Enhancing Multivariate Time Series Forecasting with Global Temporal Retrieval
Authors: Fanpu Cao
Lu Dai
Jindong Han
Hui Xiong
Venue: ICLR 2026 Poster (2026)
Keywords: Time-series forecasting
model plugins
Primary area: learning on time series and dynamical systems
TL;DR: A lightweight, model-agnostic plug-and-play module for time-series forecasting models.

Abstract: Multivariate time series forecasting (MTSF) plays a vital role in numerous real-world applications, yet existing models remain constrained by their reliance on a limited historical context. This limitation prevents them from effectively capturing global periodic patterns that often span cycles significantly longer than the input horizon—despite such patterns carrying strong predictive signals. Naïve solutions, such as extending the historical window, lead to severe drawbacks, including overfitting, prohibitive computational costs, and redundant information processing. To address these challenges, we introduce the Global Temporal Retriever (GTR), a lightweight and plug-and-play module designed to extend any forecasting model’s temporal awareness beyond the immediate historical context. GTR maintains an adaptive global temporal embedding of the entire cycle and dynamically retrieves and aligns relevant global segments with the input sequence. By jointly modeling local and global dependencies through a 2D convolution and residual fusion, GTR effectively bridges short-term observations with long-term periodicity without altering the host model architecture. Extensive experiments on six real-world datasets demonstrate that GTR consistently delivers state-of-the-art performance across both short-term and long-term forecasting scenarios, while incurring minimal parameter and computational overhead. These results highlight GTR as an efficient and general solution for enhancing global periodicity modeling in MTSF tasks. Code is available at this repository: https://github.com/macovaseas/GTR.

Published as a conference paper at ICLR 2026
ENHANCING MULTIVARIATE TIME SERIES FORECAST- ING WITH GLOBAL TEMPORAL RETRIEVAL
Fanpu Cao', Lu Dai Jindong Han', Hui Xiong
'The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China The Hong Kong University of Science and Technology, Hong Kong SAR, China Shhnndng University, Jinan, China
Ecao6288connee hkust-uuu perst-gz.o gz edu, cm; ddaiaadeeee aeriee ust.hk; jindong han edu. cn; xionghu xionghui@ust.hur @ust.hk
ABSTRACT
Multivariate time series forecasting (MTSF) plays a vital role in numerous real- world applications, yet existing models remain constrained by their reliance a limited historical context. This limitation prevents them from effectively capturing global periodic patterns that often span cycles significantly longer than the input horizon- Norizon-despite such patterns carrying strong predictive signals. Naïve solutions, such as extending the historical window, lead to severe drawbacks, including over- fitting, prohibitive computational costs, and redundant information processing. To address these challenges, we introduce the Global Temporal Retriever (GTR), lightweight and plug-and-play module designed to extend any forecasting model's temporal awareness beyond the immediate historical context. GTR maintains an adaptive global temporal embedding of the entire cycle and dynamically retrieves and aligns relevant global segments with the imput sequence. By jointly modeling local and global dependencies through 2D convolution and residual fusion, GTR effectively bridges short-term observations with long-term periodicity without alter- ing the host model architecture. Extensive experiments six real-world datasets demonstrate that GTR consistently delivers state-of-the-arg performance across both short-term and long-term forecasting scenarios, while incurring minimal parameter and computational overhead. These results highlight GTR as an efficient and general solution for enhancing global periodicity modeling in MTSF tasks. Code is available at this repository: https: /gi thub. com wtt.co/cccaaaeecceeeee httmm//acvaaaaaeeeeeaa GTR.
INTRODUCTION
Multivariate time series forecasting (MTSF) is critical task with widespread applications in numer- ous domains, including energy grid management (Alvarez et al., 2010), climate modeling (Mudelsee, 2010), macroeconomic planning (Granger & Newbold, 2014) and traffic flow management (Ishak & Al-Deek, 2002). Accurate forecasting in these areas is essential for resource optimization, strategic planning, and risk mitigation. In recent years, deep learning-based based methods have achieved state- of-the-art performance in MTSF tasks, with a variety of architectures including MLPs (Das et al., 2023), RNNs (Lin al., 2025c), CNNs (Liu al., 2022a), Transformers (Zhou et al., 2021) and Mambas (Zhang et al., 2023) demonstrating strong performance.
fundamental challenge in time series forecasting lies in effectively modeling periodicity. Real- world time series data often exhibit complex periodic patterns at multiple scales, which can be broadly categorized into local and global cycles (Wang al., 2024c). Local periodic patterns, such as daily fluctuations, are characterized by their high frequency and distinct, repetitive nature, making them easy for models to capture from limited historical window. contrast, global periodic patterns-la like weekly, monthly, or seasonal patterns gradually unfold over long time spans, occur less frequently within look-back window, and often obscured by non-stationary phenomena such as extreme values, missing data, and noisy perturbations (Liu et al., 2022b). Despite these difficulties, effectively capturing global periodic
more significant challenge. These
"Corresponding author.

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Published as a conference paper at ICLR 2026
information is crucial, the predictive signal from global cycle can be much stronger than that from local, adjacent patterns. As illustrated in Figure 1, the correlation between a time segment and its distant counterpart in the global cycle is often higher than its correlation with its immediate neighbors. This demonstrates that global dependencies can be more informative for forecasting than adjacent temporal data, making them essential to harness for achieving high-accuracy predictions.
To capture complex periodic dynamics, researchers have explored several strate- gies. One prominent line of work em- ploys seasonal-trem decomposition, iso- lating periodic components from the series for specialized modeling (Wu et al., 2021; Zhou et al., 2022a; Zeng et al., 2023; Wang al., 2024c; 2025a). Another strategy operates in the frequency domain, using tools such as the Fast Fourier Transform (FFT) (Brigham & Morrow, 1967) cap- ture cyclical signals more explicitly (Zhou al., 2022b; Xu al., 2024; Yi al., 2024). A third stream focuses on reshaping data representations; for instance, Times- Net (Wu et al., 2022) transforms ID se- quences into 2D tensors better capture both intra-ped antra-period and inter-perion varia- tions. These approaches have led notable progress, but they all share a fundamental limitation: they operate strictly within a fixed look-back window. As result, when the true cycle length extends far beyond the observed history. global periodic patterns remain invisible to the model.
Global cycle
Local cyole
500
811
802
8:3
804
1
2
0.95
6
0.85
11
0.90
0.94
0.88
0.04
0.85
1.00
Figure Pearson correlation matrix of time series segments from the Electricity dataset. We divided the series into several sub-series by the local-cycle length. The series demonstrates both the local-cycle pat- tern (e-g., Corr S13) 0.94, Corr S14) 0.88) and global-cycle pattern (e.g., Corr(Si2 St)
A straightforward remedy is simply tend the look-back back window, but this ap- proach quickly proves impractical for 0.96). Critically, the global-cycle pattern stronger than local-cycle pattern (e.g.. Corr(S12, Corr(S12. S13), Corr(S12. S14)).
eral interconnected reasons (Tong & Yuan, 2025). First, as the input length grows, models risk overfitting to spurious noise, which undermines forecast stability rather than improving it. Second, longer input windows substantially inflate both computational and memory costs, often exceeding practical resource budgets. Finally, even with abundant history available, extracting truly relevant signals from overwhelming amounts of data remains inherently difficult, as models must distinguish meaningful long-term patterns from redundant or irrelevant information. Thus, capturing global periodicity requires more principled solution than brute-force window extension.
To address this issue, introduce the Global Temporal Retriever (GTR), lightweight and plug-and- play module designed to extend a forecaster's 's temporal awareness beyond the immediate historical context. At its core, GTR maintains adaptive global temporal embedding that encodes the long- range periodic structures across the entire cycle. For each input sequence, GTR first identifies its absolute position within the global cycle and retrieves the corresponding temporal segment from the learned global embedding. The retrieved segment is then aligned with the local input and fused through lightweight 2D convolution, enabling joint modeling of both local-cycle dynamics and global-cyce dependencies. The resulting enriched representation is finally integrated back into the forecasting backbone via residual connection, enhancing predictive power without altering its original architecture. Extensive experiments demonstrate that combining GTR technique with simple MLP backbone achieves state-of-the-ee performance on wealdworld multivariate datasets by effectively capturing long-cycle dependencies. Importantly, GTR is highly efficient, introducing negligible parameter and runtime overhead, and can be seamlessly integrated into a wide range of forecasting backbones.
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The primary contributions of this work are follows:
We pinpoint core limitation in current MTSF methods: fixed look-back windows often obscure global periodic patterns whose cycles exceed the observed history.
We present the Global Temporal Retriever (GTR), a lightweight, aoug-and-lay, model- agnostic module that uses absolute temporal indexing to retrieve from an adaptive global cycle embedding and fuses local and global cues via 2D convolution convolution-requinne requiring no changes to the host forecaster.
Across six benchmarks and both long- and short-term settings, GTR consistently improves diverse forecasting backhones and achieves overall stateoff-the-art accuracy with minimal parameter and runtime overhead.
RELATED WORK
Multivariate time series forecasting (MTSF) has widespread applications in various domains. In recent years, deep learning-basee based methods have achieved great success in MTSF tasks, including RNN-based methods (Lin et al., 2025c; Bergsma et al., 2023; Wang et al., 2024b), CNN-based methods (Liu et al., 2022a; Wu et al., 2022; Luo & Wang, 2024), Linear & MI.P-based methods (Zeng et al., 2023; Das et al., 2023; Lin et al., 2024), Transformer-base Wang et al., 2024d) and Mamba-based methods (Zhang et al., 2023; Wang et al., 2025b; Ma et al., 2025). Among these methods, explicit periodicity modeling and 2D structural transformation have rapidly evolved dominant paradigms, with the former focusing extracting multi-scale temporal patterns and the latter leveraging 2D representations to capture complex patterns beyond conventional sequential modeling.
methods (Nie et al., 2023; Liu et al., 2024b;
Modeling Periodicity of Time Series. Modeling temporal periodicity has long been used to boost forecasting accuracy. Recent methods such as Autoformer (Wu et al., 2021), FEDformer (Zhou et al., 2022a), DLinear (Zeng et al., 2023), and the TimeMixer family (Wang et al., 2024c; 2025a) perform seasonal-trend decomposition to better capture periodic components in the original time series. In parallel, trequency-domale FITS. and FilterNet use FFT-based representations to capture patterns that are hard to express in the time domain (Zhou et al., 2022b; Xu et al., 2024; Yi et al., 2024; Brigham & Morrow, 1967). CycleNet further learns recurrent cycles as explicit periodic structures (Lin et al., 2024). These methods effectively exploit multi-scale periodicity but are often bounded by the observed window or by assumptions of stationary cycles, limiting mining of information in very long cycles.
modeling has been increasingly integrated into deep networks: FiLM,
2D- Variatiss of Time Series Modeling. Transforming ID time series data into 2D representation allows models to capture more complex features that are difficult for traditional sequential methods to extract. TimesNet (Wu et al., 2022) captures the temporal DDrviiiass in 2D space by CNN-based vision backbones for the first time. LightTS (Zhang et al., 2022) leverages two distinct sampling strategies to structure the 2D time-series data and employs ML.ss for efficient feature extraction. MDCNet (Su et al., 2024) employs multi-scale 2D convolutional networks on variational mode- decomposed time series components to extract multi-frequency patterns. Times2D (Nematirad et al., 2025) converts ID time series into 2D tensors via frequency-domain periodic decomposition and derivative heatmaps, leveraging 2D convolutions to capture short- and long-term dependencies. Clustering enhanned modeling such as DUET introduces dual clustering on temporal and channel dimensions so as to capture both seraeseries patterns and inter-channel dependencies (Qiu al., 2025). Despite stronger representations, these approaches infer periodic structure indirectly from the re-layout of data and still lack consistent mechanism align with global cycles.
Forecasting, Retrieval- context by fetching similar segments from the full history or external repositories and fusing them into the predictor (Liu et al., 2024a; Han et al., 2025; Ning et al., 2025; Yang et al., 2025b). Such designs improve generalization and few-shot forecasting by exposing the model to recurring patterns beyond the current window. However, they rely heavily similarity search quality and do not by themselves provide a compact, time-aligned representation of very long cycles, motivating approaches that directly encode and align global periodicity while remaining backbone-agnostic.
