Enhancing Time Series Forecasting through Selective Representation Spaces: A Patch Perspective
Authors: Xingjian Wu
Xiangfei Qiu
Hanyin Cheng
Zhengyu Li
Jilin Hu
Chenjuan Guo
Bin Yang
Venue: NeurIPS 2025 spotlight ()
Keywords: Time Series Forecasting
Primary area: deep_learning

Abstract: Time Series Forecasting has made significant progress with the help of Patching technique, which partitions time series into multiple patches to effectively retain contextual semantic information into a representation space beneficial for modeling long-term dependencies. However, conventional patching partitions a time series into adjacent patches, which causes a fixed representation space, thus resulting in insufficiently expressful representations. In this paper, we pioneer the exploration of constructing a selective representation space to flexibly include the most informative patches for forecasting. Specifically, we propose the Selective Representation Space (SRS) module, which utilizes the learnable Selective Patching and Dynamic Reassembly techniques to adaptively select and shuffle the patches from the contextual time series, aiming at fully exploiting the information of contextual time series to enhance the forecasting performance of patch-based models. To demonstrate the effectiveness of SRS module, we propose a simple yet effective SRSNet consisting of SRS and an MLP head, which achieves state-of-the-art performance on real-world datasets from multiple domains. Furthermore, as a novel plug-and-play module, SRS can also enhance the performance of existing patch-based models. The resources are available at https://github.com/decisionintelligence/SRSNet.

Enhancing Time Series Forecasting through Selective Representation Spaces: A Patch Perspective
Xingjian Wu, Xiangfei Qiu, Hanyin Cheng, Zhengyu Li,
Jilin Hu, Chenjuan Guo, Bin Yang"
East China Normal University
{xjwu, xfqiu, hycheng, , Baarnng..zizeene Lizhengyu)$stu ecnu. edu. {jlhu, ejguo, byang ecnu. edu. cn
Abstract
Time Series Forecasting has made significant progress with the help of Patching technique, which partitionn time series into multiple patches to effectively retain contextual semantic information into representation space beneficial for modeling long-term dependencies. However, conventional patching partitions a time series into adjacent patches, which causes fixed representation space, thus resulting insufficiently expressful representations. In this paper, we pioneer the exploration of constructing selective representation space to flexibly include the most informa- tive patches for forecasting, Specifically, we propose the Selective Representation Space (SRS) module, which utilizes the learnable Selective Patching and Dynamic Reassembly techniques to adaptively select and shuffle the patches from the contex- tual time series, aiming fully exploiting the information of contextual time series to enhance the forecasting performance of patch-base models. To demonstrate the effectiveness of SRS module, we propose simple yet effective SRSNet con- sisting of SRS and an MLP head, which achieves state-of-the-ar performance on real-world datasets from multiple domains. Furthermore, as a novel soug-and-play module, SRS can also enhance the performance of existing patch-based models. The resources are available at httpss///thbb.oomocccccooclllens
Introduction
Time series organize data points chronologically and are either univariate or multivariate depending on the number of variables in each data point. Among the diverse tasks in time series analysis, time series forecasting (TSF) stands out as a critical and widely studied task. It plays crucial role in various fields such as economics, traffic, energy, and AIOps, providing insights for early warnings and proactive decision-making [Qiu al. 2024 2025a Chen al. 2024 Wu et 2024a b).
In recent years, significant progress has been made in TSF with the advancement of deep learning technologies. Among these techniques, the method of dividing time series into patches [Cirstea et al. 2022a Zhang and Yan 2022 Nie et al. 2023) has gradually gained attention. The significance of dividing time series into patches lies in the fact that single time step often lacks clear semantic meaning, while the semantic information between adjacent time points tends to be highly similar. Therefore, by performing patch division on the time series, local features and intrinsic patterns can be captured more effectively. In other words, the patching technique introduces an effective way to construct the representation space for a contextual time series, which first picks the patches adjacent, then projects them to form the representations of the contextal time series. Working upon such representations not only enhances the models' ability to understand temporal dependencies but also significantly reduces computational complexity, thereby improving overall prediction efficiency.
"Corresponding Author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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However, the commonly-use adjacent patching technique, i.e, with fixed stride, divides patches on different contextual time series with the same positions, which results in fixed representa- tion space. Though multi- scale modeling [Chen] cet al. 2024 Tang and Zhang 2025a] may cre- ate several representation spaces with different patch sizes, the fixed strides also limit the po- tential. Because fixed representation spaces sume that all information useful for forecasting evenly distributed in the contextual time ries. As shown in the upper part of Figure [ the assumption is broken due to the phenomenons of changeable periods, shifting, and anomalies. In such cases, the conventional adjacent patching may break the semantics of periods or include anomalies and the shifting processes, which re- tains information that may be harmful for fore-
Adjacent Patching
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casting into the representation space. Since the purpose of patching technique is to construct appropriate representations for contextual time series, allowing models to adaptively include useful information for forecasting a more rea- sonable solution. Therefore, this calls for a selec- tive representation space to mitigate the above phenomenons, which relies on more flexible and adaptive patching paradigm.
Avoid
antormllion
Contextual Series
Forecasting Horizon
Figure Adjacent vs. Selective Patching (both using 4 patches), Adjacent patching partitions time series into adjacent patches, lacking flexibility. Se- lective patching automatically select most relevant sub-series as patches. The upper part shows ex- amples that conventional adjacent patching may include harmful information, thus hindering the forecasting performance. The lower part shows the selected patches that are more relevant for making the corresponding forecasting, demonstrating the flexibility that selective patches offer.
Inspired by the aboved motivations, we propose SRS, plug-and- aad--alddlly module efficiently con- struct the Selective Representation Space for contextual time series. Technically, we propose the Selective Patching to select the patches from the contextual time series, and utilize the Dynamic Reassembly determine the sequence of patches. Both the Selective Patching and Dynamic Reassembly are designed through gradient-friendly paradigm and optimized by the objective of forecasting tasks pursue better prediction accuracy, thus fully exploiting the information in the contextual time series in an adaptive way. We also propose a simple yet effective SRSNet composed of SRS and an MLP head. Through comprehensive experiments on datasets from multiple domains, SRSNet achieves state-of the-art performance to demonstrate the SRS's strong capability of information integration. The contributions are summarized follows:
We propose modular SRS, which efficiently and adaptively constructs the selective representa- tion space to fully exploit the information in the contextual time series, and is able to improve the performance of patch-based models in a simple plug-and-pl paradigm.
Technically, we devise the Selective Patching and Dynamic Reassembly techniques, which able to constitute a selective representation space at the patch perspective. And they are easily to be optimized through gradient-based strategies.
Applying SRS with an MLP forms simple-yet-fffective method, called SRSNet. SRSNet achieves statc-of-the-an performance across multiple real-world datasets, demonstrating the effecttivnness of SRS module.
2
Related works
2.1
Development of Time Series Forecasting
Time series forecasting (TSF) predicts future observations based on historical observations. Early pro- posals primarily employed statistical learning methods. ARIMA [Box and Pierce 1970). ETS [Hyn. dman al. 2008), and VAR [Godahewa et al. 2021 are classical and widely utilized methods. With

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the rapid progress in machine learning technologies, new methods for TSF leveraging machine learning have been developed [Fischer et al. 2020]. Notably, XGBoost (Chen and Guestrin 2016]. Random Forests [Breiman 2001 and LightGBM [Ke et al. 2017] have been applied extensively to better accommodate nonlinear relationships and complex patterns. However, these methods still require manual feature engineering and model design. Taking advantage of the representation learning capabilities offered by deep neural networks (DNNs) on rich data, numerous deep learning- -aase methods have been proposed. TimesNet [Wu et al. 2023a| and SegRNN [Lin et al. [023] treat time series data as sequences of vectors and utilize CNNs or RNNs to capture temporal dependencies. Transformer architectures, including Informer (Zhou al. 2021]. FEDformer [Zhou al. 2022]. Autoformer [Wu et al., 2021]. Triformer [Cirstea et al., 2022b], and PatchTST (Nie et al., 2023) can capture complex relationships between time points more accurately, significantly improving forecast- ing performance. MI.P-based methods, including Sparse TSF [Lin et al. 2024a]. CycleNet [Lin et al.
2024b]. ; DUET [Qiu al. 2025a], NLinear (Zeng et al. 2023 and DLinear (Zeng al., [023]]
utilize relatively straightforwant architectures with a reduced number of parameters. Nevertheless, they have demonstrated highly competitive performance in forecasting accuracy.
2.2 Progress in Patch-based Time Series Forecastng Methods
Patching is a technique originally inspired by the Vision Transformer (Dosovitskiy et al. 2021 and was first introduced in the context of time series forecasting by Triformer [Cirstea al. 2022a and PatchTST [Nic et al. 2023]. In Triformer and PatchTST, time series are segmented into subseries- level patches, which are then treated as input tokens to the Transformer, allowing for modeling temporal dependencies at the patch level. Crossformer (Zhang and Yan 2022] further extends this idea by segmenting each time series into patches and employing self-attention mechanisms model dependencies across both variables and time dimensions. xPatch (Stitsyuk and Choil 2025a adopts the same patch segmentation strategy as PatchTST but introduces a flow-flow architecture consisting linear stream and a CNN-based nonlinear stream. This design explores the advantages of combining patching with innapel-indeeendence techniques within a nonttransformer framework. Pathformer [Chen et al., 2024] and PatchMLP [Tang and ZZhagg 2025b) delve deeper into the effectiveness of patches in time series forecasting and adopt Multi-Scale Patch Embedding. This method effectively captures multiscale relationships within input sequences, providing more enriched representation for downstream forecasting tasks. Nevertheless, current methods overlook issues related to fixed patch strides, which results in fixed representation spaces and may lead to information loss or include unhelpful information. In this paper, we introduce the Selective Representation Space (SRS) module for time series data, which adaptively selects patches and determines their sequences to fully exploit the information in the contextual time series.
of an
3 Methodology
Given contextual time series X E NXT with N channels and T observations, the objective of time series forecasting is to predict the target future horizon Y E R with I. steps. The Representation Space is constructed through the patching embedding operations upon the contextual time series, which first choose the representative subsequences, i.e., patches, and then obtain their embeddings.
Recent methods adopt adjacent patching technique [Nie et al. 2023 Zhang and Yan 2022 Stitsyuk and Choi 2025b Tang and Zhang, 2025a Chen al. 2024 Sun et al.) 2025a Niu et al. [0225] which leads to fixed representation spaces for different contextual time series by retrieving patches
from the same indices. Our proposed Selective Representation Space (SRS) Module (Figure 2). as plug-and-plat technique, aims at making full use of the contextual time series by constructing flexible Selective Representation Spaces to enhance the performance of patch-bac based models.
3.1 Structure Overview
Note that the time series data is always first processed through the Instance Normalization to mitigate the statistical differences between training and testing parts, which reduces the difficulty of model generalization. We then describe the overall pipeline of the Selective Representation Space (SRS) module in Figure by considering the data flow of an input contextual time series X NxT.
We first reintroduce the conventional patching [Cirstea et al. 2022a Nie et al.) 2023], i.e., the adjacent patching. Given the patch size p and stride length the contextual time series X E NxT
3

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Channel
Adjacent
Patch Embedding
Adaptive Fusion
Position Embedding
Patching
Selective
Patching
Dynamic Reassembly
Patch Embedding
Channel
Adjacent Patching
Patch Embedding
Adaptive
Position Embedding
Patch-based models
Selective
Patching
Dynamic
Patch Embedding
Reassembly
Channel
Adjacent
Patch Embedding
Adaptive
Position
Patching
Embedding
Selective
Patching
Dynamic
10
Reassembly
Embedding
Figure 2: The overall pipeline of the SRS module. The multivariate time series is processed with Channel Independent strategy, the Selective Patching first adaptively chooses proper patches from all potential candidate patches. Then the Dynamic Reassembly dertermines the order of the selected patches. Both the Selective Patching and Dynamic Reassembly are gradient-based and learnable. Finally, the Adaptive Fusion integrates the embeddings from Conventional Patching and Dynamic Reassembly, adds the position embeddings to construct the final representations. The subsequent backbones can used directly without changes, so that the SRS module is modular plugin.
is first padded as X' E [x and then reorganized as n [TT-ssss + P E Nxxxp The Conventional Patching stably fetches the patches of fixed indices in different contextual time series, while SRS module aims at automatically selecting patches for each contextual time series.
patches
Considering all potential patch candidates in the padded contextual time series X' R [ there totally exists K (n (2-11) our proposed Selective Patching technique able to adaptively choose n patches to spontaneously utilize the information from the contextual time series, which is continously optimized during backpropagation. The Selective Patching also allows repeated selection, which means that beneficial patches can be selected more than one time. This helps the SRS module "imagine" more suitable and useful representation space for forecasting. Statistically, there exists Ck potential options construct a representation space. We introduce the details of the Selective Putching in Section 3.2
patches. Instead of selecting fixed ones with equal space,
Since the essence of SRS module to reorganize the contextual series which treats the patches as the basic units. We study to what extent the order of selected patches matters, because most methods adopt permutation-varte variiatt components which are sensitive to the order. To this end, the Dynamic Reassembly tenchnique is designed adaptively determine the order of the selected patches of each contextual time series, which statistically provides n! potential options. The Dynamic Reassembly is also learnable, and the details are introduced in Section 3.3
In summary, the Selective Patching and Dynamic Reassembly jointly construct a search space with the size of OR +n- n!, and they are optimized efficiently through gradient-based based strategy to explore such huge search space. Finally, we conduct an Adaptive Fusion during the embedding phase to adaptively fuse the embeddings from the Conventional Patching and method, making them complement each other. We introduce it in Section 3.4 Working as a plug-and aong-and-play technique, SRS Module be easily integrated into patch-based backbones.
3.2 Selective Patching
The objective Selective Patching adaptively choose n patches with size p from the padded contextual time series X' E Nx 1j:s], align with the Conventional Patching. As shown in FigureBleffi we scan the contextual time series with stride equals 1, where all potential patches are represented P' E Nxxxp K
1.
To adaptively choose n patches from the total K ones, we devise an MI.P-based Scorer" to score each patch, and then sclect the one with the highest score based on the ranking. The sample-wised

