-stationary distribution shifts to a certain extent.\n3.\tThe experimental evaluation is thorough, covering a broad range of models, datasets, and scenarios, including few-shot, long-term, large-scale, out-of-distribution (OOD), and continual learning settings, demonstrating the method’s versatility.\n\n⸻\n\nWeaknesses\n1.\tThe proposed approach focuses on periodic biases and may not generalize well to non-periodic or abrupt structural changes commonly observed in spatio-temporal data.\n2.\tAlthough the method is designed to handle OOD scenarios, the paper lacks a formal and quantitative definition of OOD in the spatio-temporal context, and the degree of distribution shifts present in the evaluated datasets remains unclear.", "was_revised": true, "final_justification": "The authors have addressed most of my concerns regarding the effectiveness of the proposed method in the structural shift setting and have clarified my questions about the OOD setting, temporal shifts, and dynamic graphs.", "rebuttal": ""}, {"review_id": "x7leyptvk3", "reviewer": "Reviewer_T8C2", "summary": "This work proposes ​ST-TTC, a novel test-time computing paradigm for spatio-temporal forecasting that dynamically corrects prediction biases during inference, and conduct effective experiments on real-world evaluation datasets.", "questions": "1. Video prediction is widely adopted task format for spatio-temperol prediction, especially in met and traffic domains, does ST-TTS works in video prediction tasks?\n\n2. Apart form period shift, can ST-TTS face other OOD challenges, like corrupted input data, incident/extreme cases ?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength \n1. Calibration is a light-weighted test-time training method, and a good solution for maintaining a long-term deloyed spatial-temporal prediction model.\n2. Calibrate in spectral space sounds promising.\n3. The method acquires universal performance gain across multiple real-world benchmarks.\n\nWeaknesses\n1. The paper discuss the difference between test-time training and other solutions for OOD prediction, but does not conduct experiments comparing these methods. The authors need to answer with experimental results: \"In what case, we need to consider test-time training instead of CT or Online CT etc. ?\"\n2. The paper report the relative improvement ratios, but the absolute improvements seems not so significant.", "was_revised": true, "final_justification": "This paper presents Spatio-Temporal Test-Time Computing (ST-TTC), a novel lightweight calibration framework for spatio-temporal forecasting that tackles non-stationarity and distribution shifts without modifying the backbone model or needing extra training data. The paper perform detailed experiments and is well written.", "rebuttal": ""}]

Author rebuttal:

Meta-review: This paper focuses on distributional shifts in spatio-temporal data. To address this issue, the authors propose a novel test-time computing paradigm, termed learning with calibration (ST-TTC), which aims to capture periodic structural biases induced by non-stationarity during the testing phase. Overall, the work is well-presented and solid in both technical quality and experimental evaluation. All reviewers reached a positive consensus after the author–reviewer discussion stage.
Decision: Accept (spotlight)