Marrieall-Memooy-AAuggne
methods enlarge the effective
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Output-series
X R
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(54.0
Host Model MLLP)
Ditra-periad
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GTR Module
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Time-series ingut
Glotaal mmporaal entiaading
12 P-11
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Cycle information aigroment
Temporal extraction
Figure 2: Overview of the Global Temporal Retriever (GTR): plug-and-play module compatible with any MTSF forecaster. GTR operates in three stages: (1) retrieves corresponding segments from global temporal embedding; (2) aligns them with the input and uses 2D convolution to jointly model local and global periodicity; (3) fuses the result with the original input via residual connection.
METHOD
3.1 PROBLEM STATEMENT AND OVERVIEW
In multivariate time series forecasting, given historical observations X = fa1...... .T) E RTNN where T represents the number of time steps and N represents the number of variables, our target is predicting the future S time steps Y {IT+I, #T+5} } E RSxN, Critically, we focus on scenarios where the global cycle length significantly exceeds the historical input length T common yet challenging setting in real-world time series forecasting.
Method Overview, In this paper. we propose the Global Temporal Retriever (GTR) - a lightweight, aud--ndd-lay module designed extend model's temporal receptive field beyond the immediate input window. As illustrated in Figure 2, the proposed method operates in two phases: (1) The GTR module enhances global eyclic patterns by dynamically retrieving periodic information from the global temporal embedding, then fusing them with the input series through linear transformation and 2D convolution (c.f. Section 3.2). (2) The enhanced representation is subsequently processed by the backbone model (a multi-layer perceptron in this work, c.f. Section 3.3.) for final forecasting.
3.2 GLOBAL TEMPORAL RETRIEVER
To address the fundamental limitation of lookback window constraints in capturing global periodic patterns, we propose the Global Temporal Retriever (GTR), a lightweight and blug-and-play module that enables models to access temporal information beyond the immediate historical context.
The core innovation of GTR lies in maintaining an adaptive global temporal embedding that encodes the entire cycle pattern of the time series. Specifically, we introduce global parameter matrix Q E R where T. denotes the global cycle length and N represents the number of variables. This parameter is initialized to zero and automatically learns to capture the global periodic patterns inherent in each variable in the time series during training.
For notational convenience, we consider the univariate case. Given the n-th variable sequence X, E R with lookback length T, the GTR module operates through two principled stages to bridge local observations with global temporal structure:
Cycle Information Alignment. To establish continuity with the global temporal structure, we define a cycle index vector i E No that precisely locates each position within the global cycle. For a sequence starting at absolute time to, the index vector is computed
i [to mod L) r] mod L for 0..,,,..,TT- T
0,
(1)
The cycle index enables positional alignment of the input sequence within the global periodic range. Using the index vector, we retrieve corresponding temporal references from the global cycle representation:
4n Linear Linear(Q(i,nn) ERT.
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where In represents the retrieved global temporal information corresponding to the current sequence's position within the cycle. The linear mapping is utilized to enhance the representational capacity of the temporal reference. We then stack the original input sequence and the aligned global query to facilitate interaction between local patterns and global cycle information:
Fn
=
By On
E 1R22
Temporal Pattern Extraction. We apply 2D convolution operation to extract temporal patterns that span both local and global scales:
h C(F (2, 2[P/22) E RR
where C denotes the convolution operator, and is designed with P representing the dominant high- frequency period length (c.g., daily patterns in hourly data), capturing interactions across the two temporal scales while preserving the periodic structure. Finally, the extracted features are integrated with the original sequence through residual connection with dropout:
Zn X., + Dropout(h..) E RD
(S)
The key advantage of GTR is its ability to enable the model to retrieve and utilize periodic information from the entire cycle, regardless of the lookback window length. This is particularly beneficial for time series with long-term periodicities (e-g., monthly or yearly patterns) that cannot be captured within typical short lookback windows.
3.3 BACKBONE AND PROJECTION STRUCTURE
Many state-of-the-art methods in multivariate time series forecasting (MTSF) are built upon Multi- Layer Perceptrons (MLPs) (Das et al., 2023; Lin et al., 2024), demonstrating strong empirical performance and robustness. Inspired by these successes, adopt lightweight MLP-based backbone to capture temporal dependencies in the sequence.
Input Projection. Let Z E T be the representation derived from the GTR Technique, first project the representation into higher-dimensionn latent space via a linear transformation:
= Linear Z) E TR DXN
Layer Perceptron. The MLP backbone consists of two linear layers with GeLU activation functions (Hendrycks & Gimpel, 2023) and residual connection. Formally:
G: GeLu(Linear Z)) E DxN
G2 GeLne(Lnnear( (Linear(G.)) PxN
Zon G2 Z PXN.
Output Projection. The extracted features then mapped to the forecast horizon via a linear output layer, applied after a dropout layer for regularization:
Linear(Dropout( Zoom) E SXN
3.4 METHOD DETAILS
Instance Normalization. Distribution shift between training and testing data is prevalent challenge in time series forecasting (Liu et al., 2022b). Reversible Instance Normalization (RevIN) (Kim et al., 2021) 1) has been demonstrated to effectively alleviate this issue by applying instance normalization and denormalization to the inputs and outputs of the model. The module normalizes the input batch by removing mustance-specifee mean and variance, and subsequently reverses this operation on the model outputs. We adopt RevIN to stabilize the non-stationarity of the input time series.
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Seamless Compatibility. GTR preserves input dimensionality while integrating global periodic patterns, enabling plug-and-play integration with any forecasting backbone without architectural modifications. It processes imput series to generate enhanced feature representations, directly fed into the backbone for end-to-end training.
Complexity Analysis. Reversible instance normalization operates O(NT) complexity. Series embedding requires (NTdd) operations due to projection into the hidden dimension. The GTR module's 's linear mapping dominates with O complexity, while the 2D convolution is negligible since cycle length P is a small constant. The backbone and predictor exhibit O(Nd)) and ( Sd) complexity, respectively. The total complexity O(NT + Nd + NTd + Sd). which is linear to N, and S. When T is significantly smaller than d, the complexity is dominated by the O (N)?) term.
4 EXPERIMENT
4.1 EXPERIMENT SETUP
Dataset. We evaluate the proposed method on six widely used real-world datasets, including the ETT series (Zhou et al., 2021), PEMS series (Liu et al., 2024b), Electricity, Traffic, Solar-Energy and Weather datasets (Wu et al., 2021). A detailed description of this part is provided in Appendix A.
Evaluation. We use Mean Squared Error (MSE) and Mean Absolute Error (MAE) as the core metrics for the evaluation. To fairly compare the forecasting performance, we follow the same evaluation protocol, where the length of the historical horizon is set as T 96 for all models. We set the prediction lengths S to {12, 24, 48, 96) for PEMS dataset and {96, 192, 336, 720} for others.
Baselines. To evaluate the performance of the proposed method, we compare it against several recently well-acknowledged forecasting models, including RAFT (Han al., 2025), S-Mamba (Wang et al., 2025b), TQNet (Lin et al., 2025a), TimeXer (Wang et al., 2024d), CycleNet (Lin et al., 2024), SOFTS (Han al., 2024), Tixe (Wang et al., 2024c), iTrransformer (Liu et al., 2024b), PatchTST (Nie et al., 2023) and DLinear (Zeng et al., 2023).
Implementation Details. All experiments are implemented in PyTorch (Paszke et al., 2019) and conducted on a single NVIDIA RTX 3090 24GB GPU. We use the Adam optimizer (Kingma & Ba, 2015) with learning rate selected from (le-3, 3e-3, 5e-4). The hidden dim for MLP backbone D is set to 512. For additional details on hyperparameters and settings, please refer to the Appendix A.3.
4.2 EXPERIMENTS RESULTS
4.2.1 LONG-TERM FORECASTING
Table I:
Long-term forecasting results. The look-back length 7' is fixed at 96. All results are averaged across four different forecasting horizons S E {96, 192, 720]. The best results are highlighted in bold, while the second- best results are underlined. Count row counts the number of times each model ranks in the top 2. See Table in Appendix C.1 for the full results.
Model
(Ous)
GIR
(3025)
RAFT
5-Minta (3025))
(3025)]
TUNA
TimeXer (20041)
CydtNN
(2004)
SOIUS (2004)
TimeMiser (2004))
stneolomer (20240)
PheeTIST (2023)
Dllnne
(2025)
MSE
MSE
MSE
MSE
MSE
MSE
MSE
ETTM
0.409
0.434
0.425
0,43
0.455
0.400
0.441
0434
0411
0437
3455
01441
0.449
16465
1U442
01640
14454
0.445
0.409
0.865
0.882
0.367
0.389
0.381
0,400
0.395
0,805
0.112
0.352
0.353
0.397
0.319
0.396
0.395
0.00
0.351
0.396
0.00
0.410
0.387
0.400
0.403
0.007
ETTu2
1.208
0.315
002281
0.285
0.27
0.374
0.366
0.314
0.357
0.375
0.388
0.281
0.350
Bleansity
0.196
0.260
0.175
0.272
0.170
0.265
0.164
0,259
0.171
0.188
0.159
0.114
0.366
01162
0.273
0.108
0.200
0.205
0,200
0,212
0.300
Swar
0.194
0.24
0.301
0.937
00.40
0.233
0.188
0/317
0.300
5/300
0.16
0.320
01256
11216
(1300)
10:55
01267
(0.20)
0.007
00.90
0.401
Trafiic
12014
0/414
0/445
0/466
0.472
6,009
0.455
01475
(0:08)
013003
00,05
Weather
0.239
0.366
0.200
0.305
| 0.25
0.276
0.242
0,362
| 0.24)
0.371
0.343
0.371
0.255
0.378
0,240
0,272
10258
0.278
0.25)
0.273
00203 0.31
Results. Table shows GTR outperforms other models in long-term forecasting across various datasets. Across 16 prediction tasks, GTR achieved top-2 performance in 10 of them. Due to the traffic dataset's strong spatiotemporal dependencies and temporal lag effects, GTR exhibits higher MSE than S-Mamba. SOFTS and iTransformer, these models better capture critical inter-variable relationships. GTR is good at handling complex high-dimensions time series. For example, on the challenging Solar-Energy dataset, it exceeds the CycleNet by 8.2% in MSE and 6.5% in MAE.

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Published as a conference paper at ICLR 2026
4.2.2 SHORT-TERM FORECASTING
Table 2: Short-term forecasting results. The look-back length T is fixed at 96. All results are averaged across four different forecasting horizons S E {12, 24, 48, 96). The best results are highlighted in bold, while the second-bee results are underlined. Count row counts the number of times each model ranks in the top 2. See Table 7 in Appendix C. for the full results.
Modkd
(0em))
GTR
(3255
RAFF
S-Manie (30750
(30254)
TONe
TieeNer (30741)
CycleNet (200))
50FTS (303
TimeMisar (0344
Franddrnee
(h00ing
PachitST
(2003)
Dllver
(2011)
Mesio
MB5
MAE
MSS
MAE
MSE
MAE
M55
MAA
MAS
MAE
MAE
MBE
MAE
[
MSS
MAB
MSE
MMB
PEMSO0
0.987
0.189
10.44
0,200
10322
0.228
0000
0.303
0.002
0,214
0,318
0,22
00.00
0210
0.154
0.288
0.11
0.222
0.080 0,291 0.288
0.305
PEMSOL
1.877
11389
0.104
0.230
0.106
0.311
1101
0.021
0.105
0.209
0.119
02222
10.00
0.268
0.156
0.282
10.11
0.221
[ 0.155
0.307
0.295
0.385
0,14
0,339
PEMSO8
IU142
01222
1015)
0.234
00846
0.224
0.230
0.175
0.250
10150
00246
[ 0.138
0.230
0255
0.556
00.10
0.236
[ 0.260
0.321
10.599 0.415
Results. Table 2 shows GTR outperforms sfate-of-the-ar models across all metrics. Across 8 prediction tasks, GTR achieved top-2 performance in all of them. Compared to iTransformer, GTR reduces MSE by 18.7% and MAE by 12. 1.11% 1% on average across all datasets and horizons; compared to S-Mamba, it achieves 15.7% MSE and 9.6% MAE reductions, with the most significant gains observed in PEMS03, achieving 28.7% MSE and 20.6% MAE reduction.