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Selective Patching
Dynamic Reassembly
Embedding
selected Indices (just an example)
22
scan with stride
Scorer
Patch
Embedding
Fused with embedding from Adjacent Patching
Generate scores all
Scorer
patches each sampling
scores selected patches
SampleNum= f1
SampleNume 1?
Position
argmax
Embedding
Legend
Learnable
Sort the patches by scores
Selected Representation
PatchNum K (stride 1)
PatchNum = (stride 1)
Patches
Figure 3: The detailed architecture of the SRS module. The Selective Patching allows sampling with replacement. It scans all the potential patches with stride equals I, generates n scores for each, then retrieves the patches with max scores in each sampling. Then the Dynamic Reassembly generates scores for selected patches, and sorts them based on the scores to determine the sequence. In the Embedding phase, both the embeddings from the Dynamic Reassembly and Conventional Patching are adaptively fused to form the representations.
process is inspired by Selective State Space Models such as Mamba [ao and Gu 2024 which maintains real-time scores based on the data characteristics. Furthermore, to support selection with replacement, we generate n scores for each patch, denoting the scores of times of sampling:
Scorer RNXXXP RxKxx
S (coorer(PP),TI Argmax(S").
(2)
where S* E Nx denotes the scores of times of sampling, and I E Rxxix dentoes the indices of patches with maximal scores. However, the Argmax operation interrupts the gradient propagation, and existing soft sorting methods [Cuturi al. 2019 Blondel et al. [020)] keep gradient propagation introduce noise and inaccuracies, making the sorting non-intuitive. To mitigate this, we devise a method to achieve differentiable sorting and keep accurate the traditional methods. Note that gradients are attached to S*, we intuitively reuse with a simple yet effective method:
S. = (1 Sim = detach(1/S, man
maz = P' [T', S O S:
(4)
P: max
Pr ④ E
(5)
where [-] means retrieving values based on the indices, Smanr S Nxn denote the maximum scores and their reciprocal. We take the Hadamard product of the selected patches Pa Paaa E R Xxxx xm to attach the gradients to Pixx R XXXp through tensor broadcast along the dimension of patch size. Obviously, E is all-one matrix with gradients, because detach St from the calculation graph to make a hard connection to create the paths gradients.
with E N'n
3.3 Dynamic Reassembly
After obtaining the selected patches De Paax Nxxxxp the order of them is further considered to enhance the construction the representation space. As shown in Figure middle, the Dynamic Reassembly devised to adaptively learn an order reorganize the selected patches.
Following the design of Selective Patching, we also utilize an MLP-based Scorer" to score the selected patches Pi E R. xnxp, Different from Selective Patching, the Dynamic Reassembly processes the permutation problem that the Scorer" only generates score for each selected patch:
Scorer" := R. Nxaxp Nxn
(6)
S = Scorer' (Pimaz),I' Argsort(S"),
(7)
where S" E Nx denotes the scores selected patches, I' E Nxx denotes the indices sorted by the scores Sr, We then sort the patches according the indices I" and use the same technique in
5

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Selective Patching to keep gradient propagation:
Sort S -'[I", Sno detacc((1 (1/ach)) P sort = P: imar [T), =======-
(8)
= =Stort @ Sioe
(9)
p= P sort ① E",
(10)
where Sorts Sin E RR denote the sorted scores and their reciprocal. The P Xxxxp denotes the sorted patches, and P xxxx denotes the sorted patches attached with gradients.
E" E RRRX is obtained by the same way as E
3.4 Embedding
Through Selective Patching and Dynamic Reassembly, P E RNxxp are the finally determined patches represent the contextual time series X E RXxT, which also determines the structure of the representation space. We then manage to obtain the embeddings of these patches to feed the patch-based backbones.
To fully utilize the information from both the constructed patches P E R. R.vxxnn xxxx and the conventional adjacent patches P E IR N xxxp, we design the Adaptive Fusion to fuse their patch embeddings. Technically, construct convex combination between their patch embeddings:
PatchEmbedding' PatchhEmeedding" : R Nxaxp Nxaxd
(11)
E PatchEmbeddding' (P), PatchEmbedding (P)).
(12)
a E + (1 - a) E
(13)
where PatchEmbedding denotes linear projection and is commonly used in time series analysis to encode the patches as embeddings. For embeddings from conventional patching E E R x and our proposed method 8x IR Ngxxxx, they are balanced with E [0, 1 (broadcast) to work in complementary manner. Note that [0, 1]nxd dimension N may be vague some special circumstances such as pretraining. Finally, we add the PositionEmbedding such Sinusoidal Embedding /Vaswani et al. 2017 supplement location information.
x is the most suitable case beacuse the channel
3 = E + PositionEEmbedding(())
(14)
where the & R are the embeddings generated by our proposed SRS Module. Subsequently. they are fed into the patch-based based backbones [Tang and Zhang 2025a Nie et al. 2023 Zhang and
Yan| 2022 Stitsyuk and Choi [0055b] extract the interrelationship. These backbones often consist of an Encoder to further extract the representaions of these embeddings, and a Decoder (linear heads or autoregressive heads) to make forecasts based on the representations. SRS Module directly affects the representation space of Encoders through an adaptive way, so that it is named as "Selective Representation Space".
4 SRSNet
To demonstrate the strong ability of the SRS module fully utilize contextual time series at a Patch Perspective, we design simple yet effective model named SRSNet. It consists of SRS module and Linear/MLP Head (5 2 layers), which can theoretically fit any continuous function according to the universal approximation theorem (Lu et al. 2021]. SRSNet is trained through Mean Squared Error (MSE) for forecasting tasks:
Flatten = Nxnxd (x(xxd) MLP = N (x(xxd) + NKL
(15)
Ý MLP(Flatten(E)) Loss = || Y
(16)
As shown in Section the strong performance of SRSNet demonstrates that SRS module makes full use of the contextual time series, and performs well without a complex backbone.

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5 Experiments
5.1 Experimental Details
Datasets To conduct comprehensive and fair comparisons for different models, we conduct experi- ments on eight well-known forecasting benchmarks as the target datasets, including ETT (4 subsets), Weather, Electricity, Solar, and Traffic, which cover multiple domains-see Table 1
Table I: Statistics of datasets.
Dataset
Domain
Frequency
Lengths
Dim
Split
Description
ETTh1
Electriitty
1 hour
14,00
6:2:2
Power transformer I, comprising seven indicatiors such as eil lemperature and uscful load
ET
Electricity
hour
14,400
6:2:2
Power transformer 2. comprising seven indicators such as oil temperature and useful load
ETTml
Electricity
mins
57,600
6:2:2
temperature and useful load Power transfommer 2, comprising seven indicators such as temperature useful load
Power transformer 1. comprising seven indicators such
ETTm2
Electricity
mins
57,600
Woather
Eavironment
mins
$2.696
21
7:1:2
Recunded every for the whole year 2020, which contains meteorological indicators
Electricity
Elecriiitt
hour
26.304
321
7:1:2
Elecariiity recodds the electricity conumption in kWh every I hour from 2012 to 2014
Solar
Fieery
10 mins
$2,560
137
6:2:2
Solor production records collected from 137 PV plants in Alahama
Traffe
Traffic
hour
17,544
862
7:1:2
Road occupancy measured by 862 sensors San Francisco Bay area freeways
Baselines We compare
SRSNet against state-of-the-arr models in recent years, including
TimeKAN (Huang et al. 2025a], Amplifier [Fei et al. 2025], iTransformer (Liu et al.
2024
TimeMixer Wang et al. 2024), PStehTST [Nie et al. [2023], Crossformer (Zhang and Yan 2022
TimesNet [Wu et al. 2023a DLinear [Zeng et al.] 2023]. Non-stationary Transformer (Station-
ary) [Liu | and Fedformer (Zhou al. 2022].
Implementation Details To keep consistent with previous works, we adopt Mean Squared Error (mse) and Mcan Absolute Error (mac) as evaluation metrics. We consider four forecasting horizon F: [96, 192. 336, 720} for all datasets. Since the size of the look-back window can affect the performance of different models, we choose the look-back window size in [96, 336, 512) for all datasets and report each method's 's best results for fair comparisons.
5.2 Main Results
Comprehensive forecasting results are listed in Table with the best in red bold and the second blue underlined. We have the following observations: 1) Compared with forecasters of different structures (Transformer, CNN, KAN, MLP, Linear). SRSNet achieves an excellent predictive performance. achieves most first rankings in average results and results of different forecastings horizons (Table g in Appendix [A]. 2) Compared to other methods with fixed representation space constructed through conventional adjacent patching (such PatchTST and Crossformer), SRSNet introduces adaptive patching mechanism to construct selective representation spaces, demonstrating superior performance across wider range of datasets. To demonstrate the selective representation spaces that are more helpful for forecasting, we offer intuitive visualization results in Figure 7 in Appendix [5] which demonstrates the capability of SRS in selecting most relevant patches for subsequent forecasting. In summary, with the innovative design of SRS Module, even the simple SRSNet (SRS + MLP) can flexibly handle datasets with diverse characteristics, thus standing out in various scenarios.
Table 2: Multivariate forecasting average results with forecasting horizons F E (96. 192, 336, 720) for the datasets. Red: the best, Blue: the 2nd best. Full results are available in Table of Appendix A
Dutasets
ETTbl
ETTh2
ETTml
ETTm2
Weather
Electriityy
Solar
Traflic
Metries
mac
mac
mse
mic
PEDiommer [2022]
0.433
0.454
0.406
0:438
0.567
0.519
0.335
0,312
0.356
0.219
0.330
0.626
0.620
0.382
Sturknary [2022]
0.667
0.568
0.377
0.419
0.531
0.472
0.384
0.
0.390
0.287
0.310
0.194
0.205
0.990
0.387
0.622
0.340
DLinear [2023]
0.430
0.443
0.470
0.468
0.356
0.378
0.259
0.324
0.242
0.295
0.167
0.264
0.224
0.286
0.418
0.287
TimosNoi [2023]
0.468
0.459
0.390
0.417
0.408
0.415
0.292
0.331
0.255
0.282
0.190
0.284
0.211
0.281
|
0.617
0.327
Crossformer [2023]
0.439
0.461
0.894
0.680
0.464
0.456
0.501
0.505
0.232
0.294
0.171
0.263
0.205
0.232
0.522
0.262
PaccTTT [2023
0.419
0.436
0.351
0.395
0.349
0.381
0.256
0.314
0.224
0.262
0.171
0.270
0.200
0.284
0.397
0.275
TimeMixer [2024]
0.427
0.394
0.356
0.380
0.257
0.225
0.265
0.185
0.284
0.200
0.261
0..40
0.279
Transformer [2024]
0.440
0.445
0.396
0.317
0.378
0.318
0.232
0.270
0.163
0.202
0,260
|
0,397
0.281
Ampliser [2025]
0.421
0.402
0.353
0.379
0.256
0.318
| 0.223
0.261
0.163
0.256
0.202
0.256
0.417
0.290
Tin [2025]
0.409
0.427
0.350
0.397
0.344
0.380
0.260
0.318
0.226
0.268
0.164
0.258
0.198
0.263
0.420
0.286
SRSNet
0.404
0.424
0.334
0.385
0.351
0.378
0.252
0.314
0.226
0.266
1.101
0.254
0.183
0.239
0.392
0.270
7