4.3 ABLATION STUDIES AND ANALYSIS
Effectiveness of GTR. To evaluate this, we conducted comprehensive ablation studies across three highly periodic benchmark datasets. Table systematically quantifies both the intrinsic contribution of GTR within our framework and its cross-model generalization capability when integrated into diverse state-of-the-ard architectures.
Table 3: Ablation studies of the GTR technique. Left: Generalization performance of GTR technique on different models. Right: Ablation study revealing the effectiveness of the GTR technique. The look-back length is fixed at 96 for all the experiments.
Supore
Teqecte
Tepeove
Oripnal
Metee
M1B
MAA
MAR
1455
MAX
MNG
KTNG
MA6
MAR
MAR
MM
MAN
MNR
MAR
MAR
MSS
MAN:
NSG
MAV
Rearsit
56.
111.0
0,331
10.77
1.50
B.355
8,233
11199
333
6141
0.31
50 50
15:00
8.33
8:128
3.4%
9.395
8.122
12.25
5,855
0,37
0.173
0.254
19,95
7.5%
0.290
0,277
8.711
0.264
11.75
4.5%
(1210
0.300
0.386
9.355
4.1%
9.32
01300
4.5%5
0.244
0.30
0.206
0.365
15:45
6.1%
0.390
0.312
0.28
10.35
4.9%
Ang
10173
0.267
0.162
0.356
5.25
3.3%
0.351
16261
0.367
0.364
14.75
0,470
01:30
0.35
0,10
0.207
24.25
1,5%%
0.390
0,21
0.506
0,568
16:25
0.1%
0.55
27.00
3,055
0.106
0.31
23
0.251
0.177
0,877
34.55
13,65
(U000
BU774
1.776
17
11:05
01213
8.81
0.17%
0.104
0.364
75.90
13335
0.213
0.770
0.172
17.15
3.155
15.00
0.315
17.75
11/44
3.45
61141
0.506
71.0%
46.26
9.254
11.00
01311
0.256
35.75
25.2%
01455
0.00
0,199
0.25
154.5
17.20
0,305
0.300
0.277
0.258
00/76
71.9%
111.0
6496
9.38
10.09
$6.90
11300
0.99
0,196
41.75
33.04
0.30
0999
6153
0.3
100.1
$3.00
1.115
0.24
9.897
6,509
15.19
$0.90
7D4004
14297
233
BUTH
0.31
24.7%
14.99
8.12
14231
0.881
0.877
46.95
13.1%
01111
018T
0.113
0.25
40,40
33
18
0.109
0191
0,255
8.75
8.177
06.95
21.9%
0L176
0.64
6111
0.31
55.7%
38.5%
9331
00303
8.136
0.300
42.99
39.7%
04444
0.386
110.%%
61.40
0.244
0.28
0.14
63119
40.95
01.20
19,99
1.130
1421
0.99
0.20
31.5%
0.361
9332
6.356
0.355
91.75
40.27%
0.331
0.21
0.877
Key findings are twofold. First, GTR significantly enhances our MLP backbone, reducing average MSE by 14.4% (Electricity), 55.1 1% (PEMS03), and 73.5% (PEMS04). Second, GTR consistently improves all evaluated models across all datasets and prediction horizons, with particularly pro- nounced gains in traffic forecasting. For instance, on PEMS04, GTR reduces MSE by 91.9% for DLinear and 56.2% for PatchTST, underscoring its robustness in complex temporal contexts, While the GTR module itself is designed with a channel-independdnt architecture, when integrated with the iTransformer, which is specifically built to capture relationships between different variables, the GTR module still delivered significant improvements, reducing MSE by 62.2% on PEMS03 and 37.9% on PEMS04. These improvements are achieved through trivial integration during training, demonstrating GTR's capability with diverse architectures.
Influence of look-back length. Figure 3 demonstrates GTR's 'T''s performance across varying look-back window lengths on four benchmark datasets. Two critical observations emerge: First, GTR exhibits consistent performance improvement as the look-back length increases, demonstrating effective utilization of additional temporal context. More significantly, GTR substantially outperforms all baseline methods across all window lengths, with the largest gains occurring at the shortest input horizons. Notably, on Electricity and Solar- Coler-Energy datasets, baseline models experience exponential error growth as window length decreases, while GTR maintains remarkable stability with only
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Published as a conference paper at ICLR 2026
Electricity
Solar- Energy
PEMS03
PEMS04
iTaralenc
0.6
0.24
0.4
MSE
0.22
0.4
0.4
0.20
0.3
0.18
0.2
0.2
192
336
48
96
336
24
48
12
48
96
Look-back Length
Look-back Length
Look-back Length
baok- Length
Figure 3: Influence of look-back length. Forecasting horizons are fixed at 336 for Electricity and Solar-Energy, and 96 for PEMS03 and PEMS04. GTR consistently outperforms other models across varying look-back lengths, particularly at the shortest window length.
marginal performance degradation. This resilience in ultra-short input scenarios directly validates our core innovation-by establishing temporal continuity beyond the immediate observation window, GTR successfully leverages global periodic information that remains inaccessible to baseline methods when cycle lengths exceed the input horizon. The consistent superiority across all window lengths confirms that GTR effectively bridges local pattern extraction with global temporal structure, making particularly valuable for practical applications where historical data may be severely limited.
Model Efficiency. The proposed GTR tech- nique operates as an efficient plug-and-ple module with minimal computational overhead. As shown in Table 4, the GTR technique alone consumes merely 40.1K parameters and 4.50M MACs. When integrated with a pure MLP backbone for complete forecasting capa- bility, the combined system maintains remark- able efficiency with just 0.98M parameters and 306.91M MACs, representing only 19.0% of iTransformer's parameter count while achiev- ing comparable or superior prediction accuracy as demonstrated in our main results. With training time of 22.3 seconds per epoch, the combined system is surpassed only by DLinear 118.1s), highlighting its strong efficiency while maintaining superior modeling capability. This makes GTR Technique particularly suitable for resource-constree coourre-constrained forecasting applications while maintaining the capacity to capture both short- term patterns and long-range dependencies.
Table 4: Efficiency comparison between GTR and other models on the Electricity dataset with look- back length T 96 and forecast horizon S = 720. Training Time denotes the average time required per epoch for the model.
Model
Parameters
MACs
Training Time(s)
Informer (2021)
12.53M
3.97G
70.1
Autoformer (2021)
12.22M
4.41G
107.7
FEDfonmer (2022a)
17.98M
444G
238.7
DLinear (2023)
139.6K
44,91M
18.1
PatchTST (2023)
10.74M
25,87G
129.5
Transformer (2024b)
5.15M
L.65G
35.1
GTR Tech.
40.1K
4.50M
MI. M-Layrr
0.98M
306.91M
22.3
Correlation Alignment. To further investigate how the GTR module models global temporal dependencies, we conducted a visualization experiment using the Pearson correlation coefficient to analyze multivariate correlations. As shown in Figure 4, selected test sequences from 4 different datasets. The visualization compares input and GTR-enhanced output against the ground-tro -truth correlation computed across the entire dataset. The results clearly demonstrate that, after applying the GTR module, the learned multivariate correlations align significantly more closely with the global temporal structure. This improvement is particularly meaningful in real-world scenarios, where time series may be distorted by non-stationary disturbances. The GTR module enhances the model's s robustness to such perturbations, enabling more reliable and structure prreturvii representations even under imperfect input conditions.
LIMITATIONS AND FUTURE WORK
While our proposed GTR module offers flexible, plug-and-play solution for enhancing long- term time series forecasting through explicit periodic pattern modeling, it exhibits several inherent limitations stemming from its architectural assumptions and computational design.
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EThh
Betore GUR module
After GTR module
Ground Truth
Before GEX coodule
Afler GTR module
Ground Trath
Eleenery
Weatbe
Before GTR module
GTR module
Truth
Hefore GTR module
Afler module
Ground Traths
Figure 4: Visualization for multivariate correlation analysis on 4 datasets. The visualization is implemented based on the Pearson Correlation Coefficient. The Ground Truth denotes the correlation computed across the entire dataset. The two columns on the left denote the correlation between the variables before and after the GTR module, respectively. It shows that the model drives the learned multivariate correlations closer to the global correlation structures through the GTR module.
Fixed Cycle-Length Assumption. GTR assumes a single, fixed cycle length for the entire input sequence. This assumption may result in suboptimal performance on datasets with time-varying periodicity, such as physiological signals whose dominant frequencies shift over time. Moreover, GTR enforces shared cycle length across all input channels, which is ill-suited for multivariate time series which different variables may exhibit heterogeneous periodic patterns. Although this limitation could be mitigated through channel-sper -ppeciffc modeling preprocessing, such solutions introduce additional architectural complexity or mata-handling overhead. GTR further assumes that time series simultaneously exhibit both local and global periodic structures. Consequently, it may underperform on time series characterized by single dominant periodicity.
Challenges in Modeling Long-Range Cycles: Although GTR theoretically accommodate long cycles by adjusting the cycle-length parameter, its practical applicability is often constrained by data scarcity. Accurately learning yearly multi-year periodic patterns typically requires decades of continuous, high-quality historical data condition rarely satisfied in real-world settings. Moreover, when the base cycle length becomes large, the width of the 2D convolution kernel increases linearly with P. Consequently, the convolution operation incurs computational complexity of O(NTP), where T denotes the sequence length. For large-scale time series and ultra-long cycles, such complexity becomes computationally prohibitive. Additionally, the number of kernel parameters also scales linearly with P, increasing memory overhead and exacerbating the risk overfitting in data-scarce scenarios. Future work may investigate hierarchical or memory- augmented mechanisms to better extrapolate long-range periodic structures from limited observations.
Scalability with Long Input Sequences. GTR preserves the input sequence length and employs linear projection layer with size T. This results computational complexity of (NT2) for the linear operation. When T is large, the quadratic complexity becomes prohibitive, the number of operations scales with the square of the sequence length. Although the GTR module is designed for short look-back windows, it becomes inefficient for long sequences.
These limitations highlight specific scenarios where the GTR module may not be the optimal solution. They also motivate future research into developing adaptive cycle modeling, handling cross-channel periodic heterogeneity, and improving the efficient learning of extreme Long-horizon periodicity.
6 CONCLUSION
In this work, we address the challenge that existing multivariate time series forecasting (MTSF) models are limited by their historical context, which prevents them from effectively capturing global periodic patterns. To overcome this, we introduce the Global Temporal Retriever (GTR), lightweight and plug-and-plas module that allows any forecasting model to access and utilize temporal information from the entire cycle. Extensive experiments six real-world datasets demonstrate that GTR consistently delivers state-of-the- performance both short-term and long-term forecasting scenarios, highlighting GTR as an efficient and general solution for MTSF tasks.

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Published as a conference paper at ICLR 2026
7 ETHICS STATEMENT
Our work only focuses on the time series forecasting problem, so there is no potential ethical risk.
REPRODUCIBILITY STATEMENT
In the main text, we have strictly formalized the model architecture with equations, All the imple- mentation details are included in the Appendix, including dataset descriptions, metrics, model, and experiment configurations. The code has been made public.
ACKNOWLEDGMENTS
This work was supported in part by the National Key R&D Program of China (Grant No. 2023YFF0725001), in part by the National Natural Science Foundation of China (Grant No. 92370204), in part by the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2023B15151 100507) in part by the Key-Area Special Project of Guangdong Provincial Ordinary Universities (Grant No. 2024ZDZX1007), and in part by the Red Bird MPhil Program at the Hong Kong University of Science and Technology (Guangzhou).
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A IMPLEMENTATION DETAILS
A. DATASETS DETAILS
We conduct extensive experiments five widely-used time series datasets for long-term forecasting and PEMS datasets for short-term forecasting, We report the statistics in Table 5. Detailed descriptions of these datasets are follows:
(1) ETT (Electricity Transformer Temperature) dataset (Zhou al., 2021) encompasses temper- ature and power load data from electricity transformers in two regions of China, spanning from 2016 2018. This dataset has two granularity levels: ETTh (hourly) and ETTm (15 minutes).
(2) Weather dataset (Wu et al., 2022) captures 21 distinct meteorological indicators in Germany, meticulously recorded at 10-minute intervals throughout 2020. Key indicators in this dataset include air temperature, visibility, among others, offering comprehensive view of the weather dynamics.
(3) Electricity dataset (Wu et al., 2022) features hourly electricity consumption records in kilowatt-hours (kWh) for 321 clients. Sourced from the UCL Machine Learning Repository, this dataset covers the period from 2012 to 2014, providing valuable insights into consumer electricity usage patterns.
(4) Traffic dataset (Wu et al., 2022) includes data hourly road occupancy rates, gathered by 862 detectors across the freewaas of the San Francisco Bay area. This dataset, covering the years 2015 to 2016, offers detailed snapshot of traffic flow and congestion.
(5) Solar-Energy dataset (Lin et al., 2024) contains solar power production data recorded every 10 minutes throughout 2006 from 137 photovoltaic (PV) plants in Alabama.
(6) PEMS dataset (Liu et al., 2022a) comprises four public traffic network datasets (PEMS03, PEMS04, PEMS07, and PEMS08), constructed from the Caltrans Performance Measurement System (PeMS) across four districts in California. The data is aggregated into 5-minute intervals, resulting in 12 data points per hour and 288 data points per day.
Table 5: Dataset detailed descriptions. "Dataset Size" denotes the total number of time points in (Train, Validation, Test) split respectively. "Prediction Length" denotes the future time points to be predicted. "Frequency" denotes the sampling interval of time points.
Tasks
Dataset
Dim
Prediction Length
Dataset Size
Frequency min
ETTml
7
(96, 192, 336, 720)
(34465, 11521, 11521)
ETTm2
7
(96, 192, 336, 720)
(34465, 11521, 11521)
15 min
ETThl
(96, 192, 336, 720)
(8545, 2881, 2881)
min
Long-term
ETTh2
(96, 192, 336, 720)
(8545, 2881, 2881)
min
Forecasting
Weather
21
(96, 192, 336, 720)
(36792, 10540)
10 min
Electricity
321
(96, 192, 336, 720)
(18317, 2633, 3261)
1 hour
Traffic
862
(96, 192, 336, 720)
(12185, 1757, 3509)
hour
Solar-Fnergy
137
(96, 336, 720)
(36601,5161 10417)
10 min
PEMS03
358
(12,24,45 48, 96)
(15617,5135, 5135)
min
Short-term
PEMS04
307
{12, 24, (6)
(10172, 3375, 3375)
5 min
Forecasting
PEMS07
883
{12, 24, 48, 96)
(16911,562) 5622)
5 min min
PEMS08
170
{12, 48,
(10690, 3548, 265)
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A.2 METRIC DETAILS
Regarding metrics, utilize the mean square enror (MSE) and mean absolute enror (MAE) for long-term forecasting. The calculations of these metrics are:
T Σ
MSE-
UU y1)
MAE-
91
341
A.3 EXPERIMENT DETAILS
All experiments are implemented in PyTorch (Paszke et al., 2019) and conducted on single NVIDIA RTX 3090 24GB GPU. We the Adam optimizer (Kingma & Ba, 2015) with learning rate selected from { [1e-3, 3e-). The hidden dim for MLP backbone set to 512. The dominant high-frequency period length P is set to 24 for all datasets. Table 6 provides detailed hyperparam- eter settings for each dataset. During data preprocessing, we set the timestamp (4n) of the initial observation in the entire dataset to O the reference point. In main experiment, for all baseline methods, we adopted the hyperparameter settings from their respective original publications. For the ablation experiment of the GTR module Table the baseline methods utilized their original hyperparameter settings as specified in their respective publications for an input length of T=96. The GTR module was then directly integrated, and the entire model was trained end-to-end without any further hyperparameter optimization.
Table 6: Hyperparameter settings for different datasets. "Ir" denotes the learning rate. "Cycle.len
denotes the length of global cycle.
Tasks
Dataset
Cycle_len (T)
Ir
Batchsize
Epochs
Use_revin
ETTml
96
1e-3
256
True
ETTm2
96
le-3
256
30
True
ETTh1
24
le-3
256
True
Long-term
BTTh2
24
le-3
256
30
True
Forecasting
Weather
144
le-3
30
True
Traffic
168
3e-3
16
30
True
Electricity
168
3e-3
32
30
True
Solar-Energy
144
3e-3
64
30
False
PEMS03
288
3e-3
30
False
Short-term
PEMS04
288
3e-3
32
30
False
Forecasting
PEMS07
288
3e-3
False
PEMS08
288
3e-3
32
30
Truc
The hyperparameter which denotes the global cycle length of the entire dataset, established via two primary methods. The first relies on domain-specifee knowledge of intrinsic periodic patterns and the sampling intervals of data, as suggested by prior work (Wu et al., 2022; Lin et al., 2024). The selected L values are summarized in Table 6.
Alternatively, L can be estimated using computational techniques, most notably the autocorrelation function (ACF) (Madsen, 2007). The ACF measures the linear dependence between a time series and a lagged version of itself. For discrete time series y/: length with sample mean 7. sample autocorrelation тą at lag l is formally defined as the ratio of the sample autocovariance "y to the sample variance Yo:
T-K (yt (V++* - 1==
Yo
Σt (U:
7)
In this context, a significant peak the ACF plot at a specific lag suggests a strong periodic component, justifying the selection of I.
15

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Published as a conference paper at ICLR 2026
B MORE DETAILS OF GTR
Algorithm 1 Overall Pseudocode of GTR
Require: Historical look-back input X E RTXN, starting absolute position En. Forecasting output Y E R Initialize learnable parameters Q RIXN 0
Ensure:
2: if Instance Normalization is applied then
3: 1,,0 <- -Mean (),, (X)
4: X
X-# Vo==E
5: end if
6: // GTR part.
7: i EENN No - [Lo mod L) + +T] mod T. for 7= 0. 1.
8: DERT Linear Qiū,:))
X
9: F E R2XTXN t
Q
10: H HERTYN D(F)
11: Z RTXN t +
12: // Host model part.
13: Z E DxN <- Linear( Z)
14: Z RDD
Multi-Layer Perceptron(Z) + Z
15: Y E RRCH + -Linear(rropou((] (2)
if Instance Normalization applied then
17: Y Y +e+1
18: end if
The GTR framework processes temporal sequences through a structured pipeline that integrates cyclic pattern modeling with residual learning (Algorithm 1). Initially, optional instance normalization standardizes the input E RT using per-sequence statistics and a.. The core innovation lies in the cyclic indexing mechanism: learnable embedding matrix E RLLN is dynamically indexed via [(fo mod L.) +r] mod for O,.... T 1, generating position-aware queries Q through linear transformation. This indexed query concatenated with the normalized input along the channel dimension to form F E [22x1'X which is processed by a 2D convolutional layer to extract spatiotemporal features H. residual connection Z H X preserves input integrity while enhancing representational capacity. The resulting features Z are then projected to the host model's s input dimension, enabling seamless transition to downstream forecasting components.
Critically, GTR is designed as a plug-and-play module that requires architectural modifications to the host model. As delineated the pseudocode, the separation between the GTR part and Host model part ensures compatibility with any forecasting architecture (e.g.. Transformers, RNNs, or MLPs). The host model receives Z as a direct replacement for its original input, eliminating the need for re-engineering existing layers attention mechanisms. During training. all components-inccludig Q. the convolutional layer, and host model parameters are jointly optimized end-to-end, allowing GTR to adaptively refine cyclic representations while the host model leverages these enriched features. This integration strategy significantly boosts forecasting accuracy by injecting explicit periodicity awareness without compromising the host model's 's inductive biases increasing inference complexity, as evidenced by our empirical results across diverse benchmarks.
C MORE EXPERIMENT RESULTS
C.I FULL FORECASTING RESULTS
The full multivariate forecasting results are provided in this section due to the space limitation of the main text. We extensively evaluate competitive counterparts challenging forecasting tasks. Table 7 contains the detailed results all prediction lengths of the 12 well-acknowledded forecasting benchmarks. GTR achieves comprehensive state-offthh-aat in real-world forecasting applications.
16

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Published as a conference paper at ICLR 2026
Table 7: Full multivariate time series forecasting results for all prediction horizons. The look-back length T is fixed at 96. The best results are highlighted in bold, while the second-best results are underlined, Avg means the average results from all four prediction lengths.
Model
IChum)
GTR
RAFT
(21711
S-Marrto
TONer (700560)
Timeoor (313440
CyclsNoe (10011)
SEIFTS (7001)
iTanddermir E1I01:
PaeckTNT (3021)
TH invor
(h001)
Meric
MSS
MAA
MAE
MANE
M55
MAB
MS6
MA5
MSB
MAB
MISE
MAE
MSB
MAE
MSE
MAE
MSE
MAE
MSS
MAF
56
0.367
0.391
0.576
0.401
0.396
0.445
0.371
0.303
0.382
0.405
0.375
0.355
0.351
0.359/
0.375
0.800
0.366
0,405
0.14
0,415
0.385
0,400
0.417
0.457
0.47
0.501
0.481
720
00,03
0.476
01,655
0.405
0,500
0.489
0.467
0.470
0.461
0.530
0.484
0.499
0.485
0.488
0.422
0.593
0.491
0,500
0,488
0,319
0.316
10,409
0.434
10,429
00455
0.400
01.41
0.434
0.437
0.457
04457
0.441
0.449
0.443
0,447
0/400
0,454
0.445
0,469
0,455
00455
66.
10.200
00.533
10.200
0.562
10 11246
0.585
00.00
0.365
0.386
0L38K
0.396
01366
01397
0.367
0.289
0.341
0.291
0.340
0.901
0.545
0:511
0.55
E2712
192
0.362
0,.899
11:00
0.000
0.506
0.300
0.567
0.305
1.365
1.00
0.122
0.30
03313
0.764
0.312
0.702
0.360
0.400
0.398
0.900
0.77)
0.475
0.434
0.431
01412
0.422
B431
0.419
54410
0.386
0.41
0.415
0.394
0:541
0.431
Aug
10:97
03.000
10:30
0.000
11:00
0:005
0.775
0.00
11
1.10
0.
0.009
0.373
0/400
0.365
0,365
0.361
0:407
0.387
0.907
0.595
0.515
ETitel
193
0.349
0.375
0.564
1.500
0350
0.500
0.375
0.350
0.361
0.317
0.367
0.300
336
0.389
0.348
0.591
0.007
0 0.
0.413
0.5
0.00
0355
0.00
075
0.455
0.405
0.413
0.500
0.004
0/476
0.430
0.399
0.400
0:11
0.413
730
0.435
0.436
0.241
0.55
0.475
0.653
01000
0.53
0.641
0.47
0.441
0.466
0.41T
0.444
0.441
0.491
0.459
0.451
0.439
0.474
0.453
0.267
0,289
0.000
9M6
0:405
0.901
0.79
0.766
0-405
0.761
0.366
0.407
0.410
0.357
0.900
0.493
0.164
0.389
0.176
0.64
0170
0:3
0.73
0.56
0171
0.56
6363
0:36
0.50
0.66
0.75
0.118
0180
0.155
0.255
0.193
B7T
0.387
0.503
0.585
0359
0.301
0.300
0.358
0.355
0.758
0.340
03311
0.355
0.365
730
0.386
0.790
01401
0.005
01411
0:000
0.50
0.306
0350
0.76
0.789
0.391
0.405
0.401
0.391
0.306
0.413
0.407
0.403
0.000
0.554
0.53
10%
10.201
0.313
0,200
0.500
0.288
0.332
0.77
0.53
0.322
0.266
0.314
0.257
0.300
0.25
03333
0226
0.333
0.20
0.326
0.350
56
0.134
0.229
0.133
0.257
0..59
0.235
0.154
0.229
0.140
0.242
0.136
0.229
0.143
0.235
0.153
0:347
0314
0.300
0.191
0
0.197
0.282
192
8.152
01251
1.155
0159
6157
0.256
0.15
6:244
0155
0:246
0.56
0226
0153
0253
0115
0:214
0.19
0.235
206
0.171
0.304
01221
0176
0176
0:15
6:70
6118
0.24
0.209
0,300
0.000
0225
022
0.245
Aug 13.155
01:000
012222
11
0:300
0.259
0.200
0.106
0.229
0.264
0.192
02215
0.2/0
0,205
0,200
0.212
0.390
191
8.197
1.304
12509
11000
0256
1.