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5.3 Ablation Study and Analysis
To investigate the effectiveness of SRS, we conduct comprchensive experiments on four datasets from multiple domains with different lengths and numbers of variables: ETTh1, ETTm2, Solar, and Traffic. The experiments include two parts, one is to analyze the effectiveness of SRS to enhance the prediction accuracy of patch-based based models, and the other is to analyze the influences of different components in SRS, i.e., Selective Patching, Dynamic Reassembly, and Adaptive Fusion.
Ablation study of SRS To demonstrate the SRS's capablities of working as a modular plugin to enhance the prediction accuracy of patch-based models, we combine SRS with naive MLP, i.e.,
SRSNet, classic models Crossformer (Zhang and Yan [022] and PatchTST (Nie al. 2023 and recent state-of-the -or-----rttttttt art models xPatch [Stitsyuk and Choil 2025b] and PatchMLP [Tang and Zhang 2025a The average results of different horizons are shown in Table
First, when combining SRS with a naive MLP, significant improvement of prediction accu- racy (approximately 5% to 15%) is observed. This demonstrates the impressive performance of SRSNet comes from the SRS module, which helps fully exploit the information of contextual time series by adaptively constructing a selec- tive representation space with Selective Patching and Dynamic Reassembly. It also indicates that consitituting superio representation space is somewhat more efficient and easier than design- ing complex models to refine representations in
Table 3: Ablation study of SRS. Five models are considered to show the effectiveness of SRS to work as a plugin. Black: the improvement. Full results are available in Table II o2 Appendix A
Dataeets
ETMM
BTTa2
5:1x
Traffe
Metiaa
MSE
MAE
MAA
MSE.
MAR
MAE
MIP
0410
0461
0.273
0.336
0.219
0217
00415
01.84
588
0.404
0/455
0.28
0.315
0.081
0.319
0.30
0.270
Inprwe
6866
7,09
1M47%
4.88%
PuCTTT
0419
0.466
0.25
0.314
0.500
0.264
0.307
0.275
Improe
348%
2.0%%
2.35%
K.7%
11.15%
3.45
3.54%
0.419
1R5
0.432
0.455
0.45
0.402
0.193
0.225
0.512
0.224
mediocre representation space. Because the former aims at lightening the burden on mod- els by providing more effective representations, thus especially effective for simple MLPs due to the universal approximation theorem [Lu et al. 202I]. while the latter hopes model itself to ex- tract the intricate inductive bias in data, thus unstable to different scenarios, c.g., Crossformer performs well on Solar while poorly on ETTm2. This may be the main reason why SRSNet gains the most improvements than other models.
Impowe
1.55%
1.8%%
9.0%
5.22%
5,89%
2.25
1884
1.45%
94415
0.465
0.261
0,322
0.191
0.250
04415
0.287
588
0.413
0.466
0.55
0.15
0.77
0.31
0.00
0.777
2.99%
2319
3.1%%
sPach
0.466
0429
0.299
0,308
0.186
0.210
0,308
0.248
Impros
2.W5
1.65
3,995
1885
4.1%%
2.05
317%
3,30%
Second, we further demonstrate that SRS is also useful for other patch-based models by providing a better representation space. It is observed that incoperporating SRS still improves the predic- tion accuarcy of existing patch-based models, with an average approximately 5% improvement on PatchTST, Crossformer, xPatch, and PatchMLP. And it is also orthogonal to multi-scale techniques. For PatchMLP which utilizes different sizes of patches to capture the multi-scale structural informa- tion, SRS can be incorporated in the patch embedding part of each scale to pursue more flexible construction of representation spaces.
Ablation study of key components in SRS As SRS consists of Selective Patching, Dynamic Reassembly, and Adaptive Fusion, it is important to analyze the influences of these components. As shown in T we conduct experiments on four variants, eliminating the three key com- ponents respectively (w/o Selective Patching, w/o Dynamic Reassembly, and w/o Adaptive Fusion) to verify their effectiveness, analyzing their collaboration capability by comparing with the naive MLP (w/o SRS).
Table 4: Ablation Study of key components in SRS. Four key components in SRS are verified as to whether they are effective. Red: the best. Full results are available in Table 90 Appendix A
Ditasets
ETTal
BTTml
Solax
Traffic
Metrics
MSC
MAG
MSD
MAB
|
MSB
MAB
MSC
MAD
Experimental results show that the Selective Patching consistently has the greatest impact. Theoretically, Selective Patching determines which patches to be chosen to represent a contex- tual time series, mainly affecting the construc- tion of the representation spaces. The Dynamic Reassembly and Adaptive Fusion are also effec-
weo
0.430
0451
0.233
0.336
| 0.119
0.277
0.413
0.284
Selective Patching
0.423
0.411
0.277
0.331
0.15
0.271
0,408
0.277
Dynmic Ressimblly
0.413
0:428
0.261
0.524
0.193
0.246
0.607
0.278
Fusion
Aduptive
0.412
0.429
0.263
0.326
0.196
0.251
0,402
0.277
SRSNer
0.404
0.424
0.314
0.183
0.392
0.270
tive. The Dynamic Reassembly supports SRS to adaptively reassemble the selected patches to provide
8

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more potentially useful candidates of representation space. The Adaptive Fusion makes convex combination of the embeddings from both the conventional patching and SRS, providing complemen- tary enhancement. Additionally, all these components cooperate with each other to construct the SRS Module, producing positive impact on forecasting performance.
5.4 Efficiency Analysis
Our proposed SRS, as a modular plugin, mainly consists of two MLPs: Scorer" and Scorer". The SRSNet consists of SRS and MLP layer, is also significantly lightweight compared other multi-layer stacked neural networks. Table 6 o the efficiency of SRSNet the SRS module.
Table 5: Efficiency comparison between SRSNet and other baselines on ETThl and Solar datasets with look-back length equals 512, forecasting horizon equals 720, and batch size equals 32. The Max GPU Memory (MB) and Training Time (s) per batch are reported as the main metrics.
Table 6: Efficiency analysis of the SRS mod- ule (the same settings as in Table (5). The Max GPU Memory (MB), Inference Time (s) per batch, Training Time (s) per batch, and Multiply- Accumulate Operations (MACs) are reported as the main metrics.
Datsors
Vorients
Memory (MIl)
Infermnco (o)
Trinnng (5)
MACx
2,837
5,07h
5,131
Dlear
+SRS
2,907
5,722
5,665
16.98 105
Angeter
266
1:3
113
14.30
Overteal
+2.47%
+12.73%
+12.31
+4.25%
CNN
Traabli
2
14:5
13,44
181244
Cunsfrmrrr
4011
27.505
32613
56.250
+SRS
4.159
30.311
35.276
56.625
Staveay
196277
Overheaal
+8.17%
Tranderer
Oraderne
5906
1315
16.05
PRESIST
1,44
2077
13780
+SRS
29.767.0
613.790
Overkzaal
+13.029
+14.95%
+2.25%
Crosforee
17.385
70.031
82.472
61,822
ML.
TasKAN
1.06
230
1300
104.5
-SR3
56.074
1301
36.99
+0.571%
The results in Table that SRSNet has significant advantages when compared with Transformer- based models such as Crossformer, FEDformer, and PatchTST. For I'Transfomme, though it performs more efficiently due to its embedding of the whole series, it consistently performs worse that SRSNet under all the scenarios. When compared with recent state-of-the--r baselines TimeMixer and TimeKAN, SRSNet also shows better efficiency. Though DLinear and Amplifer are the most efficienct model due to their non-patch design and simple structures, they perform poorly large datasets such as Solar and Traffic, reflecting an insufficient capability in modeling long-term dependencies and nonlinear learning. In summary, SRSNet achives good balance between efficiency and performance, demonstrating the SRS module organizes effective representation spaces for pattern learning.
In Table 6 the results further reveal the overhead introduced by the SRS module. Integrated like plugin into classical patch-based models PatchTST and Crossformer, the SRS module only introduces about 10% increasement of Max GPU Memory, Inference Time, and Training Time, and under 5% increasement of MACs, demonstarting the strong practicality in weal-world applications.
5.5 Parameter Sensitivity
0.50
0:43
1.82
035
0.37
M12
0.10
Saler
ETThL
0.32
Sea
Taffic
0.2
0.20
422
Layer
(a) Patch Size
(b) Look Back Window
(c) Hidden Layer
(d) Hidden Dimension
Figure Parameter sensitivity studies of main pypae-parameters SRSNet.
We study the parameter sensitivity of SRSNet. Figure 4a shows the performance of SRSNet under different patch sizes. Since the SRS module adaptively selects useful patches contruct the represen- tation space, it shows robust performance and often choose 16 or 24 as common configurations.

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Figure demonstrates the capability of SRSNet to fully utilize the historical information. As the length of Look Back Window extends, the performance becomes better. Figure 44 and Figure 4c show the influences of the hidden layer and hidden dimension in the Scorer and Scorer' of SRS, which determine the capacity of constructing the Selective Representation Space. The common configurations of Scorer" and Scorer" are 2 hidden layers with hidden dimension equals 128.
Discussion
Potential limitations The SRS module demonstrates its efficacy on SRSNet and other patch-baser models in LTSF scenarios. However, there are several potential limitations of SRS that warrant discussion here:
Impractical to non-patch models: The SRS module may not be suitable for those state-of- the-art models which dose not adopt patching techniques. it is used compulsorily, it can be regarded as the case where the patch size equals 1. However, this will lose the semantics of the patch itself and cause additional computational complexity overhead, which is not practical. Luckily, current works about expert models and foundation models mainly focus on patch-based modeling, thus providing more application prospects for the SRS module.
Scaling law: We observe that the SRS module works stably with fixed hyperparameters such as the hidden size and layer number end-to-end scenarios. In the pretrain scenarios, which adopt foundation models with billion-scale time series corpus, the effectiveness and generalization of the SRS module need to be furtherly verified. Whether the SRS module obeys the scaling law also needs more practical evidence.
Interpretability: Since the SRS module also optimized through gradient descent and the gradient flow is coupled with the subsequent patch-based models, selected patches are useful for forecasting, but not all of them are interpretable. Therefore, we choose allow maximum freedom of the SRS module adaptively dertermine which patches to choose and the order of them.
only ensure the
The initialization of the weights a seems to be important. Although a random initialization of can also lead to best forecasting performance under few epochs, we recommend to manually initialize it when the prior knowledge of datasets is acquired, such as increasing it when the datasets are periodic and stationary. and decreasing it when the datasets are non-stationary and shifting. This can help enchance the convergence and stability of the SRS module.
Initialization:
Future work The current SRS module is purely data-driven, which preserves lightweight but lacks interpretability. In the future, hope devise an environment-aware mechanism perceive the patch-wise data distributions and patterns more explictly, which provides a potential solution for designing the representation spaces adaptively and explainably. To further enhance the practical value of SRS in Time Series Foundation Models, we think its capacity needs to be expanded to memorize and distinguish heterogeneous data patterns, where the coatuure-of-Exeerte (MoE) with strong enough router can be good solution. To solve the initialization problem in the SRS modlue, more efficient update mechanism for a deserves exploration. A potential solution is to design a module to supervise the sample-wist data patterns, constructing a more explict optimization objective between data patterns and a, which can also enhance the interpretability of the SRS module.
7 Conclusion
In this paper, we propose modular SRS mainly composed of the Selective Patching and Dynamic Reassembly, which adaptively select the patches and then reassemble them to fully exploit the infor- mation in the contextual time series, thus mitigating the adverse effects from special phenomenons like changable periods, anomalies, and shifting. The SRS module is gradient-based and works in a alug-and-plas paradigm to enhance the patch-based models in forecasting tasks. We also proposes a simple yet effective SRSNet composed of the SRS module and an MLP head. Comprehensive experiments real-world datasets demonstrate that SRSNet achieves ofate-of-the-art performance, and the SRS module can effectively improve the performance of patch-based models.
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Acknowledgments and Disclosure of Funding
This work was partially supported by the National Natural Science Foundation of China (62472174, 62372179), and ECNU Multifunctional Platform for Innovation (001). Bin Yang is the corresponding author of the work.
References
Xiangfei Qiu, Jilin Hu, Lekui Zhou, Xingjian Wu, Junyang Du, Buang Zhang, Chenjuan Guo, Aoying Zhou, Christian S. Jensen, Zhenli Sheng, and Bin Yang. TFB: towards comprehensive and fair benchmarking of time series forecasting methods. In Proc. VLDB Endow., pages 2363-2377 2024.
Xiangfei Qiu, Xingjian Wu, Yan Lin, Chenjuan Guo, Jilin Hu, and Bin Yang. Duet: Dual clustering enhanced multivariate time series forecasting. In SIGKDD, 2025a.
Peng Chen, Yingying Zhang, Yunyao Cheng, Yang Shu, Yihang Wang, Qingsong Wen, Bin Yang. and Chenjuan Guo. Pathformer: Multi-scale transformers with adaptive pathways for time series forecasting. In ICLR, 2024.
Xinle Wu, Xingjian Wu, Bin Yang, Lekui Zhou, Chenjuan Guo, Xiangfei Qiu, Jilin Hu, Zhenli Sheng, and Christian S Jensen, Autocts++: zero-shot joint neural architecture and hyperparameter search for correlated time series forecasting. The VLDB Journal. 33(5):1743-17700 2024a.
Xinle Wu, Xingjian Wu, Dalin Zhang, Miao Zhang, Chenjuan Guo, Bin Yang, and Christian S Jensen. Fully automated correlated time series forecasting in minutes. arXiv preprint arXiv:2411.05883. 2024b.
Cirstea, Chenjuan Guo, Bin Yang, Tung Kieu, Xuanyi Dong, and Shirui Pan. Tri- former: Triangular, variable-specift attentions for long sequence multivariate time series forecast- ing. In IJCAI, pages 1994-2001, 2022a.
Yunhao Zhang and Junchi Yan. Crossformer: Transformer utilizing cross-dimension dependency for multivariate time series forecasting. In ICLR, 2022.
Yuqi Nie, Nam H. Nguyen, Phanwadee Sinthong, and Jayant Kalagnanam. time series is worth 64 words: Long-term forecasting with transformers. In ICLR, 2023.
Peiwang Tang and Weitai Zhang. Unlocking the power of patch: Patch-based mlp for long-term time series forecasting. In Proceedings of the AAAI Conference on Artificial Intelligence, 2025a.
George EP Box and David A Pierce. Distribution of residual autocorrelations in autoregressive- integrated moving average time series models. Journal of the American statistical Association, 65 (332):1509- 1526, 1970.
Rob Hyndman, Anne Kochler, J Keith Ord, and Ralph D Snyder. Forecasting with exponential smoothing: the state space approach. 2008.
Rakshitha Godahewa, Christoph Bergmeir, Geoffrey I Webb, Rob J Hyndman, and Pablo Montero- Manso. Monash time series forecasting archive. arXiv preprint arXiv:2105.06643, 2021.
Jan Alexander Fischer, Philipp Pohl, and Dietmar Ratz. machine learning approach univariate time series forecasting of quarterly earnings. Review of Quantitative Finance and Accounting, 55: 1163-1179, 2020.
Tianqi Chen and Carlos Guestrin. Xghoost: scalable tree boosting system. In SIGKDD, pages 785-794, 2016.
Lco Breiman. Random forests. Machine learning, 45:5-32, 2001.
Guolin Ke, Qi Meng, Thomas Finley, Taifeng Wang. Wei Chen, Weidong Ma, Qiwei Ye, and Tie- Yan Liu. Lightghm: highly efficient gradient boosting decision tree. Advances in Neural Information Processing Systems, 30, 2017.