0350
0.56
0330
0355
6361
0331
0.561
0361
0.310
0.530
136
8:311
81320
6.111
12 8264
100
11
2217
6211
0208
0.733
5250
6.315
0.311
0.11
770
0.315
(1251
0.315
0.305
120
1170
0.706
6255
0.366
0245
0.315
0.75
0.345
0.49
0.749
0.517
0.356
0.41
0.194
0.345
10.001
0.300
0.235
0.256
0.257
0.30
0110
0:351
0239
0.556
0216
0.200
0223
00652
0,21
0.307
0.330
0.40
0.490
0.301
0.305
0.201
0. 1200
0.301
0411
0.261
0428
6458
0:306
0,65
0.395
0.463
0.240
0.600
Tiafle
720
536
0.514
03:001
0.250
11411
01:01
11 (1000
0347
11300
0.205
0556
03380
0.307
0410
0500
0.30
0.314
6447
0.360
0.387
0.50
0.315
0411
0.451
0.301
0.514
0.43
0.910
0.330
0.6
0.00
0.34
Aug.
10.47
0.414
0.254
0.206
0.58
0472
0,455
0.458
0.401
0.015
Weziees
192
36
0.202
0.115
0.300
03244
01185
0.37
0.241
0.27
0
0.2
0.30
0.00
020
015
035
0.00
076
0.57
D36
0.305
0200
0.55
0.47
0.208
0217
0.166
0:55
0.306
0206
0163
0.250
0.209
0221
0.174
0.254
0.214
0.215
0.137
0.250
0.210
0.196
0.23
0.255
0.2%6
0.200
0000
020
020
0300
026
0252
0.30
6:51
020
0.27
0.291
0.307
0.343
0.349
A0%
0.239
0.206
0.270
0.300
0.551
0.270
0.44
0.39
0241
0.271
0245
0.211
0255
0.275
0240
0.72
0255
0.29
0.299
0.273
0.263
0317
8.157
01001
PEMS0S
0.778
0.172
01091
0.301
0100
1100
100
1002
1000
0.301
0285
036
0034
0361
5141
0.30
0.307
0.136
0.133
0.203
815
0135
812
0,796
02367
0334
0:223
000
0025
02215
0211
0.33
0.425
0.127
0.301
0.301
0.30
0.192
0.262
0156
9258
0354
0221
0.299
0.453
0.315
83167
0.189
00:44
12
0116
0.336
0.304
0:310
0315
0.190
0.20
9.21
PEASSL
0.164
0.317
0.10
0.26
M014
0.178
0.018
0.116
0014
0100
01228
0018
0.105
0:148
0.222
08.99
0.111
0.11
0115
0110
0.116
0.368
0.30
0.500
0167
0.268
0.30
0.315
0:315
8.114
0.211
0.137
0.50
0157
0.5
03511
0.167
0.761
0.35
0.744
0.31
0.355
0.150
0.763
0.51
0.380
0.453
0.901
0.195
PEMSIS PEMS0O
8.151
0.142
0.11%
01677
01788
0.550
1178
00063
01811
015
0001
0.4
0057
8.79
177
D062
B:66
0.300
0.362
D057
0/86
6111
0.315
0.055
0.057
0.08
0.90
0.165
0,885
0.10
0.207
0.363
0.110
0.11
0.312
0.768
0.110
0.345
0.94
Ang 0.075
0.169
0.094
0.193
0.000
0.185
0.875
0.121
0.065
0.162
0.115
0.314
0566
0.344
0.145
0.259
0.101
0.204
0.213
0,303
0.305
0.345
0.176
0.165
0089
0.79
0.165
0.154
8,055
0.182
0.102
0.215
0.104
0.399
0,0%
0.10
0.112
0.201
0.117
0.236
0.104
0.201
01166
02333
0.115
0.19
0.244
0.201
0.248
0.353
0.145
0,234
0.183
0.244
0.107
0.100
0.344
0155
0.348
0.369
0.66
0164
0.35
0.70
0:369
0.166
0.235
0.21
0.354
0.40
0.470
0.307
0.259
0.309
0.377
0.35
0.306
6.111
0.353
0,466
3.21
0.263
0,415
0.674
Aak
0.1422
0.222
0.151
0.234
0.144
0.224
0.142
0.230
0.115
0.150
0.150
0.346
0.136
0.230
02553
0.336
0.150
0.235
0,290
0,321
0.379
0.416
32
4
0
0
0
C.2 MORE ABLATION RESULTS
To further validate the architectural decisions of the Global Temporal Retriever (GTR) and assess the robustness of its components, we conducted a comprehensive ablation study focusing on two key aspects: the impact of Reversible Instance Normalization (RevIN) (Kim et al., 2021) and the design of the temporal pattern extraction module. The experimental results are summarized in Table 8.
C.2.1 IMPACT OF REVERSIBLE INSTANCE NORMALIZATION
We first investigate the contribution of Reversible Instance Normalization (RevIN) to the model's performance. RevIN is designed to mitigate the distribution shift problem in time series forecasting by normalizing the input and denormalizing the output.
As observed in the left part of Table 8, the standard GTR (w. RevIN) significantly outperforms the version without RevIN (w/ RevIN) on the majority of datasets, particularly the ETT series and Weather datasets. For example, on the ETTh2 dataset (prediction horizon 720), removing RevIN
17

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Published as a conference paper at ICLR 2026
Table 8: Ablation results of RevIN and Model Variants. The best results in each comparison group are highlighted in bold.
GTR w. RevIN
GTR w/o, RevIN
Original 2D Conv.
Variant Concat
Variant Inception
Variant ID Conv,
Model
Mctric
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
96
0.367
0.391
0.380
0.402
0.367
0.391
0.369
0.393
0.371
0.395
0.369
0.392
El'hh ETTT]
192
0.420
0.421
0.433
0.437
0.420
0,421
0.423
0,423
0.423
0,422
0.427
0.423
336
0.476
0.447
0,480
0.464
0.476
0.447
0.472
0,448
0.481
0.451
0.479
0.448
720
0.493
0.476
0.540
0.529
0.493
0.476
0.490
0.473
0.507
0.476
0.513
0.487
96
0.290
0.342
0.315
0,363
0.290
0.342
0.293
0.344
0.291
0.341
0.297
0.346
192
0,362
0.389
0.422
0.430
0.362
0.389
0.375
0.394
0,369
0.391
0.372
0,393
336
0.414
0.429
0,567
0,518
0.414
0.429
0.416
0.428
0,422
0.433
0,420
0.431
720
0.423
0.442
0.872
0.649
0.423
0.442
0.452
0.455
0.424
0.443
0.424
0.442
96
0.305
0.349
0.315
0.358
0.305
0.349
0,306
0.351
0.313
0.358
0.307
0,351
El1m2 E11ml
192
0.349
0.375
0.356
0.389
0.349
0.375
0.350
0.376
0.352
0.377
0.355
0.378
336
0.380
0.398
0.378
0.403
0.380
0.398
0.377
0.397
0.379
0.398
0.382
0.398
720
0.435
0.436
0.442
0.451
0.435
0,436
0.434
0.435
0.442
0.436
0.433
0.434
0.168
0.249
0.190
0,285
0.168
0.249
0.169
0.250
0.167
0.251
0.168
0,251
192
0.232
0.292
0.285
0.355
0.232
0.292
0,237
0.295
0.235
0.295
0,233
0,293
336
0.287
0.330
0.526
0.474
0.287
0.330
0,290
0.333
0.291
0.332
0,289
0,333
720
0,386
0.390
0.798
0.610
0.386
0.390
0.390
0.392
0.390
0.391
0.389
0.392
Electricity
96
0.134
0.229
0.132
0.230
0.134
0,229
0.136
0.228
0.135
0.229
0.135
0.229
192
0.152
0.245
0.151
0.248
0.152
0.245
0.154
0.247
0.153
0.246
0.154
0.248
336
0.171
0.264
0.167
0.267
0.171
0.264
0.172
0.263
0.169
0.264
0,170
0.264
720
0.208
0.300
0.208
0.305
0.208
0,300
0,209
0.300
0.207
0.298
0.209
0,300
96
0.181
0.237
0.176
0.235
0.176
0,235
0.182
0.234
0.180
0.237
0.181
0.237
Solar
0.196
0.245
0.193
0.244
0.193
0.244
0.192
0.245
0.195
0.243
0.196
0,245
336
0,210
0,259
0.201
0.250
0.201
0.250
0.207
0.256
0.205
0.252
0.210
0,259
720
0.232
0.277
0.205
0.251
0.205
0.251
0.212
0.266
0,212
0.255
0.232
0.277
Weather
96
0.154
0.200
0.157
0.220
0.154
0.200
0.156
0.201
0.156
0.201
0.156
0.201
192
0,202
0.244
0.208
0.269
0.202
0.244
0.203
0.245
0.203
0.245
0.205
0.246
336
0,259
0.287
0.263
0.318
0.259
0.287
0.262
0.288
0.261
0.288
0.261
0.288
720
0.341
0.342
0.357
0.382
0.341
0.342
0.343
0.343
0.343
0.342
0.340
0.341
1s Count
20
23
9
19
18
6
3
2
results in a catastrophic increase in MSE from 0.423 to 0.872. This confirms that RevIN is crucial for handling data with significant non-stationarity and distribution shifts.
Notably, the Electricity and Solar datasets exhibit a deviation from this trend, where the exclusion of RevIN yields superior performance. This phenomenon can be attributed to the prevalence of continuous zero-value segments (e.g., zero power generation at night), which may bias the mean statisties estimated by RevIN. Despite these specific instances, retain RevIN the default configuration to ensure general robustness across diverse forecasting scenarios.
C.2.2 ANALYSIS OF EXTRACTION VARIANTS
The core of the GTR module is the extraction of temporal patterns by fusing the local observation Xn E RT and the retrieved global context qn E R². Our proposed method utilizes a lightweight 2D convolution. To verify the optimality of this design, we compare it against three distinct variants:
Variant (Point-wise Fusion): This variant assesses whether temporal convolution is necessary. We concatenate x,, and qu along the feature dimension and apply linear projection posnt-wise at each time step. This removes the receptive field, relying solely on the immediate alignment of local and global values:
hn Linear(Concatee qn))
(6)
Variant 2 (Inception Module): To test whether multi-scale temporal patterns enhance the effec- tiveness of the feature fusion process, we replace the original single-kemnel convolution with an Inception block (Szegedy et al., 2015). The Inception operator applies several parallel convolutions
18

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Published as a conference paper at ICLR 2026
with different kernel widths and aggregates their outputs through x fusion layer. Formally, denote the entire multi-branch operation as:
hp Inception Fx),
7 is the stacked local and global features (same as in Equation 3), and Inception(-) represents the multi-scale convolutional extraction followed by channel-wise fusion.
where F, E 2
Variant 3 (ID Convolution): This variant treats the local observation and global context as two separate channels of a ID sequence. It applies ID convolution over the time dimension:
h Conv I in out=1 (F,))
The right side of Table 8 presents the comparison among these variants. The results demonstrate that our Original 2D Convolution strategy yields the most consistent and superior performance, achieving the best MSE in 19 out of 40 cases and the best MAE in 18 cases.
Necessity of Convolution: The inferior performance of Variant (Concat) compared to the Original model (c.g.. ETTh2 horizon 720 MSE 0.423 vs. 0.452) highlights the importance of the receptive field provided by convolution operations capture temporal dependencies.
Efficiency vs. Complexity: Surprisingly, the multi-scale Variant 2 (Inception) does not outperform the simpler single-kemel 2D convolution. While theoretically more powerful. the increased parameter count may lead to overfitting on shorter sequences, or it suggests that the dominant periodicity is well-captured by single, optimally sized kernel.
Structure Bias: The Original 2D Conv outperforms Variant 3 (ID Conv). We hypothesize that the 2D convolution kernel enforces a stronger structural prior for aligning the local and global rows compared treating them abstract channels, thereby learning more robust fusion of the retrieved global information.
In conclusion, the ablation studies confirm that the GTR module with 2D convolution and RevIN represents the most effective and robust configuration for multivariate time series forecasting.
C.2.3 CAPABILITY WITH
MODELING
Despite its strong performance across various datasets, the channel-independent architecture of GTR presents challenge in domains where data exhibits strong spatio-temporal dependencies. For instance, the Traffic dataset exhibits sigmificant vater-variable dependencies, as road network flows are highly correlated. Models that effectively capture these relationships typically outperform channel- independent approaches on such datasets (Liu et al., 2024b; Wang et al., 2024d). To demonstrate GTR's adaptability and its ability to integrate with inter-channel modeling, introduce novel Global Token Aggregation (GTA) module.
The GTA (Global Token Aggregation) module is designed to distill the most salient inter-channel relationships into single, comprehensive global representation. This is achieved by first transforming the input embedding tensor Q RTXN where T is the sequence length and N is the number of channels into a global token This global token is computed via channel-wise weighted aggregation, where the weights are derived from a softmax over the channel dimension. The resulting global context is then broadcast and fused back with the original channels to guide each channel's s prediction with unified global awareness.
Formally, given the input global representation Q E R the process proceeds as follows:
1. Channel Aggregation: Compute channel-wise attention weights using softmax along the channel dimension (dimension 1, assuming 0-indexed axes). Then, aggregate across channels to obtain a global token g E 7'
weight Softmax (Q) TxN
Q... weight E Tx1
n=1
Here, Q.,, denotes the n-th channel across all time steps, and the weighted sum produces a single global token per time step.
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Published as a conference paper at ICLR 2026
2. Re-broadeast and Fusion: global guidance tensor, which is then fused (e.g., via addition or concatenation - though your formula suggests replacement) with the original representation:
The global token g is broadcast across all N channels to form
Qused = g 11x RR
where 1IxN is a row vector of ones, and broadcasting replicates across the channel dimension.
By injecting this globally aggregated token into each channel, the GTA module enables each channel's prediction to be informed by the collective dynamics of all channels, thereby capturing inter-variable dependencies in parameter-efficient manner.
The integration of the GTA module significantly boosts GTR's performance on the challenging traffic dataset, shown in Table 9. The aggregated token provides the necessary inter-channel context, resulting in substantial reduction in both Mean Squared Error (MSE) across all prediction horizons.
Table 9: Performance Comparison on the Traffic Dataset.
Setup
GTR
GTA module
Improvement (%)f
T
S
MSE
MAE
MSE
MAE
MSE 4
MAE
96
96
0.440
0.264
0.399
0.265
9.3%
-0.4%
96
192
0.459
0.275
0.418
0.273
8.8%
0.7%
96
336
0.473
0.283
0.431
0.279
8.8%
1.4%
96
720
0.515
0.302
0.462
0.298
10.4%
1.3%
This remarkable improvement confirms that while GTR is designed channcl-independent model, its core architecture is highly adaptable. When augmented with a mechanism to incorporate inter- variable dependencies, it achieve state-of-the-art performance challenging datasets where such relationships are critical.
C.3 ERROR BAR ANALYSIS
To further evaluate the robustness of our method, we conducted comprehensive error bar analysis by evaluating GTR across multiple random seeds on diverse benchmark datasets. For each dataset, we report the standard deviation of MSE and MAE over independent runs with different initialization seeds. As shown Table 10 and Figure 5, GTR exhibits remarkably low variance (mostly below 0.001) across all datasets and forecasting horizons. This strongly indicates the robustness of GTR.
0.28
0.26
0.30
0.28
MSE
MAE
0.26
0.24
0.18
0.16
0.14
0.20
2024
2025
2026
2027
2025
2026
2027
Random Seed
Random Seed
Figure 5: Performance of GTR under different random seeds on several datasets. The look-back
length T' and forecasting horizon S are fixed 96.
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Published as a conference paper at ICLR 2026
Table 10: Full results of different models with the look-back length 7=96. The reported results with standard deviation of GTR are averaged from 5 runs (with different random seeds of {2025, 2026, 2027, 2028, 2029)). The best results are highlighted in bold, while the second- best results are underlined.
Time (2024c)
iTransformer (2024b)
CycleNet (2024)
TimeXer (2024d)
GTR (Ours)
Model
Metric
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
96
0.375
0.400
0.386
0.405
0.375
0.395
0,382
0,403
0.367 = 0.002
0.391 = 0.001
192
0.429
0.421
0.441
0.436
0.436
0.428
0,429
0.435
0.420 1 0.002
0.421
0.001
336
0.484
0.458
0.487
0.458
0.496
0.455
0.468
0.448
0.476 + 0.006
0.447
0.001
720
0.498
0.482
0,503
0.491
0.520
0.484
0.469
0.461
0.493 = 0.021
0.476
0.011
Avg
0.447
0.440
0.454
0.448
0.457
0.441
0.437
0.437
0.439 1 0.007
0.434
0.003
96
0.289
0.341
0.297
0.349
0.298
0.344
0.286
0.338
0.290 + 0.002
0.342
0.001
ET
192
0.372
0.392
0.380
0,400
0.372
0.396
0.363
0.389
0,362 + 0.002
0.389
0.001
336
0,386
0.414
0.428
0.432
0.431
0.439
0.414
0.423
0.414 = 0.003
0,429 = 0.002
720
0.412
0.434
0.427
0.445
0.450
0.458
0.408
0.432
0,423 + 0.008
0.442
0.004
Avg
0.365
0.395
0.383
0.407
0.388
0.409
0.368
0.396
0.372 + 0.003
0,400
0.002
96
0.320
0.357
0.334
0.368
0.319
0.360
0.318
0.356
0,305 + 0.001
0.349
0.001
FTTml
192
0.361
0.381
0.377
0.391
0.360
0.381
0.362
0.383
0.349 - 0.001
0.375
0.001
336
0.390
0.404
0.426
0.420
0.389
0.403
0.395
0.407
0,380 + 0.001
0.398
0.001
720
0.454
0.441
0.491
0.459
0.447
0.441
0.452
0.441
0.435 = 0.001
0.001 0.436
Avg
0.381
0.396
0.407
0.410
0.379
0.396
0.382
0.397
0.367 = 0.001
0,389
0.001
96
0.175
0.258
0.180
0.264
0.163
0.246
0.171
0.256
0.168 + 0.001
0.249
0.001
FTTm2
192
0.237
0.299
0.250
0.309
0.229
0.290
0.237
0.299
0.232 1 0.001
0.292
0.001
336
0.298
0.340
0.311
0.348
0,284
0.327
0.296
0.338
0.287 + 0.001
0.330
0.001
720
0.391
0.396
0.412
0.407
0.389
0.391
0.392
0.394
0.386 = 0.001
0,390
0.001
Avg
0.275
0.323
0.288
0.332
0.266
0.314
0.274
0.322
0.268 + 0.001
0.315
0.001
Electricity
96
0.153
0,247
0.148
0.240
0.136
0.229
0.140
0,242
0.134 - 0.001
0.229
0.001
192
0.166
0.256
0.162
0.253
0.152
0.244
0.157
0.256
0.152 1 0.001
0.245
0.001
336
0.185
0.277
0.178
0.269
0.170
0.264
0.176
0.275
0.171 + 0.001
0,264
0.001
720
0.225
0.310
0.225
0.317
0.212
0.299
0.211
0.306
0.208 + 0.001
0. 0.300
0.001
Avg
0.182
0.273
0.178
0,270
0.168
0.259
0.171
0.270
0.166 1 0.001
0.260
0.001
Solar- Energy
96
0.189
0,259
0,203
0.237
0.190
0.247
0.215
0.295
0.176 + 0.004
0.235 0.008
192
0.222
0,283
0.233
0.261
0.210
0.266
0.236
0.301
0.193 = 0.004
0.244 = 0.007
336
0.231
0.292
0.248
0.273
0.217
0.266
0.252
0.307
0.201 T 0.004
0.250
0.008
720
0.223
0.285
0.249
0.275
0.223
0.266
0.244
0.305
0.205
0.004
0.251
0.003
Avg
0.216
0,280
0.233
0.262
0.210
0.261
0.237
0.302
0.194 = 0.004
0.245 = 0.006
96
0.163
0.209
0.174
0.214
0.158
0.203
0.157
0.205
0.154 + 0.001
0.200) = 0.001
Weather
192
0.208
0.250
0.221
0.254
0.207
0.247
0.204
0.247
0.202 1 0.001
0.244 = 0.001
336
0,251
0,287
0.278
0.296
0.262
0.289
0.261
0.290
0.259 + 0.001
0.287 0.001
720
0,339
0.341
0.358
0.349
0.344
0.344
0.340
0.341
0.341 = 0.001
0.342 = 0.001
Avg
0.240
0.272
0.258
0.278
0.243
0.271
0.241
0.271
0.239 1 0.001
0.268 0.001
C.4 FULL RESULTS WITH LONGER LOOK-BACK WINDOW
With the recent development of model light weighting techniques, particularly the adoption of hhunnel-indeeenemt strategies (first applied in DLinear (Zeng et al., 2023) and PatchTST (Nie et al., 2023)). more models have started to experiment with longer look-back windows in pursuit of higher predictive accuracy. For instance, DLinear and PatchTST default to using look-back windows of T 336, while RAFT (Han et al., 2025) and Sparse (Lin et al., 2025b) default to using = 720. To explore GTR's performance with longer look-back windows, we compared GTR with these advanced models using their respective default, longer look-back windows in Table 11.
It can be seen that GTR maintains a significant performance advantage even when compared against state-of-the tf- baselines utilizing extended historical contexts. Specifically, GTR achieves the best MSE performance in 19 out of 32 metrics under the T = 336 setting and 15 out of 32 metrics under the T 720 setting, consistently surpassing strong competitors like PatchTST, SparseTTFF, and
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Published as a conference paper at ICLR 2026
Table 11: Full results of different models with longer look-back lengths T' E {336, 7203. The best results are highlighted in bold and the second best are underlined.