---

Haixu Wu, Tengge Hu, Yong Liu, Hang Zhou, Jianmin Wang, and Mingsheng Long. Timesnet: Temporal 2d variation modeling for general time series analysis. In ICLR, 2023a.
Shengsheng Lin, Weiwei Lin, Wentai Wu, Feiyu Zhao, Ruichao Mo, and Haotong Zhang. Seg- rnn: Segment recurrent neural network for long-term time series forecasting. arXiv preprini arXiv:2308. 12000 2023.
Haoyi Zhou, Shanghang Zhang, Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, and Wancai Zhang. Informer: Beyond efficient transformer for long sequence sime-series forecasting. In AAAI, volume 35, pages 1110--1115, 2021.
Tian Zhou, Ziqing Ma, Qingsong Wen, Xue Wang. Liang Sun, and Rong Jin. Fedformer: Frequency enhanced decomposed transformer for long-term series forecasting. In ICML, pages 27268-27286, 2022.
Haixu Wu, Jiehui Xu, Jianmin Wang, and Mingsheng Long. Autoformer: Decomposition transformers with auto correeattll for long-term series forecasting. In NeurIPS, pages 22419-22430 2021.
SazzannGabbied Cirstea, Chenjuan Guo, Bin Yang. Tung Kieu, Xuanyi Dong, and Shirui Pan. Tri- former: Triangular, variable-specific attentions for long sequence multivariate time series forecast- ing. In IJCAI, pages 1994-2001, 2022b.
Shengsheng Lin, Weiwei Lin, Wentai Wu, Haojun Chen, and Junjie Yang. Sparsetsf: Modeling long-term time series forecasting with 1k parameters. In JCML, pages 30211-30228 2024a
Shengsheng Lin, Weiwei Lin, HU Xinyi, Wentai Wu, Ruichao Mo, and Haocheng Zhong. Cyclenet: Enhancing time series forecasting through modeling periodic patterns. In NeurlPS, 2024b.
Ailing Zeng, Muxi Chen, Lei Zhang, and Qiang Xu. Are transformers effective for time series forecasting? In AAAI, volume 37, pages 11121-11128 2023.
Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn. Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszkoreit, and Neil Houlsby. An image is worth 16x16 words: Transformers for image recognition at scale. In ICLR. OpenReview.net, 2021.
Artyom Stitsyuk and Jaesik Choi. xpatch: Dual-stream time series forecasting with exponential seasonal-trend decomposition. AAAI, 2025a.
Peiwang Tang and Weitai Zhang. Unlocking the power of patch: Patch-based mip for long-term time series forecasting. In AAAI, 2025b.
Artyom Stitsyuk and Jaesik Choi. xpatch: Dual-stream time series forecasting with exponential seasonal-trend decomposition. In Proceedings of the AAAI Conference on Artificial Intelligence, 2025b.
Yanru Sun, Zongxia Xie, Dongyue Chen, Emadeldeen Eldele, and Qinghua Hu. Hicrarchical classification auxiliary network for time series forecasting, In AAAI, volume 39, pages 20743- 20751, 2025a.
Wenzhe Niu, Zongxia Xie, Yanru Sun, Wei He, Man Xu, and Chao Hao. Langtime: A language- guided unified model for time series forecasting with proximal policy optimization. In ICML. 2025.
Tri Dao and Albert Gu. Transformers are ssms; generalized models and efficient algorithms through structured state space duality. In Proceedings of the 41st International Conference on Machine Learning, pages 10041-10071, 2024.
Marco Cuturi, Olivier Teboul, and Lean-Philippe Vert. Differentiable ranking and sorting using optimal transport. Advances in neural information processing systems, 32, 2019.
Mathieu Blondel, Olivier Teboul, Quentin Berthet, and Josip Djolonga. Fast differentiable sorting and ranking. In International Conference Machine Learning, pages 950-959, PMLR, 2020.
12

---

Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention all you need. In NeurIPS, pages 5998-6008, 2017.
Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, and George Em Karniadakis. Learning nonlinear operators via deeponet based on the universal approximation theorem of operators. Nature machine intelligence, 3(3):218 2299,,2222222222 2021.
Songtao Huang. Zhen Zhao, Can Li, and LEI BAI TimeKAN: KAN-based frequency decomposition learning architecture for long-term time series forecasting. In ICLR, 2025a.
Jingru Fei, Kun Yi, Wei Fan, Qi Zhang, and Zhendong Niu. Amplifier: Bringing attention to neglected low-energy components in time series forecasting. In AAAI, 2025.
Yong Liu, Tengge Hu, Haoran Zhang, Haixu Wu, Shiyu Wang, Lintao Ma, and Mingsheng Long. itransformer: Inverted transformers are effective for time series forecasting. In ICLR, 2024.
Shiyu Wang. Haixu Wu, Xiaoming Shi, Tengge Hu, Huakun Luo, Lintao Ma, James Y. Zhang, and Jun Zhou. Timemixer: Decomposable multiscale mixing for time series forecasting. In ICLR, 2024.
Yong Liu, Haixu Wu, Jianmin Wang, and Mingsheng Long. Non-stationary transformers: Exploring the stationarity in time series forecasting. In NeurlPS, 2022.
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Köpf, Edward Z. Yang. Zachary Vito,o Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala. Pytorch: An imperative style, high- performance deep learning library. In NeurlPS, pages 8024-8035 2019.
Xiangfei Qiu, Xiuwen Li, Ruiyang Pang, Zhicheng Pan, Xingjian Wu, Liu Yang, Jilin Hu, Yang Shu, Xuesong Lu, Chengcheng Yang, Chenjuan Guo, Aoying Zhou, Christian S. Jensen, and Bin Yang. EasyTime: Time series forecasting made easy. In ICDE, 2025b.
Xiangfei Qiu, Hanyin Cheng, Xingjian Wu, Jilin Hu, and Chenjuan Guo. A comprehensive survey of deep learning for multivariate time series forecasting: A channel strategy perspective. arXiv preprint arXiv:2502. 000.50222.771111 10721, 2025c.
Peiyuan Liu, Hang Guo, Tao Dai, Naiqi Li, Jigang Bao, Xudong Ren, Yong Jiang, and Shu-Tac Xia. Calf: Aligning 1lms for time series forecasting via cross-modal fine-tuning, AAAI, 39(18): 18915-18923, 2025a.
Xinle Wu, Dalin Zhang, Miao Zhang, Chenjuan Guo, Bin Yang, and Christian S Jensen. Autocts+: Joint neural architecture and hyperparameter search for correlated time series forecasting. In SIGMOD, volume 1, pages 1 1-26. 2023b.
Xvyuan Liu, Xiangfei Qiu, Hanyin Cheng, Xingjian Wu, Chenjuan Guo, Bin Yang, and Jilin Hu. Astgi: Adaptive spatio-temporal graph interactions for irregular multivariate time series forecasting. arXiv preprini arXiv:2509.23313: 2025b.
Hua Lu, Bin Yang, and Christian S Jensen. Spatio-temporal joins on symbolic indoor tracking data.
In ICDE, pages 816-827, 2011.
Zhicheng Pan, Yihang Wang, Yingying Zhang, Sean Bin Yang. Yunyao Cheng, Peng Chen, Chenjuan Guo, Qingsong Wen, Xiduo Tian, Yunliang Dou, et al. Magicscaler: Uncertainty-aware, predictive autoscaling. Proc. VLDB Endow., (6(12)3308-3322 2023.
Shilin Lu, Yanzhu Liu, and Adams Wai-Kin Kong. Tf-icon: Diffusion-based training-fres free cross- domain image composition. In ICCV, pages 2294-2305, 2023.
Shilin Lu, Zilan Wang, Leyang Li, Yanzhu Liu, and Adams Wai-Kin Kong. Mace: Mass concept erasure in diffusion models. In CVPR, pages 6430-6440, 2024a.
Shilin Lu, Zihan Zhou, Jiayou Lu, Yuanzhi Zhu, and Adams Wai-Kin Kong. Robust watermarking using generative priors against image editing: From benchmarking to advances. arXiv preprint arXiv:2410.18775. 2024b.
13

---

Leyang Li, Shilin Lu, Yan Ren, and Adams Wii-Kin Kong, Set you straight: Auto-steering denoising trajectories to sidestep unwanted concepts. arXiv preprint FXXv:2504.12782., 2025a.
Chen Yang. Yangfan He, Aaron Xuxiang Tian, Dong Chen, Jianhui Wang, Tianyu Shi, Arsalan Heydarian, and Pei Liu. Wedr: World-centric diffusion transformer for traffic scene generation. arXiv preprint arXiv:2404.02082, 2024.
Yiyang Zhou, Yangfan He, Yaofeng Su, Siwei Han, Joel Jang, Gedas Bertasius, Mohit Bansal, and Huaxiu Yao. Reagent-v: A reward-driven multi-agent framework for video understanding. arXiv preprint arXiv:2506. 000.500000000 01300, 2025.
Yunyao Cheng, Peng Chen, Chenjuan Guo, Kai Zhao, Qingsong Wen, Bin Yang. and Christian S Jensen. Weakly guided adaptation for robust time series forecasting, Proc. VLDB Endow. 17(4): 766-779, 2023.
Xiang Li, Yangfan Hc, Shuaishuai Zu, Zhengyang Li, Tianyu Shi, Yiting Xie, and Kevin Zhang Multi-modal large language model with rag strategies in soccer commentary generation. In WACV, pages 6197-6206, 2025b.
Ruoyu Wang, Yangfan He, Tengjiao Sun, Xiang Li, and Tianyu Shi. Unitmge: Uniform text-motion generation and editing model via diffusion. In WACV, pages 6104-6114, 2025a.
Xingjian Wu, Xiangfei Qiu, Hongfan Gao, Jilin Hu, Bin Yang, and Chenjuan Guo. VA A goopman-kalman enhanced variational autoencoder for probabilistic time series forecasting. In ICML, 2025.
Chenjuan Guo, Christian S Jensen, and Bin Yang. Towards total traffic awareness. In SIGMOD, volume 43, pages 18-23, 2014.
Xiangfei Qiu, Yuhan Zhu, Zhengyu Li, Hanyin Cheng, Xingjian Wu, Chenjuan Guo, Bin Yang, and Jilin Hu. Dag: A dual causal network for time series forecasting with exogenous variables. arXiv preprint Xrx: 00.55099.4933. /4933, 2025d.
Tao Dai, Beiliang Wu, Peiyuan Liu, Naiqi Li, Jigang Bao, Yong Jiang, and Shu-Tao Xia. Periodicity decoupling framework for long-term series forecasting. In ICLR, 2024a.
Yifan Hu, Peiyuan Liu, Peng Zhu, Dawei Cheng, and Tao Dai. Adaptive multi-scale decomposition framework for time series forecasting. In AAAI, 2025a.
Tao Dai, Beiliang Wu, Peiyuan Liu, Naiqi Li, Xue Yuerong, Shu-Tao Xia, and Zexuan Zhu. Ddn: Dual-domain dynamic normalization for non-stationary time series forecasting, In NeurIPS, 2024b.
Xvyuan Liu, Xiangfei Qiu, Xingjian Wu, Zhengyu Li, Chenjuan Guo, Jilin Hu, and Bin Yang. Rethinking irregular time series forecasting: A simple yet effective baseline. arXiv preprint vrXiv:2505.11255 2025c.
Qichao Shentu, Beibu Li, Kai Zhao, Yang Shu, Zhongwen Rao, Lujia Pan, Bin Yang, and Chenjuan Guo. Towards a general time series anomaly detector with adaptive bottlenecks and dual adversarial decoders. In ICLR, 2025.
Beibu Li, Qichao Shentu, Yang Shu, Hui Zhang, Ming Li, Ning Jin, Bin Yang, and Chenjuan Guo. CrossAD: Time series anomaly detection with cross-scale associations and tross-winded modeling. In NeurlPS, 2025c.
Xiangfei Qiu, Zhe Li, Wanghui Qiu, Shiyan Hu, Lekui Zhou, Xingjian Wu, Zhengyu Li, Chenjuan Guo, Aoying Zhou, Zhenli Sheng, Jilin Hu, Christian S. Jensen, and Bin Yang. Tab: Unified benchmarking of time series anomaly detection methods. In Proc. VLDB Endow. pages 2775-2789, 2025e.
Xingjian WL, Xiangfei Qiu, Zhengyu Li, Yihang Wang, Jilin Hu, Chenjuan Guo, Hui Xiong, and Bin Yang. Catch: Channel-aware multivariate time series anomaly detection via frequency patching. arXiv preprint 210.::221..102.11.1.. 2024c.
14

---

Yuanyuan Yao, Yuan Dong Lu Chen, Kun Kuang, Ziquan Fang, Cheng Long, Yunjun Gao, and Tianyi Li. Arrow: Accelerator for time series causal discovery with time weaving. In Forty-second International Conference Machine Learning.
Yuanyuan Yao, Lu Chen, Ziquan Fang, Yunjun Gao, Christian S Jensen, and Tianyi Li. Camel: Efficient compression of floating-point time series. Proceedings of the ACM Management of Data, 1-6): 2024a.
Xiangfei Qiu, Xingjian Wu, Hanyin Cheng, Xvyuan Liu, Chenjuan Guo, Jilin Hu, and Bin Yang. DBLoss: Decomposition-oon based loss function for time series forecasting. In NeurlPS, 2025f.
Yuanyuan Yao, Shenjia Dai, Yilin Li, Lu Chen, Dimeng Li, Yunjun Gao, and Tianyi Li. A demon- stration of tends: Time series management system based model selection. Proceedings of the VLDB Endowment, 1 ((12))4357-43300 2024b.
Yuanyuan Yao, Hailiang Jie, Lu Chen, Tianyi Li, Yunjun Gao, and Shiting Wen. Tsec: An efficient and effective framework for time series classification. In 2024 IEEE 40th International Conference on Data Engineering (ICDE), pages 399-1406. IEEE, 2024c.
Yanru Sun, Zongxia Xie, Haoyu Xing, Hualong Yu, and Qinghua Hu. Ppgf: Probability pattern- guided time series forecasting. IEEE Transactions on Neural Networks and Learning Systems, 2025b.
Yuanyuan Yao, Dimeng Li, Hailiang Jie, Lu Chen, Tianyi Li, Jie Chen, Jiaqi Wang. Feifci Li, and Yunjun Gao. Simplets: An efficient and universal model selection framework for time series forecasting. Proceedings of the VLDB Endowment, 16( 16(12):3741-3753 2023.
Chenxi Liu, Shaowen Zhou, Qianxiong Xu, Hao Miao, Cheng Long, Ziyue Li, and Rui Zhao. Towards cross-modality modeling for time series analytics: A survey in the 11m era. In IJCAI, 2025d.
Hao Wang, Lichen Pan, Yuan Shen, Zhichao Chen, Degui Yang, Yifei Yang, Sen Zhang, Xinggao Liu, Haoxuan Li, and Dacheng Tao. Fredf: Learning forecast in the frequency domain. In The Thirteenth International Conference on Learning Representations, 2025b.
Hao Wang, Haoxuan Li, Xu Chen, Mingming Gong, Zhichao Chen, et al. Optimal transport for time series imputation. In The Thirteenth International Conference Learning Representations, 2025c.
Hao Wang, Zhiyu Wang, Yunlong Niu, Zhaoran Liu, Haozhe Li, Yilin Liao, Yuxin Huang, and Xinggao Liu. An accurate and interpretable framework for trustworthy process monitoring. IEEE Transactions on Artificial Intelligence, 5(5):2241-2253) 2023.
Xinyu Li, Yuchen Luo, Hao Wang, Haoxuan Li, Liuhua Peng. Feng Liu, Yandong Guo, Kun Zhang, and Mingming Gong. Towards accurate time series forecasting via implicit decoding. Advances in Neural Information Processing Systems, 2025d.
Wenzhen Yue, Yong Liu, Hao Wang, Haoxuan Li, Xianghua Ying, Ruohao Guo, Bowei Xing, and Ji Shi. Olinear: A linear model for time series forecasting in orthogonally transformed domain. Advances in Neural Information Processing Systems, 2025a.
Wenzhen Yue, Xianghua Ying, Ruohao Guo, DongDong Chen, Ji Shi, Bowei Xing, Yuqing Zhu, and Taiyan Chen. Sub-adjacent transformer: Improving time series anomaly detection with reconstruction error from sub-adjacent neighborhoods. arXiv preprint arXiv:2404. 18948, 2024.
Wenzhen Yue, Yong Liu, Xianghua Ying, Bowei Xing, Ruohao Guo, and Ji Shi. Freeformer: Frequency enhanced transformer for multivariate time series forecasting. arXiv preprini arXiv:2501. 13989, 2025b.
Haotian Wang, Haoxuan Li, Hao Zou, Haoang Chi, Long Lan, Wanrong Huang, and Wenjing Yang. Effective and efficient time-varying counterfactual prediction with state-space models, In The Thirteenth International Conference Learning Representations, 2025d.
15