Lookback
T = 336
7' = 720
Model
DLincar (2023)
PacchTST (2023)
CycleNet (2024)
GTR
RAFT (2025)
SparseTSF (2025b)
CycleNet (2024)
GTR
(Ours)
(Ours)
Metric
MSB
MAB
MSE
MAB
MSE
MAE
MSE
MAE
MSE
MAR
MSB
MAF
MSE
MAE
MSE
MAB
96
0.374
0.385
0.405
0.374
0.396
0.395
0.367
0.397
0.362
0.379
0.403
0.368
0.400
ETThl
192
0.430
0.440
0.414
0.421
0.406
0.415
0.409
0.420
0.411
0.427
0.403
0.411
0.416
0.425
0.409
0.424
336
0.442
0.445
0.440
0.440
0.431
0.430
0.432
0.454
0.436
0.442
0.434
0.428
0.447
0.445
0.443
0.449
730
0.497
0.507
0.456
0.470
0.450
0.464
0.451
0.463
0.467
0.478
0.426
0.447
0.477
0.483
0.464
0.476
Avg
0.436
0.448
0.424
0.434
0.415
0.426
0.415
0.428
0.420
0.436
0.406
0.419
0.430
0.439
0.421
0.437
96
0.281
0.347
0.275
0.337
0,279
0.341
0.274
0.341
0.276
0. 343
0.294
0. 0.346
0.271
0.337
0.275
0.343
ET112
192
0.367
0.404
0.338
0.379
0.342
0.385
0,340
0.385
0.347
0.393
0.339
0.377
0.332
0.380
0.340
0.388
336
0.438
0.454
0.365
0.398
0.371
0.418
0.363
0.44
0.376
0.425
0.359
0.397
0.362
0.408
0.377
0.416
720
0.598
0.391
0.429
0.426
0.451
0.405
0.439
0.473
0.383
0.415
0.449
0.406
0.442
Avg
0.421
0.4.9
0.342
0.386
0.355
0.398
0.345
0.393
0.359
0.409
0.344
0.386
0.345
0.394
0.349
0.397
96
0.307
0.350
0.291
0.343
0,299
0.348
0.283
0.337
0.302
0. 3.949
0.312
0.354
0.307
0.353
0.290
0.345
BTTml
0.340
0.334
0.370
0.334
0.367
0.323
0.365
0.329
0.367
0.347
0.376
0.337
0.371
0.328
0.371
336
0.377
0.397
0.367
0.392
0.368
0. 0.386
0.355
0.384
0.355
0.383
0.367
0. 386
0,364
0.387
0.357
0.388
720
0.433
0.433
0.422
0.426
0.417
0.414
0.420
0.422
0.406
0.413
0.419
0.413
0.410
0.411
0.417
0.420
Avg
0.364
0.388
0.354
0,383
0.355
0.379
0.345
0.377
0.348
0.378
0.361
0.382
0.355
0.381
0.348
0.381
96
0.165
0.257
0.164
0.254
0.159
0,247
0.161
0.252
0.164
0.256
0.163
0.252
0.159
0.249
0.169
0.258
ETTam2
192
0.227
0.307
0.221
0.293
0.314
0.286
0.221
0.292
0.219
0.296
0.217
0.290
0.214
0.289
0.220
0.295
336
0,304
0.362
0.276
0.328
0,269
0.322
0.278
0.326
0.275
0.336
0.270
0.527
0.268
0.326
0,270
0.328
730
0.431
0.441
0.366
0.383
013663
0.382
0,359
0.388
0.359
0.392
0.352
0.379
0.353
0.384
0.355
0.389
Avg
0.282
0.342
0.257
0.315
0.309
0.254
0.314
0:254
0.320
0.251
0.312
0.249
0.253
0.317
Electicity
96
0.140
0:237
0.131
0.225
0.128
0.223
0.127
0.222
0.133
0.232
0.138
0.233
0.128
0.221
0.128
0.226
192
0,153
0.250
0.148
0.240
0.144
0.237
0.147
0.242
0.149
0.247
0,151
0.244
0.143
0.237
0.146
0.244
336
0.169
0.267
0.165
0.259
0.160
0.254
0,165
0.260
0.161
0.259
0.166
0.159
0.162
0.261
720
0,203
0.299
0.202
0.291
0.198
0,287
0.199
0.292
0.197
0.297
0.205
0.293
0.197
0.287
0.197
0.295
Avg
0.166
0,263
0.162
0.254
0.158
0.250
0.159
0.254
0.160
0.259
0.165
0.258
0.157
0,250
0.158
0.256
Solar Errengy
96
0.222
0.292
0,190
0.278
0,200
0,250
0.180
0.237
0.192
0.251
0.195
0.243
0.194
0.255
0.178
0.242
192
0.249
0.313
0,206
0,252
0.221
0,261
0.196
0.254
0.247
0.323
0.215
0.254
0.205
0.251
0.198
0.260
336
0,268
0.327
0.217
0.254
0.236
0.272
0.201
0.257
0.240
0.300
0,232
0. 0.262
0.218
0.257
0.202
0.264
720
0,271
0.526
0.219
0.255
0,245
0,277
0.205
0.258
0.246
0.311
0.237
0.263
0,239
0.278
0.209
0,369
Avg
0.253
0.315
0.208
0.260
0.226
0.265
0.196
0.252
0,231
0.296
0.220
0.256
0.214
0.260
0.197
0.259
0.174
0.235
0.155
0.204
0.167
0.221
0.147
0.199
0.232
0.169
0.223
0.164
0.220
0.200
Weather
192
0.219
0.281
0.195
0.242
0.212
0.258
0.192
0.240
0.211
0.264
0.214
0.262
0.209
0.258
0.192
0.244
336
0,264
0.317
0,249
0.283
0.260
0.293
0.243
0
0.260
0.302
0.257
0.293
0.255
0.292
0.243
0,283
720
0.324
0.321
0.334
0.328
0.339
0.324
0.337
0.355
0.321
0.320
0.338
0.317
0.336
Avg
0.245
0.299
0,230
0.266
0.242
0,278
0.227
0.264
0.241
0. 0.286
0.240
0.280
0.237
0.277
0.225
0,266
1d Count
4
13
13
3
11
13
15
7
RAFT. Notably, on the Solar-Energy dataset with T = 336, GTR reduces MSE by 13.2% compared to the CycleNet, and on Weather with T = 720, it outperforms RAFT by 6.7% in MSE.
Crucially, although the architectural design of GTR primarily targets scenarios with restricted historical contexts (Figure 3). it exhibits remarkable adaptability when scaled to extended horizons. As evidenced by the results, GTR does not merely function as a remedial solution for short inputs but continues to deliver competitive, tffe--of-the-ar performance under long look-back settings. This confirms that GTR's 's mechanism for explicit global cycle retrieval is robust and effective.
5.5 COMPARISON WITH TTMESTAMP-BASEE APPROACHES
Distinct from methods that learn periodicity directly from historical data, another prevalent paradigm in long-term forecasting leverages explicit timestamp information (e.g., time-of-day, day-of-week) to model global temporal dependencies (Wang et al., 2024a; Yang et al., 2025a). These approaches typically operate as modular plugins, designed to augment existing backbones by injecting global guidance derived from calendar features. Specifically, they model timestamps to capture global contexts and adaptively fuse these signals with local observations.
To comprehensively evaluate the effectiveness of our proposed GTR module, we conducted comparative study using GLAFF (Wang et al., 2024a) as a representative baseline. We integrated both our proposed GTR module and the GLAFF module into two distinct backbones, DLinear (Zeng et al., 2023) and iTransformer (Liu et al., 2024b), and evaluated their performance on the Electricity and Weather datasets. The detailed results are presented in Table 12.
22

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Published as a conference paper at ICLR 2026
Table 12: Ablation study of GTR and GLAFF modules with the look-back length T 96. All results in this table are reproduced using the official GLAFF implementation. We compare the performance (MSE, MAE) and efficiency (Training Time, Memory Cost) across four prediction horizons (T' E [96, 192, 336, 720)) on Electricity and Weather datasets. The best performance in each setting highlighted in bold.
Model
Horizon
Modules
Electricity
Weather
GTR
GLAFF
MSF
MAB
Time(s)
Mem(MB)
MSF
MAE
Time(s)
Mem(MB)
0.2073
0.2948
52.04
0.31
0.1974
0.2572
26.08
0.12
96
0.1653
0.2602
23.85
4.85
0.2070
0.2653
38.89
4.36
DLinear
V
0.2042
0.2939
46.64
0.38
0.2410
0.2963
30.78
0.19
X
v
0.1851
0.2747
32.47
4.92
0.2530
0,3069
39.17
4.43
336
V
x
0.2197
0.3117
36.72
0.49
0.2871
0.3347
15.94
0.30
0.2179
0.3053
22.35
0.2955
0,3397
37.35
4.54
720
V
x
0.2569
0.3448
19.09
0.77
0,3554
0.3887
8.68
0.58
x
0,2904
0,3553
19.13
5.31
0.4542
0,4180
27.99
4.82
V
0.1476
0.2411
86.33
0.1731
0.2168
61.77
48.53
96
iTransformer
0.1504
0.2434
45.34
53.26
0.2028
0.2410
78.12
52.77
V 0.1680
0.2610
74.71
48.91
0.220M4
0.2615
55.42
48.72
x
0.1922
0,2685
36.50
53.45
0.2476
0.2797
54.04
52.96
V
0.1838
0.2781
36.83
49.19
0.2829
0.3061
29.95
49.00
336
0.2343
0.2968
34.68
53.73
0.3398
0.3322
51,46
53.24
V
0.2178
0.3047
34,97
49.95
0.3711
0.3614
27.25
49.75
720
X
0.5529
0.4208
103.07
54.00
0.6578
0.4316
51.02
54.00
Prediction Accuracy and Robustness. As shown in Table 12, the GTR module demonstrates superior performance and robustness compared to the timestamp- based GLAFF, particularly in long-term forecasting scenarios. While timestamp-based methods can capture explicit cyclic patterns shorter horizons (e.g.. DLinear Electricity at 7 = 96), they struggle to generalize to longer prediction windows due to the potential overfitting of rigid calendar features. Notably, at the prediction horizon of 720, the performance of GLAFF degrades significantly both datasets (c.g., iTTrnsformer, the MSE on Electricity spikes to 0.5529). In contrast, GTR maintains stable and accurate predictions (MSE 0.2178), indicating that learning periodicity directly from time-series tata-rathhr than relying on external timestamss-yeelds better robustness for long-term modeling.
Computational Efficiency. Beyond prediction accuracy, GTR exhibits significant advantage in computational efficiency. Timestamp-base approaches like GLAFF typically require additional em- bedding layers and complex attention or mixing mechanisms to process high-dimensional timestamp features, leading to increased memory usage and training time. GTR incurs negligible memory over- head compared to the backbone models (e.g.. ~0.3 MB vs. ~4.8 MB on DLinear). This lightweight characteristic makes GTR more practical solution for real-world deployments where computational resources are constrained, achieving better trade-off between performance and cost.
C.6 VISUALIZATION RESULTS
To provide clear and comprehensive comparison among different models, we present supplementary
prediction visualizations on the PEMS datasets in the accompanying figures (6; 7; 8; 9;). Among all evaluated models, GTR consistently demonstrates the highest precision in capturing future traffic series variations and exhibits superior overall forecasting performance.
Furthermore, we conduct a direct visual comparison between GTR and its underlying MLP backbone model. The results reveal a striking improvement: GTR significantly enhances the fitting accuracy of the original MLP, effectively mitigating its tendency to oversmooth temporal dynamics and miss subtle yet critical traffic patterns. Notably, across multiple visualization scenarios, the input sequences exhibit little to no pronounced periodicity yet GTR is still able to accurately capture and forecast the underlying future trends. This highlights GTR's R's robustness in modeling complex, non-stationary traffic dynamics even in the absence of strong periodic patterns, further underscoring the effectiveness of its architectural design in learning global temporal representations.
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Figure 7: Visualization of 1aput-96-preddeee results on the PEMS04 dataset.
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Figure 8: Visualization of capput-9--prediee results on the PEMS07 dataset.
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Figure Visualization of 9reeict9- results on the PEMS08 dataset.
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Published as a conference paper at ICLR 2026
D THEORETICAL ANALYSIS
In this section, we provide a rigorous theoretical analysis of the GTR module. We demonstrate that GTR reduces the estimation error of multivariate correlations by leveraging global temporal information, using a Bayesian estimation framework with strict mathematical derivation.
D.1 PROBLEM SETUP AND ASSUMPTIONS
Consider two variables n and m in a multivariate time series. Let Y, and Ym represent the ground- truth periodic patterns of these variables, which are zero-mean random variables with variance oy and correlation E[Y,Y, /
We make the following assumptions:
1. Observation Error:
The observed segment T, = +/o, where 7/n ~ NO, represents the error term caused by non-stationary phenomena.
2. Global Embedding Error: The global temporal embedding On Yn En where En ~ (0, o²) independent embedding error.
3. Independence: All error terms The Mms Ens Em are mutually independent.
D.2 GTR A BAYESIAN ESTIMATOR
During the inference stage of GTR, the operation of combining observed segments 2n and global embeddings Qn is pure linear combination:
-2 + 0
(8)
o + o
This formulation corresponds to the posterior mean estimator in a Bayesian framework, where:
In represents the likelihood of observing Yn.
Qn represents the prior information about Y,
The weights of and of proportional to the inverse of the noise variances
D.3 THEORETICAL RESULT
Theorem D.1. Given the above assumptions, of < o. then:
|Corr(Zn, (Zn, Zm) pl < |corr(In, 3m) pl
(9)
where coIr(In, Im) is the correlation of raw observations, and corr Zns Zm) is the correlation after GTR module processing.