---

Lei Wang, Shanshan Huang, Chunyuan Zheng, Jun Liao, Xiaofei Zhu, Haoxuan Li, and Li Liu. Mitigating data imbalance in time series classification based on counterfactual minority samples augmentation. In Proceedings of the 3 lst ACM SIGKDD Conference on Knowledge Discovery and Data Mining V. 2, pages 2962-2973 2025e.
Jiaming Ma. Binwu Wang, Guanjun Wang. Kuo Yang, Zhengyang Zhou, Pengkun Wang. Xu Wang, and Yang Wang. Less but more: Linear adaptive graph learning empowering spatiotemporal forecasting. In Advances in Neural Information Processing Systems, 2025a.
Jiaming Ma, Binwu Wang, Qihe Huang, Guanjun Wang, Pengkun Wang, Zhengyang Zhou, and Yang Wang. Mofo: Empowering long-term time series forecasting with periodic pattern modeling. In Advances in Neural Information Processing Systems, 2025b.
Jiaming Ma, Zhiging Cui, Binwu Wang, Pengkun Wang. Zhengyang Zhou, Zhe Zhao, and Yang Wang. Causal learning meet covariates: Empowering lightweight and effective nationwide air quality forecasting. 2025c.
Jiaming Ma. Binwu Wang, Pengkun Wang, Zhengyang Zhou, Xu Wang, and Yang Wang. Bist: A lightweight and efficient bi-directional model for spatiotemporal prediction. Proceedings of the VLDB Endowment, 1866):66631167, 2025d.
Jammng Ma, Binwu Wang. Pengkun Wang, Zhengyang Zhou, Yudong Zhang, Xu Wang, and Yang Wang. Mobimixer: A multi-scale spatiotemporal mixing model for mobile traffic prediction. IEEE Transactions Mobile Computing, 2025e.
Jiaming Ma, Binwu Wang, Pengkun Wang. Zhengyang Zhou, Xu Wang, and Yang Wang. Robust spatio-temporal centralized interaction for ood learning. In Forty-second International Conference on Machine Learning, 2025f.
Qihe Huang, Zhengyang Zhou, Yangze Li, Kuo Yang, Binwu Wang, and Yang Wang. Many minds, one goal: Time series forecasting via sub-task specialization and inter-agent cooperation. In Advances in Neural Information Processing Systems, 2025b.
Qihe Huang, Zhengyang Zhou, Kuo Yang, Zhongchao Yi, Xu Wang, and Yang Wang. Timebase: The power of minimalism in efficient long-term time series forecasting. In Forty-second International Conference on Machine Learning, 2025c.
Qihe Huang, Lei Shen, Ruixin Zhang, Shouhong Ding, Binwu Wang, Zhengyang Zhou, and Yang Wang. Crossgnn: Confronting noisy multivariate time series via cross interaction refinement.
Advances in Neural Information Processing Systems, 36:46885-46902 2023.
Qihe Huang, Lei Shen, Ruixin Zhang, Jiahuan Cheng, Shouhong Ding, Zhengyang Zhou, and Yang Wang. Hdmixer: Hierarchical dependency with extendable patch for multivariate time series forecasting. In Proceedings of the AAAI conference on artificial intelligence, volume 38, pages 12608-12616, 2024.
Yifan Hu, Guibin Zhang, Peiyuan Liu, Disen Lan, Naiqi Li, Dawei Cheng, Tao Dai, Shu-Tao Xia, and Shirui Pan. Timefilter: Patch-specific spatial-tempont graph filtration for time series forecasting. ICML, 2025b.
Peiyuan Liu, Beiliang Wu, Yifan Hu, Naiqi Li, Tao Dai, Jigang Bao, and Shu-tao Xia. Timebridge: Non-stationarity matters for long-term time series forecasting. In ICML, 2025e.
Yihang Wang. Yuying Qiu, kai Zhao, Yang Shu, Zhongwen Rao, Lujia Pan, Bin Yang, and Guo Chenjuan. Towards general time series forecasting model with unified representation and adaptive transfer. ICML, 2025f.
Yihang Wang, Yuying Qiu, Yang Shu, Zhongwen Rao, Lujia Pan, Bin Yang, and Guo Chenjuan. Lightgts: A lightweight general time series forecasting model. In ICMI., 2025g.
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A Experimental Details
Table 7: Statistics of datasets.
Dataset
Domain
Frequency
Lengths
Dim
Split
Description
ETTh1
Electricity
hour
14,400
6:2:2
Power transformer 1. comprising seven indicators such temueraatre and useful load
ETTh2
Electricity
bour
14,400
temneeratrr useful load Power transformer I. comprising seven indicaturs such as cil temperature and usefal load
Power transformer 2. comprising seven indicators such
ETIml
Electricity
mins
57,500
6:2:2
ETTm2
Electricity
15 mins
57,600
7
6:2:2
Power transfommnr 2. comprising seven indications such as eil lemperatune and usctul load
Weather
Environment
10 mins
52,696
21
7:1:2
Recorded every for the whole year 2020, which contains 21 meseoralogical indicatoos
Electricity
Electricity
bour
26.304
321
7:1:2
Electricity records the electricity consumption in kWb every hour from 2012 to 2014
Solar
Enengy
mins
52.560
6:2:2
Solar peoduction records collected from 137 PV plants in Alabuma
Thaflie
Traflic
hour
17,544
862
7:1:2
Road occupancy rales measured by 862 sensors on Sun Francisco Bay area froeways
We utilize the TFB code repository for unified evaluation, with all baseline results also derived from TFB. Following the settings in TFB Qiu et al. [2024), we do not apply the "Drop Last" trick to ensure a fair comparison. All experiments of SRSNet are conducted using PyTorch Paszke et al. [019 in Python 3.8 and executed on an NVIDIA Tesla-A800 GPU. The training process is guided by the MSE loss function and employs the ADAM optimizer. The initial batch size is set to 64, with the flexibility to halve it (down to a minimum of 8) in case of an Out-Of-Memory (OOM) issue.
A.1 Full results
Table 8: Multivariate forecasting results with forecasting horizons F E 196, 192, 336, 720} for the datasets. Red: the best, Blue: the 2nd best. The standard deviation of SRSNet calculated through random seeds are also reported.
Modes
(02>)
(2125)
(2025)
(2004)
(2124)
(2X22)
(2025)
(2023)
(2025)
(2002)
(2022)
Matri
302
6.420
0.455
11413
0.450
11424
425
I1,54
3:158
IL491
11427
DUSES
08540
356
0.013
0.442
0.450
0.658
0.436
0,450
01431
0
0,433
0.657
0.523
(L48)
TUS02
0.551
0.456
192
0L572
01.23
9,55
0.348
0,500
03341
0.384
0.349
0,587
0.345
0.354
0.323
0.60
0.434
0.415
0.367
0.435
0.579
0.4.8
04415
0.438
11307
0.10
11377
0116
11.90
11300
197
0.306
0.36
0.337
0 116
0.333
0331
0.51
0335
0373
033
0366
0.334
0410
0.90
8.604
0.396
0.994
0.851
1.575
0.16
B:235
0.354
1035
0.366
01335
0.88
01322
0.00
0413
0422
06423
0.42
11307
0.385
0,977
0344
IL230
EL280
0.:34
0 0.300
16226
11234
2306
1333
025
8200
0415
11354
0310
1L234
0.304
0.333
IL377
0330
0.88
11.99
0.367
0368
1355
3357
0361
0.415
13554
ILDM
18.00
0444
14304
03R1
033
1L306
03 380
03334
0.52
0.300
01317
3.400
0.300
0356
0.355
0.385
0.35
0.55
0.304
0.35
0.9%
0.315
0-225
0.418
11:35
01311
0250
0155
025
01:51
6511
0351
0271
03311
01355
0.543
0.24
14543
0155
0300
0155
0260
0.866
0.200
0..54
0.50
01500
0.26
1L315
0.15
11355
0.239
0.20
1350
022
0350
0234
0.00
0.337
0.314
0.356
0.25
0.333
0.300
0.221
0.31
0.299
0.354
0L367
00:877
0.235
14.75
0.237
0.33
0.234
01:33
0.395
0.70
11199
0.225
03365
0.350
0.51
11:14:
7006
0770
0354
0308
0336
0.76
(175)
0.783
11:003
01 186
0.115
0.117
730
0.351
11.00
0 730
01.33
0.300
0.:11
0.300
0.11
0.57
0.05
0.30
03355
0.30
0.784
0.533
0.30
0.775
0.31
06655
0.63
1L351
11.05
0.200
16.211
0.277
11353
0.36
0.226
11370
0.212
(1.26
0.39
11535
0.12
11:35
0.275
0U903
0.330
11913
01325
14402
14025
0.30
11384
11400
0221
11300
11353
0.63
1433
11477
1611
0.318
16614
01383
0.375
730
14434
0.233
14455
0.31
14454
0312
41445
0.48
04422
0.16
11415
3.50
01552
0300
03335
0.400
11454
0.308
16540
0.350
1664)
01304
1d Chass
0
0 0 0
Table 9: Ablation Studies with forecasting horizons F E {96, 192, 336, 720} for the datasets. Red: the best.
Dotasets
ETThI
ET71m
Hurizoas
192
336
720
720
Metrics
MAD|
MSD
MAD
MSD
MAE|
MSB
MSC
MAD
MSE
MAE
MAD
MAE
0.385
0/12
0.427
0.448
0.447
0,461
0.462
0.483
0.178
0,273
0.243
0,316
0.291
0.352
0.402
Selective Patching
0.381
0.407
0.418
0.428
0.441
0.457
0.452
0.471
0.177
0.271
0.229
0.304
0.290
0.353
0.372
0.395
Dynamic Reuseembly
0.373
0.398
0.405
0.417
0:429
0,436
0.443
0.189
0,263
0.231
0.306
0.275
0.335
0.391
Adlupeive Fusion
0.371
0.397
0.423
0:478
0.434
0.437
0.461
0.173
0,266
0.237
0.311
0.276
0.339
0.388
SRSNes
0.394
0.415
0.424
0.426
0.164
0.254
0.220
0.29
0.328
0.380
24

---

Table 10: Ablation Studies with forecasting horizons F E {96, 192, 336, 720} for the datasets. Red: the best.
Datasets
Solar
Trafficc
Horizons
96
192
336
720
96
192
336
7.00
Metrics
MSE
MAR
MSR
MAF|
MSF
MAR
MSR
MAF
MSF
MAR
MSR
MAR
MSE
MAR
MSF
MAF
W/o SRS
0.192
0.243
0.215
0.271
0.228
0.202
0.239
0.301
0.387
0.272
0.402
0,275
0.412
0.284
0.452
0.304
w/o Selective Patching
0.139
0.241
0.200
0.254
11.233
10.25
0.237
0.304
0,385
0.268
0.299
0,272
0.410
0.273
0,437
0.296
w/o Dynamic Reaseembly
0.186
0.227
0.196
0.241
0.192
0,253
0.199
0.262
0.351
0.264
0.403
0,277
0.398
0.214
0,446
0.295
wio Adaptive Fasion
0.182
0.226
0.115
0.239
0.199
002262
0.207
0.278
0,578
0.262
0.369
0,200
0.399
0.276
00,443
0,301
SKSNet
0.167
0.222
0.182
0.237
0,188
0.245
0.195
0.251
0
0.254
0.380
0.363
0.392
0.270
0.434
0.293
Table 11: Plugin Studies with forecasting horizons F E {96, 192, 336, 720} for the datasets. Black: the improvement.
Danseess
ETTaI
ETT=2
Hocizons
96
192
336
720
96
192
336
720
Metrics
MSL
MAU!
|
MSE
MABI
MSB
MAG
| MSU
MAB
MSD
MAE
MSE
MAB
MSE
MAE
MSE
MAB
0.355
0.412
|
0.448
0.447
0.461
| 0.462
0.483
0.178
0.272
0.243
0.316
0.291
0.352
0.378
0.402
SRS
0.366
0.394
0.400
0.415
0.424
0.400
0.426
0.455
0.164
0,254
0.220
0.296
0.711
0.325
0.253
0.380
Impeove
| 494%
437%
|
6.32%
7.37%
5..15%
6.72%
7.79%
5,80%
7.87%
6.62%
9.47%
6.33%
6.87%
6.2%%
6.61%
5.47%
PatchTST
0.425
0.431
0,448
0.477
0.165
0.255
0.221
0.276
0.327
SSSS
0.364
0.395
0.398
0.419
0.422
0.438
0.453
0.159
0.248
0.213
0.264
0.256
0.319
0.377
Impeowe
|
3.5%%
1.11%
|
2.69%
1.41%
2.09%
1.35%
5.69%
5.03%
364%
2.75%
3.62%
3.07%
3.62%
2.45%
1.10%
1.06%
Crossonmer
0.411
0.435
0.409
0.438
0.433
0.457
0.501
0.514
0.296
0.391
0.369
0.416
0.558
0.500
0.612
0.401
0.423
0.432
0.428
0.452
0.494
0.513
0.276
0.356
0.324
0.396
0.454
0.495
0.601
Impeove
2.3%%
2.76%
1.33%
1.37%
1.15%
1.09%
1.40%
0,58%
6.76%
8.95%
12.30%
4.81%
17.69%
17.33%
2.67%
1.80%
PaicMMLPP
|
0.380
0.995
|
0.490
0.441
0.451
0,453
| 0.479
0.484
0.168
0.259
0.228
0.300
0.275
0,330
0.371
0.398
0.378
0.393
0.430
0.428
0.447
|
0.475
0.161
0.251
0.222
0.294
0.258
0.323
0.390
Impeove
0.53%
0.51%
2.56%
2.49%
55.10%
1.32%
3.76%
1,86%
4.17%
3.09%
2.63%
2,00%
2.55%
2.12%
2.43%
2.01%
xPatch
|
0.368
0.396
0.409
0.421
0.436
0.435
0.483
0,465
0.160
0.345
0.219
0.267
0.272
0.325
0.361
0,378
-SR5
0.417
0.428
0.431
0.157
0.341
0,209
0.261
0.317
2.45%
1.77%|
1.47%
0.95%
1.83%
0.92%
A.78%
3.01%
1.88%
1.63%
4.87%
2,09%
4,04%
1.86%
3.88%
1.88%
Table 12: Plugin Studies with forecasting horizons F E 196, 192, 336, 720} for the datasets. Black: the Improvement.
Donnetts
Solar
Traffic
Hodions
96
192
336
720
96
192
336
720
MAR:
MIP
0.193
0.345
0.21
0.771
0.226
0.292
0.33
0.301
0.367
0.272
0.400
0.275
0.412
0.764
0.452
0.904
0.107
0.182
0.237
0,188
0.245
0.195
0.361
0.254
0.392
0.444
0.293
Improwe
13.82%
8.64%
15.85%
12.85%
17.54%
16.10%
18418
16615
672%%
6.62%
5.47%
4.36%
4.8%%
4.98%
3.98%
3.25%
PasNTST
0.120
0.234
|
0.204
0.302
0.112
0.203
0.115
0.307
0.370
0.262
0.386
0.395
0.275
0.435
0.205
0.164
0.226
0.180
0.244
0.181
0.246
0.266
0.352
0.255
0.300
0.268
0.433
0.292
Inpeove
3.33%
3.42%
|
11.76%
17.55%
14.2%
16.047
5.88%
7.49%
4.86%
5.73%
3.37%
4.00%
2.27%
2.55%
0.46%
1.02%
Chosdformer
0.183
0.208
0.212
0.239
0.215
0.526
0.376
0.301
-RRS
0.176
0.20%
0.186
0.932
0.706
0.236
0.199
0.340
0.518
0.779
0.49%
0.285
0.090
0.269
0.337
0.243
Impeswe
A80%
3.40%
|
281%%
10.23%
PuchbMLL
0.173
0.234
0.192
0.247
0.199
0.255
0.208
0.264
0.389
0.273
0.399
0.277
0.412
0.286
0.452
0,313
-RRS
0.163
0.322
0.178
0.244
0.183
0.247
0.193
0.356
0.361
0.266
0.389
0.400
0.439
0.298
Improwe
5.64%
5.66%
7.19%
1.18%
7.92%
3.14%
7.26%
3.14%
1.86%
3.36%
2.518
3,08%
2.98%
2.98%
2.92%
4.25%
sPacc
0.169
0.190
| 0.186
0.208
0.191
0.213
0.201
0.223
0.388
0.230
0:387
0.244
0.395
0.247
0.441
0.266
1.55
0.162
0.191
0.179
0,182
0.203
0.192
0.238
0.256
Inpeove
4.14%
1.55%
2.7%%
2,40%
471%
4,0%%
4.48%
1.79%
2.11%
1.42%
1.53%
2.28%
2.78%
6.00%
3.27%
3.66%
25

---

A.2 Showcases
-10
Ground
-12
200
175 700
200
GroundTuuhh
GrounsTuth Prodiction
GroundTuth
Picdiction
Figure 5: Visualization of processes the special cases with the help SRS module. The grey rectangles are the selected patches with the size of 24.
results the ETThl dataset. SRSNet effectively
-22
-0.1
-04
-00
GroundTutth Prediction
-00
GroundTuuh Pesdictionn
Groundfhuuth
-00
Predictoor
0:25
-0.
GrunnTuuth
-6.75
GroundThum
Groundthhsth
Predictio
Preciction
-1.0
Pheducior
Figure 6: Visualization of input-96 -9-eeddietrd results on the ETTm2 dataset. SRSNet effectively processes the special cases with the help of SRS module. The grey rectangles are the selected patches with the size of 24.
Chounddruth
Groundfrithh
Groundtituth
Pred crion
Rediction
Presicttion
-30
-10
300
250 175
100
125
20
Figure 7: Visualization of sopptt96-predict-9o results on the Traffic dataset. SRSNet effectively processes the special cases with the help of SRS module. The grey rectangles the selected patches with the size of 24.
B Related Works
Time Series Analysis is very important in many fields like economy
Qiu et al.
2025b c
Liu et al.
2025a Wu al. 2023b), transportation [Wu et 2024a Liu [025bb
Iu all
Pan
al. 2023
health [u et al. 2023 2024a b), weather [L et al. 2025a Yang et al.
2024
Zhou et al.
26

---

2025
Cheng et al.
2023 energy Li et al. 2025b Wang et al.
2025a
Wu et al.
2025
Guo ct al.
2014 including multiple key tasks like forecasting
QQuu et al.
2025d
Dai et
2024a
Hu al.
2025a
Dai et al.
2024b Liu et al. 2025c anomaly detection
Shentu et al. 2025
[ et al. 2025c
Qiu al. 2025e Wu et al. 2024c classification
[u al.
2023a
Wang et al.
2024
Liu al.
2024], imputation Yao et al. 2024a], and others
[Qiu et al.
2025f
Yao et al. 2024b c
Among
them, Time Series Forecasting is most widely used in real-world applications.
Time series forecasting (TSF) [Sun et al. 2025b Yao et al.
2023
Liu et al. 2025d] involves the
prediction of future observations grounded historical ones. Research findings have indicated that
features derived through learning processes may exhibit superior performance compared to human-
engineered features (Wang et 2025b 2023 Li al. 2025d Yue al. 2025a 2024| [025b]
Wang et al. 2025d e Ma et al.) 2025a b Huang et al. 20.55bee 2023
2024]. By capitalizing
on the representation learning capabilities deep neural networks (DNNs), numerous deep-learning
approaches have come into existence. Methods such as TimesNet [Wu et al. 2023a and SegRNN [Lin
al. 2023 model time series as vector sequences, utilizing convolutional neural networks (CNNs)
or recurrent neural networks (RNNs) to capture temporal dependencies. Moreover, Transformer architectures, including Informer [Zhou et al. 2021] TimeFilter [Hu et al. 2025b). TimeBridge [Liu
al. 2025e]. PDF [Dai et al. 2024a], Triformer [Cirstea al., [022aa] PatchTST (Nie et al. [023]
ROSE [Wang et al. 2025f]. and LighTGTS [Wang et al. 2025g]. are capable of more accurately capturing the intricate relationships between time points, thereby significantly enhancing forecasting performance. MLP-basse based methods, including DUET [Qiu et al. 2025a], AMD [Hu et al.] [025a].
Sparse (Lin et al. 2024a], and CycleNet (Lin et al. 2024b], adopt relatively simpler architectures with fewer parameters yet still attain highly competitive forecasting accuracy.
27