Proof. First, we compute the correlation of raw observations:
[n
E[(Yn + 7n) + Tmn)
=EYY, Ym) + E E/mn Vm) + Bmn
=o? +0+0+0 o
= + o²
Var(x,) E[x²] (B[x,])²
E((Y, + 7n )
=| + 1
= + of
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Therefore:
poj + o
2 2
corr Tm)
(10)
Var F. Var
oy + o
The estimation error for raw observations is:
pog + o
[corr(Tn: Tm) - pl
0y + o
pot o
p
po
0y 0
o p)
oy + 0
Next, we compute the correlation after GTR processing. First, the expectation:
(ofun + o 2n + o3(mm)
2m = E
(0)) + 222²
o. B[xnIIm + B(xn + (0 [0( [ + o?)²
Calculate each term:
Bm pay + o;
B|r, Qml EI(Y,, + mm)) + Em) = poy
B[Q (Y + eY + mm] = poty
E[QuQm] B( eY +em]] = + +
Substituting these values:
Bn mm]
(:0 2 + -20 + ( + 0,0000
+ +o2)
( + o2)2
20:0
+ 0
po
(oū + o?)2
1 (0 02)² 2 oz)
(o + o.)2
20 oox 2z + o
Now calculate the variance:
Var(zn) B[23]] (E[zn])²
na + 0 2n ? o²
= E
A + 20
+ +
(0? + o?)²
Calculate each term:
E[ = o + o
B o + 2
E x Q.] E((Y, + my, + en)] =
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Substituting these values:
1
Var(zn)
0: (0 + t 20 to + +
(0) + o?)o
1
o (0 20 +0:00 0000
(0) + o2)²
0 ( + +20
(0) + o2)²
02
oy + o +
Therefore, the correlation after GTR processing is:
E[2, 2m 2m
corr (Zn: 2m)
Var((z, (zn) (ar(Zm)
0.00
po + ottoo
o7 + ofa?
a9+07
The estimation error for CTR-ppocessed data is:
po + d?0?
[corr(Zn; Zm) - -pl
0203 o2 + केt
pot of) + 0..0 pap 1 -
o.)
(o + o.) + o
o2 p) oz + o?) + o?.
Now, we compare the two errors:
02 1-pl
corr (2n 2m pl
(03 +00
corr (Iny Tmm) p)
1-p-p
aGt0z
02 + o
(o) - o3)
o
2202
We need show this ratio is less than I when 02 < o
02 + t < (0 + o,)
+0.0 202
o'o2 + o000 < of + oooo + o.00
<<
Since of and of > the inequality holds. Therefore:
[corr(En, 7m) pl < |corr($nns pl
(11)
This completes the proof.
GTR fuses global information sources to produce more accurate correlation estimates. As shown in Figure 4, GTR systematically reduces the error in correlation estimation between variables, confirming GTR's ability to better capture global temporal dependencies.
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Published as a conference paper at ICLR 2026
E EXTENDED RELATED WORK
MTSF Plugins. Recent advancements in MTSF have shifted towards "Plug-and-Play" paradigms, which decompose complex modeling tasks into modular components that can be seamlessly integrated into various backbone architectures.
primary focus of these modules is enhancing multi-correlation and inter-variable dependencies modeling. For example, to address computational efficiency in high-dimensional data, SOFTS (Han al.. 2024) incorporates the STAR module, which aggregates global information into core repre- sentation and redistributes it to individual series to model channel interactions with linear complexity. CrossLinear (Zhou et al., 2025) was proposed as a lightweight embedding module designed to capture dime-invariant dependencies between target and exogenous variables within linear predictors. TQNet (Lin et al., 2025a) utilizes TQ techniques to learns more robust multivariate correlations.
The effective utilization of timestamp information is critical for capturing the inherent seasonality and cyclic dynamics underlying time series data. While early approaches predominantly relied on handcrafted features to encode calendar timestamps, GLAFF (Wang et al., 2024a) advances learnable representations by adaptively balancing global and local temporal information to facilitate seamless integration with arbitrary forecasting backbones. Furthermore, VH-NBEATS (Yang et al., 2025a) introduces a hierarchical timestamp basis block that explicitly leverages multi-scale calendar information capture complex hierarchical temporal effects.
Accurately capturing periodic patterns and cyclic dynamics is fundamental for long-term forecasting, yet standard models often struggle disentangle these from complex trends without specialized mechanisms. To address this, CycleNet (Lin et al., 2024) introduces RCF technique that explicitly models inherent periodicities using learnable recurrent cycles, thereby allowing simple backbones to focus efficiently on predicting residual dynamics. STiD (Shao et al., 2022) identifies indistnguushabbiltty as a key challenge MTSF and introduces a simple MLP--baedd model aug- mented with spatial and temporal identity embeddings to achieve strong performance. Addressing the limitations of fixed decomposition kernels, Leddam (Yu et al., 2024) proposes learnable decom- position strategy coupled with dual attention module to adaptively separate complex intra-series variations from inter- dependencies. Furthermore, Sparse TSF (Lin et al., 2025b) utilizes a Cross- Period Sparse Forecasting technique that decouples trend and periodicity through downsampling, functioning as a structural regularization mechanism to reduce model complexity while robustly capturing cross-period trends.
Despite these methodological strides, a critical gap remains in the current landscape of plug-and-plan modules. Existing approaches lack dedicated mechanism to address the fundamental informa- tion bottleneck caused by restricted historical contexts. Specifically, when the look-back window shorter than the inherent cycle length, standard models even when augmented with current to capture global periodic dynamics due to the absence of complete cycle observa- tions. Our proposed GTR provides an efficient and universal solution that empowers host models to dynamically retrieve and leverage global temporal patterns beyond their immediate receptive field.
F
USES OF LLMS
This work was completed without the use of any LLMs or Al-assisted writing tools.
29


Reviews:
[{"review_id": "GN3Jteu8Vh", "reviewer": "Reviewer_j7zs", "summary": "The paper proposed a Global Temporal Retriever (GTR) module to model complex periodic dynamics and address the limitation that existing models have a fixed look-back window in multivariate time series forecasting. GTR overcomes this by defining a cycle index vector for cycle information alignment, which was used in retrieving temporal information from the global parameter matrix $Q$. Comprehensive experiments support the effectiveness of GTR, both when combined with a simple MLP backbone and when integrated into other architectures.", "questions": "* How did the authors decide the length of the time series segment (e.g., Figure 1)? Does it depend on the frequency of each dataset (as listed in Table 5)?\n* How did the authors determine the global cycle length $L$ for each dataset in the experiments?\n* Would this method work if the absolute time $t_0$ is shifted when pre-processing the dataset, e.g., standardizing the first observation to be 0?\n* Does this method only produce point estimates, but not probabilistic forecasting?\n* How did the authors choose the hyperparameters for baseline methods? Are these models trained from scratch, or do they reuse numbers from the literature? For example, in Table 3, the MLP-Layer (without GTR) is already competitive when compared with other state-of-the-art models (without GTR).\n\nTypo:\nIn Appendix A.2, both metrics are defined with $\\sum_0^T$, where $i=$ is missing and the index should start from $i=1$ (following the paper's notation).", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 4, "strengths": "* The paper is very organized and well-written. The visualization (e.g., Pearson correlation matrix and Figure 2) clearly delivers the message and the design of GTR.\n* The theoretical analysis and limitations are discussed in great detail, indicating the strengths and limitations of GTR that motivate future extensions. \n* While the GTR module is light-weight, the experimental results are strong.", "weaknesses": "* It would be better if the forecasting results included error bars, as the metrics have close values among different methods.\n* The experimental setup could be further elaborated, e.g., how did the authors choose the hyperparameters for baseline methods? Please see the detailed questions below.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ZBBJOAMmfe", "reviewer": "Reviewer_FfDY", "summary": "This paper proposes an adaptable and lightweight plug-and-play solution designed to mitigate the inherent lack of long-term temporal awareness in existing forecasting architectures. By enabling models to effectively access and utilize crucial global periodic patterns often missed in limited look-back windows, the proposed module significantly enhances the predictive ability, yielding superior and consistent performance gains in multivariate time series forecasting for both short-horizon and extended-horizon tasks.", "questions": "1. Is the global cycle length ($L$) a predefined hyperparameter, or is its value learned by the network during the training process?\n\n2. In the Eq.(1), what are the distinct advantages and disadvantages of the proposed positional embedding compared to conventional techniques (e.g., learnable embeddings) regarding periodicity awareness and noise robustness?\n\n3. In page 5, line 246, is the output ($Z$) maintains the same feature dimension as the original input features?\n\n4. In Table 3, can the authors explain whether these differential gains are primarily due to the inherent lack of temporal awareness in specific backbones or the unique periodic characteristics of the evaluated datasets?\n\n5. Does the author assume a linear relationship between the embeddings, or that $z$ is linearly transformed from $x$? And is there any experimental evidence provided to directly support the claims made in Theorem 3.2?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The paper is well-written, clear, and logically structured. The authors provide a well-organized explanation of the technical specifics of the proposed plug-and-play module.\n\n2. The experimental section is comprehensive. The authors have conducted extensive comparative and ablation studies on the multivariate time series forecasting task.\n\n3. The proposed module is characterized by its lightweight and plug-and-play nature. This design choice significantly increases its generalizability and practical value when integrating with existing models, marking a valuable and impactful contribution to the field of temporal awareness modeling.", "weaknesses": "1. While the proposed module demonstrates effective performance improvements, its core mechanism is not fundamentally novel.\n\n2. The clarity of the methodology are hindered by the lack of proper equation indexing, alongside several instances of ambiguous or missing variable dimensions within Section 3.\n\n3. The theoretical analysis is confusing and unmatched with the proposed method, as the simplified linear assumptions in its derivation fail to establish a clear mechanistic link to the empirical success of the non-linear fusion and prediction architecture.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "WoWM1XNr59", "reviewer": "Reviewer_L6pR", "summary": "This paper tackles the limitation of restricted input windows in time series forecasting, which prevents models from capturing global periodic patterns. The authors propose a lightweight and plug-and-play module, **Global Temporal Retriever (GTR)**. GTR performs adaptive global temporal embedding over the entire cycle and dynamically retrieves and aligns globally relevant segments with the current input. This effectively bridges short-term observations with long-term periodicity. Experiments show that GTR achieves state-of-the-art performance on both short-term and long-term forecasting tasks with minimal computational overhead.", "questions": "See weaknesses.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. Simple and efficient design, easy to follow.\n2. Clear motivation and well-organized paper structure.\n3. Practical idea with strong feasibility and expected performance gains.", "weaknesses": "1. Experiments are mostly limited to input length 96, rather than the commonly used 336 setting in PatchTST/DLinear, which weakens the persuasiveness of the results.\n2. The core idea shares similarities with models like **Cyclenet**, **TQNet** (which theoretically can learn long-term cycles from the entire training set), and **STiD**, i.e., serving as a plugin to capture long-term periodicity. This somewhat reduces novelty. The paper should compare more clearly and deeply with these methods to highlight differences.\n3. Lacks comparison with other long-term periodic modeling techniques, such as timestamp-based long-cycle modeling approaches [1,2].\n4. Baseline selection can be improved by including more recent strong models such as **SOFTS**, **TQNet**, etc.\n\n**References**\n\n[1] Variational Hierarchical N-BEATS Model for Long-term Time-series Forecasting.  \n[2] Rethinking the Power of Timestamps for Robust Time Series Forecasting: A Global-Local Fusion Perspective.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "1qVNVznlUA", "reviewer": "Reviewer_HtL7", "summary": "This paper proposes a method that maintains a global temporal embedding and retrieves the corresponding temporal segment based on the absolute position of the input within the global cycle.", "questions": "1. Provide why training this global parameter matrix $Q$ works, without any design consideration (W2).\n2. Enhance experiments with more ablation study and retrieval-based baselines (W3, W4).\n3. The conceptual example of scenario would strengthen the motivation (W1).", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The core idea is sound and empirically effective. I particularly appreciate Figure 4, which provides a clear visualization that proves the practicality of the proposed approach.\n\n2. The reported quantitative results are strong.", "weaknesses": "1. **Motivation with examples:**\nThe main motivation - namely, that certain global patterns cannot be captured within a limited lookback window - is reasonable but remains abstract. Providing a concrete conceptual example using an existing dataset would make this motivation more convincing and accessible.\n\n2. **Global information guarantee of the global parameter matrix $Q$:**\nThe method introduces a learnable global parameter matrix $Q$, intended to encode global temporal patterns. However, it is not clear how or why this matrix is guaranteed to capture such global information. While Figure 4 provides empirical evidence, a more methodological justification or theoretical explanation would strengthen the paper.\n\n3. **Weak ablation study:**\nThe ablation analysis is limited. It would be informative to include:\n\n* Variants of the temporal pattern extraction module (e.g., replacing the 2D convolution).\n\n* Experiments without instance normalization, to isolate its contribution.\n\n4. **Limited comparison with related retrieval-based methods:**\nThe paper briefly mentions retrieval-based time-series forecasting approaches but does not include direct empirical comparisons. Including at least one retrieval-based baseline would help clarify the advantage of the proposed method.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)