Reviews:
[{"review_id": "wOk9STiUJu", "reviewer": "Reviewer_xNzv", "summary": "This paper proposes the Selective Representation Space (SRS) module, a plug-and-play component for enhancing patch-based time series forecasting models. Unlike conventional adjacent patching that divides time series into fixed adjacent patches, SRS introduces adaptive patch selection through two key techniques: Selective Patching (which adaptively selects the most informative patches) and Dynamic Reassembly (which determines the optimal ordering of selected patches). The authors demonstrate the effectiveness of their approach through SRSNet, a simple model combining SRS with an MLP head, which achieves state-of-the-art performance on multiple benchmarks.", "questions": "(1) How sensitive is the method to the initialization of the scoring networks? Have you experimented with different initialization strategies?\n(2) Can you provide more analysis on the computational overhead introduced by the patch selection process during training and inference?\n(3) How does the method perform on datasets with strong seasonal patterns where adjacent patching might naturally align with the periodicity?\n(4) Could you provide more detailed analysis of the types of patches that are typically selected across different datasets and forecasting horizons?", "limitations": "Yes.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths: (1) The paper identifies a genuine limitation in existing patch-based methods - the fixed nature of adjacent patching - and proposes an innovative solution through adaptive patch selection. (2) The gradient-friendly implementation of Selective Patching and Dynamic Reassembly through clever use of score-based selection and gradient propagation techniques is well-designed. (3) The paper provides extensive experimental validation across 8 datasets from multiple domains, with thorough ablation studies demonstrating the effectiveness of each component.\n\nWeaknesses: (1) While the motivation for selective patching is intuitive, the paper lacks theoretical analysis of why and when selective patching should outperform adjacent patching. The claim that \"all information useful for forecasting is evenly distributed\" is not necessarily true for adjacent patching. (2) Although consistent, the performance improvements are relatively modest (typically 2-10%) compared to existing methods. For a NeurIPS paper, more substantial gains would be expected. (3) The additional complexity introduced by the scoring networks and dynamic reassembly may not be justified by the marginal performance gains in many cases.", "was_revised": true, "final_justification": "Based on the positive feedback from other reviewers and the author's meaningful responses, I have decided to raise my score.", "rebuttal": "**Reply to W1** \n\nThanks for your in-depth insights and suggestions. We admit that some expressions are not quite appropriate, and we will modify them later. \n\nWe first provide some intuitions. Assuming the contextual time series is a continuous interval [1, T] covering T points, the useful informative intervals in normal cases (like strong seasonality) are also the [1, T]. Adjacent Patching can well handle these normal cases. \nIn our work, we mainly consider the cases that not all of the contextual time series is useful for forecasting, such as anomalies, changeable periods, and shifting. In these cases, the contextual time series are Interrupted as $[1, T_1] \\cup [T_1, T_2], \\cdots, \\cup [T_{k-1}, T]$, containing $k$ informative sub-intervals. If the $k$ sub-intervals cover x% of the contextual time series, only x% of representations created by Adjacent Patching are useful for forecasting. In contrast, our proposed Selective Patching can choose the useful patches in the $k$ sub-intervals, and support re-selection to amplify useful patches. The Dynamic Reassembly then introduces positional information for better representational learning. We also fuse the representations from both the Selective Patching and Adjacent Patching, to ensure the ratio of useful information is greater than x%, thus handling both the normal and special cases.\n\nTo provide more empircal evidence about when the SRS outperforms the Adjacent Patching, we conduct additional experiments on datasets from TFB, a well-recognized time series forecasting benchmark. Since datasets with strong seasonality values are close to normal cases while those with strong shifting values are special ones, we choose two groups of datasets separately with descending seasonality values and shifting values. The higher the values, the stronger seasonality/shifting the time series data have. We list the statistical information:\n\n| datasets | NASDAQ | NYSE | AQShunyi |\n| --- | --- | --- | --- |\n| Shifting Values | 0.932 (Strong) | 0.620 (Modest) |     0.019 (Weak) |\n\n| datasets | PEMS08 | ZafNoo | AQWan |\n| --- | --- | --- | --- |\n| Seasonality Values | 0.850 (Strong) | 0.757 (Modest) | 0.119 (Weak) |\n\nWe conduct plugin experiments on these datasets and report the mean results:\n\n| Datasets | NASDAQ |  | NYSE |  | AQShunyi |  |\n| --- | --- | --- | --- | --- | --- | --- |\n| Metrics | MSE | MAE | MSE | MAE | MSE | MAE |\n| PatchTST | 0.972 | 0.721 | 0.483 | 0.437 | 0.703 | 0.507 |\n| + SRS | 0.757 | 0.569 | 0.418 | 0.379 | 0.641 | 0.461 |\n| Improved | **21.99%** | **21.03%** | **13.50%** | **13.50%** | **8.83%** | **9.14%** |\n| Crossformer | 1.737 | 0.992 | 0.983 | 0.909 | 0.694 | 0.504 |\n| + SRS | 1.256 | 0.709 | 0.854 | 0.785 | 0.635 | 0.455 |\n| Improved | **27.35%** | **28.10%** | **13.48%** | **13.84%** | **8.64%** | **9.71%** |\n| PatchMLP | 1.352 | 0.810 | 0.467 | 0.440 | 0.722 | 0.516 |\n| + SRS | 1.037 | 0.606 | 0.406 | 0.380 | 0.666 | 0.475 |\n| Improved | **23.31%** | **25.30%** | **13.77%** | **13.82%** | **7.78%** | **8.04%** |\n| xPatch | 1.060 | 0.708 | 0.545 | 0.474 | 0.735 | 0.509 |\n| + SRS | 0.850 | 0.563 | 0.469 | 0.408 | 0.678 | 0.464 |\n| Improved | **19.63%** | **20.32%** | **14.56%** | **14.63%** | **7.68%** | **8.75%** |\n| MLP | 1.200 | 0.803 | 0.463 | 0.432 | 0.717 | 0.513 |\n| + SRS | 0.925 | 0.600 | 0.395 | 0.366 | 0.662 | 0.467 |\n| Improved | **23.50%** | **25.50%** | **15.56%** | **15.94%** | **7.68%** | **8.89%** |\n\n| Datasets | PEMS08 |  | ZafNoo |  | AQWan |  |\n| --- | --- | --- | --- | --- | --- | --- |\n| Metrics | MSE | MAE | MSE | MAE | MSE | MAE |\n| PatchTST | 0.332 | 0.322 | 0.509 | 0.454 | 0.812 | 0.498 |\n| + SRS | 0.312 | 0.300 | 0.441 | 0.386 | 0.661 | 0.395 |\n| Improved | **6.02%** | **6.89%** | **13.29%** | **15.08%** | **18.49%** | **20.70%** |\n| Crossformer | 0.265 | 0.282 | 0.494 | 0.456 | 0.786 | 0.490 |\n| + SRS | 0.254 | 0.267 | 0.429 | 0.387 | 0.592 | 0.369 |\n| Improved | **4.23%** | **5.30%** | **13.02%** | **15.05%** | **24.86%** | **24.74%** |\n| PatchMLP | 0.306 | 0.283 | 0.531 | 0.466 | 0.829 | 0.505 |\n| + SRS | 0.294 | 0.270 | 0.457 | 0.395 | 0.637 | 0.388 |\n| Improved | **3.93%** | **4.63%** | **14.09%** | **15.23%** | **23.26%** | **23.18%** |\n| xPatch | 0.269 | 0.242 | 0.593 | 0.479 | 0.849 | 0.506 |\n| + SRS | 0.258 | 0.232 | 0.521 | 0.417 | 0.701 | 0.406 |\n| Improved | **3.61%** | **4.11%** | **12.19%** | **12.87%** | **17.37%** | **19.65%** |\n| MLP | 0.303 | 0.278 | 0.523 | 0.455 | 0.826 | 0.505 |\n| + SRS | 0.283 | 0.259 | 0.439 | 0.371 | 0.611 | 0.362 |\n| Improved | **6.59%** | **6.62%** | **16.18%** | **18.46%** | **26.11%** | **28.44%** |\n\nWe have two main observations:\n\n1. The SRS excels at datasets with high shifting values (NASDAQ) and low seasonality values (AQWan), because there exists more special samples about changeable periods, anomalies and shifting in these cases.  The SRS improves all models significantly by 17% — 28% on these datasets. \n2. When the datasets are closer to normal cases with higher seasonality values and lower shifting values, the performance improved by the SRS gradually decreases. On NYSE and ZafNoo, the performance is improved by 12% — 18%. Note that even on AQShunyi and PEMS08, the improvement still exists and is about 4% — 10%. This demonstrates that the SRS excels at both the normal and special cases. \n\n**Reply to W2**\n\nSince the SRS is proposed for special cases like changeable periods, anomalies, and shifting, we think the proportion of special samples in the dataset will affect the performance. In the Reply to W1, we make additional experiments on datasets having more special samples (NASDAQ, AQWan, NYSE, ZafNoo), and find the improvement of SRS can achieve 12% — 28% (quite non-trivial). We hope this can be considered as additional evidence. \n\n**Reply to Q3**\n\nAs you mentioned, on datasets with strong seasonality, the Adjacent Patching can well handle the information in contextual time series and form useful representations. In the reply to W1, our experiments reveal the phenomenon that the improvement of SRS decreases as the seasonality increases, while the improvement still exists and is about 4% — 10%. It is because the Dynamic Reassembly still works and reassembles the patches for better positional information, and the Adaptive Fusion can adaptively integrate the representations, which ensures the improvement even in normal cases.\n\n**Reply to W3 & Q2**\n\nWe make an analysis on the overhead introduced by the SRS on above 6 datasets. Due to the space limitation, we report the results on PEMS08 (biggest) and NYSE (smallest) here, and will release full results when the discussion phase starts. Specifically, we report the Number of Parameters, Max GPU Memory, MACs, Training Time, and Inference Time:\n\n| Datasets | Variants | Memory (MB) | Params (M) | Inference Time (s/batch) | Training Time (s/batch) | MACs (G) |\n| --- | --- | --- | --- | --- | --- | --- |\n| NYSE | PatchTST | 900 | 0.716 | 6.392 | 7.941 | 2.490 |\n|  | SRS | 928 | 0.720 | 7.246 | 8.784 | 2.524 |\n|  | **Overhead** | **3.11%** | **0.64%** | **13.36%** | **10.63%** | **1.36%** |\n|  | Crossformer | 654 | 0.129 | 19.862 | 21.569 | 0.251 |\n|  | SRS | 678 | 0.130 | 20.568 | 22.151 | 0.258 |\n|  | **Overhead** | **3.67%** | **0.57%** | **3.55%** | **2.70%** | **2.67%** |\n| PEMS08 | PatchTST | 2216 | 12.672 | 7.673 | 7.802 | 25.653 |\n|  | SRS | 2522 | 12.682 | 8.766 | 8.934 | 26.584 |\n|  | **Overhead** | **13.81%** | **0.08%** | **14.25%** | **14.52%** | **3.63%** |\n|  | Crossformer | 10414 | 11.085 | 45.100 | 45.320 | 161.376 |\n|  | SRS | 10698 | 11.093 | 50.372 | 47.478 | 162.014 |\n|  | **Overhead** | **2.73%** | **0.07%** | **11.69%** | **4.76%** | **0.40%** |\n\nIt is observed that the overhead introduced by the SRS is relatively trivial. The Memory, MACs, and Params increase little. And the Training Time and Inference Time are also controllable.\n\n**Reply to Q1**\n\nWe further study on the initialization strategies, including Constant, Xaiver, Kaiming, and Randn. We also report the standard deviation of 5 rounds:\n\n| Datasets | ETTh1 |  | ETTm2 |  | Solar |  | Traffic |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| Metrics | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE |\n| Constant | 0.413±0.002 | 0.435±0.002 | 0.259±0.001 | 0.324±0.001 | 0.187±0.002 | 0.243±0.001 | 0.392±0.001 | 0.271±0.001 |\n| Xaiver | 0.405±0.001 | 0.425±0.001 | 0.252±0.001 | 0.315±0.001 | 0.184±0.002 | 0.241±0.002 | 0.394±0.001 | 0.272±0.001 |\n| Kaiming | 0.405±0.001 | 0.424±0.001 | 0.254±0.002 | 0.316±0.002 | 0.183±0.002 | 0.238±0.002 | 0.393±0.001 | 0.271±0.001 |\n| Randn | 0.404±0.001 | 0.424±0.001 | 0.252±0.001 | 0.314±0.001 | 0.183±0.002 | 0.239±0.002 | 0.392±0.001 | 0.270±0.001 |\n\nThe results show that random-based initialization strategies such like Xaiver, Kaiming, and Randn (ours) are relatively stable. The Constant initialization strategy causes unstable training in some cases.\n\n**Reply to Q4**\n\nWe have provided some showcases in Appendix A.2 of the paper. For clarity, we label the sub-figures with (a)-(f) in the order from left to right and from top to bottom.\n\nFigure 5 (d), (e), (f), and Figure 7 (c) show the selected patches under changeable periods, which accurately picks up the correct periods most related to the forecasting horizons.\n\nFigure 6 (a), (b), and Figure 7 (a), (e), (f) show the selected patches when anomalies occur, which avoid including the abnormal patches.\n\nFigure 5 (b), (c), and Figure 6 (c), (e), (f) show the selected patches when shifting occurs, which selects the in-distribution patches for forecasting.\n\nWe also showcase some normal cases such as Figure 5 (a), Figure 6 (d), and Figure 7 (d), where the selected patches are similar to those produced by adjacent patching, demonstrating the flexibility of the Selective Patching.\n\n**Thanks for your valuable suggestions again! We will release the full results when the discussion phase starts. If you have any additional question, we can make further discussion!**"}, {"review_id": "MLxIV1gf4e", "reviewer": "Reviewer_Hryh", "summary": "This paper proposes a plug-and-play module named SRS for time series forecasting. SRS considers the selection and sequence of patches, which can construct representation spaces with richer semantics, thus enhancing the performance of time series forecasting. The authors provide comprehensive experiments to demonstrate the effectiveness of SRSNet, and also demonstrate the capability of SRS to work as a plugin on patch-based models.", "questions": "Please see W1-W3.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths:\nS1. The SRS module provides a novel perspective to consider the representation learning process in time series forecasting. Through introducing the Selective Patching and Dynamic Reassembly techniques, SRS can constructs selective patches and consider the appropriate sequence of them.\nS2. The SRS module devises a gradient-based mechanism to ensure the efficient patch selections and sequence decisions, with lightweight MLP structures.\nS3. Comprehensive experiments are conduct to demonstrate the effectiveness of the SRSNet and SRS module.\nWeaknesses:\nW1. Why should authors retain the representations generated by the Conventional Adjacent Patching instead of only using the representations constructed by the SRS module? Please provide reasonable explanations.\nW2. Explain in detail the specific meaning of the matrix below Selective Patching in Figure 3. What is the main difference from the mechanism in Dynamic Reassembly?\nW3. Please ensure that all citations are of the officially accepted versions.", "was_revised": true, "final_justification": "The article is particularly good. rebuttal perfectly solved my problem. I suggest accepting this article.", "rebuttal": "**Reply to W1:**\n\nThanks for the question. There are two main reasons we retain the representations generated by the Conventional Adjacent Patching:\n\n(1) Since the SRS is a trainable plugin, the scorers may have some randomness in the early stage of training, so it may not accurately find suitable patches. Therefore, retaining the representations generated by the Conventional Adjacent Patching and performing adaptive fusion can effectively enhance the stability of the training. As the training continues, the ability of the scorer gradually improves, enabling it to select better patches and increase the weight during fusion, thereby improving the end-to-end prediction performance.\n\n(2) The SRS is proposed for some special cases such as changeable periods, anomalies, and shifting, where the Selective Patching and Dynamic Reassembly can help retrieve useful information in the contextual time series. In common scenarios where the sample is relatively normal, the Conventional Adjacent Patching can also well handle so that we retain the representations generated by it. Through adaptively fusing the representations, SRS can handle both the common and special cases.\n\n**Reply to W2:**\n\nThanks for the question. We first explain the details of the matrix of Selective Patching. The shape of the matrix is $\\mathbb{R}^{K\\times n} $, where $K$ denotes the number of all candidate patches (generated by stride=1), and $n$ denotes the number of patches we need to pick up from all $K$ ones. Since the Selective Patching supports selection with replacement, which means one patch can be selected multiple times, so we make $\\text{Scorer}^s$ score $n$ scores for each patch, thus forming the matrix with the shape of $\\mathbb{R}^{K\\times n} $. To select the $n$ appropriate patches, we only need to check the scores of all $K$ patches each time and pick the highest ones.\n\nWe then shed light to the main differences between Selective Patching and Dynamic Reassembly. Different from Selective Patching, the nature of Dynamic Reassembly is to sort the selected patches and then reassemble them in the determined order, so that the scores are not formed like a list instead of a matrix.\n\n**Reply to W3:**\n\nThanks for your remind, we will fix these citations.\n\n**Thanks for your sincere suggestions again! If you have any additional question, we can make further discussion!**"}, {"review_id": "KCe1ng9IOy", "reviewer": "Reviewer_7m7L", "summary": "This work surfaces potential constraints with the standard approach of considering adjacent time series partitions as patches, which may be susceptible to including anomalies, misrepresenting distribution shifts, and irregular periodicity within the time series. The authors hypothesize that this inflexibility impairs the forecasting model's ability to learn truly representative spaces, which in turn impacts accuracy. In order to address this issue, the authors present a novel patching approach that (i) selects informative patches that can overlap and no longer be adjacent, and (ii) concatenates the partitions in a manner that no longer assumes them to maintain their original adjacency. Acknowledging the value of the original patching approach, the authors then introduce a fusion module that combines adjacent patches with those resulting from the selective patching/dynamic reassembly module described in this work, along with position embeddings. Experiments against competing techniques indicate nearly consistent performance improvements across all datasets, while ablation studies teasing apart the various components included in the final architecture demonstrate that these all complement each other.", "questions": "See note in section above on adding more insights/examples of where the approach may not be as beneficial as adjacent partitioning", "limitations": "N/A", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "The paper makes an incremental yet meaningful contribution to the literature on patch-based forecasting models, and I appreciated the clarity with which the authors presented the various ways in which standard patching strategies are inflexible to potential anomalies or distribution shifts (both of which are highly prevalent in real-world datasets). The diagrams are especially effective for communicating the described techniques, and there is an appropriate level of technical detail throughout the main paper. I also appreciated the variety of competing techniques evaluated in the experiments section, along with the various datasets. The ablation study validating the incremental value of each component, along with the analysis on computational and memory complexity, make the paper even more complete.\n\nOne aspect I found lacking was more insight into where this approach may not have the desired effect, or the extent to which the weight parameter in Eq. 13 tends to settle on across different datasets after training. Including a dedicated \"Discussion and Limitations\" section to go before the Conclusion section could address this current gap, although these insights could also be integrated within the methodology and experiments sections themselves.", "was_revised": true, "final_justification": "The paper is well-written, with clearly-motivated and illustrated contributions as well as extensive experiments. The authors have demonstrated they are committed to incorporate the feedback that emerged in the review period, giving me confidence in supporting the paper for acceptance.", "rebuttal": "Thanks for your in-depth insights and suggestions. Through Adaptive Fusion, the SRS can integrate both the representations from Adjacent Patching and Selective Patching with learnable weights, thus can combine the advantages of both methods.  \n\nAs you mentioned, the weight parameter in Eq. 13 can actually reflect which scenarios the two techniques separately excel at. We manage to study this by devising experiments on specific datasets and report the weight values. Intuitively, the Selective Patching may excel at datasets with shifting phenomenon and the Adjacent Patching may excel at datasets with strong seasonality. So that we conduct additional experiments on datasets with varying values of shifting and seasonality from TFB, a well-recognized time series forecasting benchmark. Specifically, we choose NASDAQ, NYSE, and AQShunyi with descending shifting values in TFB, and choose PEMS08, ZafNoo, and AQWan with descending seasonality values in TFB. The statistical details of them are as follows:\n\n| datasets | NASDAQ | NYSE | AQShunyi |\n| --- | --- | --- | --- |\n| Shifting Values | 0.932 (Strong) | 0.620 (Modest) |     0.019 (Weak) |\n\n| datasets | PEMS08 | ZafNoo | AQWan |\n| --- | --- | --- | --- |\n| Seasonality Values | 0.850 (Strong) | 0.757 (Modest) | 0.119 (Weak) |\n\nWe conduct comprehensive plugin experiments on them, reporting the average MSE and MAE metrics, and how the weight values converged.\n\n| Datasets | NASDAQ |  | NYSE |  | AQShunyi |  |\n| --- | --- | --- | --- | --- | --- | --- |\n| Metrics | MSE | MAE | MSE | MAE | MSE | MAE |\n| PatchTST | 0.972 | 0.721 | 0.483 | 0.437 | 0.703 | 0.507 |\n| + SRS | 0.757 | 0.569 | 0.418 | 0.379 | 0.641 | 0.461 |\n| Improved | **21.99%** | **21.03%** | **13.50%** | **13.50%** | **8.83%** | **9.14%** |\n| Crossformer | 1.737 | 0.992 | 0.983 | 0.909 | 0.694 | 0.504 |\n| + SRS | 1.256 | 0.709 | 0.854 | 0.785 | 0.635 | 0.455 |\n| Improved | **27.35%** | **28.10%** | **13.48%** | **13.84%** | **8.64%** | **9.71%** |\n| PatchMLP | 1.352 | 0.810 | 0.467 | 0.440 | 0.722 | 0.516 |\n| + SRS | 1.037 | 0.606 | 0.406 | 0.380 | 0.666 | 0.475 |\n| Improved | **23.31%** | **25.30%** | **13.77%** | **13.82%** | **7.78%** | **8.04%** |\n| xPatch | 1.060 | 0.708 | 0.545 | 0.474 | 0.735 | 0.509 |\n| + SRS | 0.850 | 0.563 | 0.469 | 0.408 | 0.678 | 0.464 |\n| Improved | **19.63%** | **20.32%** | **14.56%** | **14.63%** | **7.68%** | **8.75%** |\n| MLP | 1.200 | 0.803 | 0.463 | 0.432 | 0.717 | 0.513 |\n| + SRS | 0.925 | 0.600 | 0.395 | 0.366 | 0.662 | 0.467 |\n| Improved | **23.50%** | **25.50%** | **15.56%** | **15.94%** | **7.68%** | **8.89%** |\n\n| Datasets | PEMS08 |  | ZafNoo |  | AQWan |  |\n| --- | --- | --- | --- | --- | --- | --- |\n| Metrics | MSE | MAE | MSE | MAE | MSE | MAE |\n| PatchTST | 0.332 | 0.322 | 0.509 | 0.454 | 0.812 | 0.498 |\n| + SRS | 0.312 | 0.300 | 0.441 | 0.386 | 0.661 | 0.395 |\n| Improved | **6.02%** | **6.89%** | **13.29%** | **15.08%** | **18.49%** | **20.70%** |\n| Crossformer | 0.265 | 0.282 | 0.494 | 0.456 | 0.786 | 0.490 |\n| + SRS | 0.254 | 0.267 | 0.429 | 0.387 | 0.592 | 0.369 |\n| Improved | **4.23%** | **5.30%** | **13.02%** | **15.05%** | **24.86%** | **24.74%** |\n| PatchMLP | 0.306 | 0.283 | 0.531 | 0.466 | 0.829 | 0.505 |\n| + SRS | 0.294 | 0.270 | 0.457 | 0.395 | 0.637 | 0.388 |\n| Improved | **3.93%** | **4.63%** | **14.09%** | **15.23%** | **23.26%** | **23.18%** |\n| xPatch | 0.269 | 0.242 | 0.593 | 0.479 | 0.849 | 0.506 |\n| + SRS | 0.258 | 0.232 | 0.521 | 0.417 | 0.701 | 0.406 |\n| Improved | **3.61%** | **4.11%** | **12.19%** | **12.87%** | **17.37%** | **19.65%** |\n| MLP | 0.303 | 0.278 | 0.523 | 0.455 | 0.826 | 0.505 |\n| + SRS | 0.283 | 0.259 | 0.439 | 0.371 | 0.611 | 0.362 |\n| Improved | **6.59%** | **6.62%** | **16.18%** | **18.46%** | **26.11%** | **28.44%** |\n\nBased on the above results, we have two main observations:\n\n1. The SRS excels at datasets with high shifting values (NASDAQ) and low seasonality values (AQWan), because there exists more special samples about changeable periods, anomalies and shifting in these cases.  The SRS can improve all patch-based models significantly by 17% — 28% on these datasets.\n2. When the datasets are closer to normal cases with higher seasonality values and lower shifting values, the performance improved by the SRS gradually decreases. On NYSE and ZafNoo, the performance is improved by 12% — 18%. Note that even on AQShunyi and PEMS08, the improvement still exists and is about 4% — 10%. This provides evidence that the SRS can handle both the normal and special cases well.\n\nWe then report the converged mean weight values $(1-\\alpha) \\in [0, 1]$  on them. (higher values indicate more dependence on representations from Selective Patching, lower values indicate more dependence on representations from Adjacent Patching).\n\n| Datasets | NASDAQ | NYSE | AQShunyi | PEMS08 | ZafNoo | AQWan |\n| --- | --- | --- | --- | --- | --- | --- |\n| PatchTST | 0.79 | 0.58 | 0.42 | 0.33 | 0.56 | 0.69 |\n| Crossformer | 0.76 | 0.55 | 0.34 | 0.32 | 0.58 | 0.73 |\n| PatchMLP | 0.72 | 0.57 | 0.38 | 0.29 | 0.61 | 0.74 |\n| xPatch | 0.81 | 0.63 | 0.45 | 0.28 | 0.55 | 0.72 |\n| MLP | 0.79 | 0.62 | 0.48 | 0.36 | 0.57 | 0.67 |\n\nWe also have two main observations:\n\n1. When the seasonality values are higher and the shifting values are lower, models have less dependence on representations from the Selective Patching. This implies that the Adjacent Patching may well handle these common cases or the Selective Patching is gradually converged to the Adjacent Patching. \n2. When the seasonality values are lower and the shifting values are higher, models have more dependence on representations from the Selective Patching. It is because Adjacent Patching may not well process these special cases, while our proposed Selective Patching can adaptively select the patches with more useful information for forecasting.\n\n**Thanks for your sincere suggestions again! We will release the full results when the discussion phase starts. If you have any additional question, we can make further discussion!**"}, {"review_id": "7zVCnU5WyK", "reviewer": "Reviewer_Gwnu", "summary": "This work explores a Selective Representation Space (SRS) module, using Selective Patching and Dynamic Reassembly to adaptively select and shuffle patches for better context exploitation. The SRSNet, combining SRS and an MLP head, achieves state-of-the-art results on multi-domain datasets. As a plug-and-play module, SRS also boosts existing patch-based models.", "questions": "See the Weaknesses", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. The SRS module is a plugin which can enhance the time series forecasting, providing general improvement on patch-based models. \n\n2. The simple baseline SRSNet also demonstrates competitive performance against current strong baselines.\n\nWeaknesses:\n1. Please elaborate the definition or concept of Selective Representation Space in more detail and clearly. What is the main difference between patches and representations?\n \n2. Though authors have considered the SRS as a simple baseline or as a plugin, the datasets used are not enough. The \"ETT long term forecasting benchmark\" is often criticized for its flaws such as limited domain coverage and the practice of forecasting at unreasonable horizons (e.g., 720 days into the future for exchange rate or oil temperature of a transformer at a specific hour months into the future). Every new model somehow beats this benchmark; however, there is still barely any absolute progress, only an illusion of it. Please refer to the talk (and paper) from Christoph Bergmeir [1, 2] where he discusses the limitation of this benchmark and current evaluation practices. A very recent position paper [3] also conducted a comprehensive evaluation of models on this benchmark showing that there's no obvious winner. One (not so difficult) way to improve the quality of evaluation is to include results on better benchmarks [4]. \n\n[1] https://neurips.cc/virtual/2024/workshop/84712#collapse108471\n\n[2] Hewamalage, Hansika, Klaus Ackermann, and Christoph Bergmeir. \"Forecast evaluation for data scientists: common pitfalls and best practices.\" Data Mining and Knowledge Discovery 37.2 (2023): 788-832.\n\n[3] Brigato, Lorenzo, et al. \"Position: There are no Champions in Long-Term Time Series Forecasting.\" arXiv preprint arXiv:2502.14045 (2025).\n\n[4] Qiu X, Hu J, Zhou L, et al. \"TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods.\" Proceedings of the VLDB Endowment, 2024, 17(9): 2363-2377.\n \n3. Why are the datasets used in Table 4 corresponding to Efficiency Analysis inconsistent with those in Table 2 and Table 3? Can you provide more details regarding efficiency?\n \n4. I'm still confused about the mechanism of gradient propagation. Please explain the details of formulas (3)-(5).", "was_revised": true, "final_justification": "The author's rebuttal, especially the additional experiments, addressed all of my concerns. Taking all the reviewers' comments into account, I believe this work is solid. I support its acceptance.", "rebuttal": "**Reply to W1**\n\nThanks for the question. In time series forecasting, all the patch-based models obey the calculation chain: Patching —> Embedding (preliminary representations) —> Modeling (senior representations) —> Forecasting (Dimensionality Reduction). Specifically, Patching technique does not directly produce representations, but it determines where the representations come from (the candidate patches). Therefore, we think that the Patching technique actually determines the structure of the representational space, thus affecting the representations. In terms of representations, we think the Embeddings are the preliminary representations directly produced from the patches, and the hidden representations across model layers are the senior ones.\n\n**Reply to W2**\n\nThanks for the suggestion. To provide more empircal evidence, we conduct additional experiments on another 6 datasets from TFB. Their statistical information is as follows:\n\n| datasets | NASDAQ | NYSE | AQShunyi |\n| --- | --- | --- | --- |\n| Shifting Values | 0.932 (Strong) | 0.620 (Modest) |     0.019 (Weak) |\n\n| datasets | PEMS08 | ZafNoo | AQWan |\n| --- | --- | --- | --- |\n| Seasonality Values | 0.850 (Strong) | 0.757 (Modest) | 0.119 (Weak) |\n\nTo comprehensively evaluate the capability of SRS, we make plugin experiments with all 5 models in our paper on the above 6 datasets, the mean results of 4 forecasting horizons are reported as follows:\n\n| Datasets | NASDAQ |  | NYSE |  | AQShunyi |  |\n| --- | --- | --- | --- | --- | --- | --- |\n| Metrics | MSE | MAE | MSE | MAE | MSE | MAE |\n| PatchTST | 0.972 | 0.721 | 0.483 | 0.437 | 0.703 | 0.507 |\n| + SRS | 0.757 | 0.569 | 0.418 | 0.379 | 0.641 | 0.461 |\n| Improved | **21.99%** | **21.03%** | **13.50%** | **13.50%** | **8.83%** | **9.14%** |\n| Crossformer | 1.737 | 0.992 | 0.983 | 0.909 | 0.694 | 0.504 |\n| + SRS | 1.256 | 0.709 | 0.854 | 0.785 | 0.635 | 0.455 |\n| Improved | **27.35%** | **28.10%** | **13.48%** | **13.84%** | **8.64%** | **9.71%** |\n| PatchMLP | 1.352 | 0.810 | 0.467 | 0.440 | 0.722 | 0.516 |\n| + SRS | 1.037 | 0.606 | 0.406 | 0.380 | 0.666 | 0.475 |\n| Improved | **23.31%** | **25.30%** | **13.77%** | **13.82%** | **7.78%** | **8.04%** |\n| xPatch | 1.060 | 0.708 | 0.545 | 0.474 | 0.735 | 0.509 |\n| + SRS | 0.850 | 0.563 | 0.469 | 0.408 | 0.678 | 0.464 |\n| Improved | **19.63%** | **20.32%** | **14.56%** | **14.63%** | **7.68%** | **8.75%** |\n| MLP | 1.200 | 0.803 | 0.463 | 0.432 | 0.717 | 0.513 |\n| + SRS | 0.925 | 0.600 | 0.395 | 0.366 | 0.662 | 0.467 |\n| Improved | **23.50%** | **25.50%** | **15.56%** | **15.94%** | **7.68%** | **8.89%** |\n\n| Datasets | PEMS08 |  | ZafNoo |  | AQWan |  |\n| --- | --- | --- | --- | --- | --- | --- |\n| Metrics | MSE | MAE | MSE | MAE | MSE | MAE |\n| PatchTST | 0.332 | 0.322 | 0.509 | 0.454 | 0.812 | 0.498 |\n| + SRS | 0.312 | 0.300 | 0.441 | 0.386 | 0.661 | 0.395 |\n| Improved | **6.02%** | **6.89%** | **13.29%** | **15.08%** | **18.49%** | **20.70%** |\n| Crossformer | 0.265 | 0.282 | 0.494 | 0.456 | 0.786 | 0.490 |\n| + SRS | 0.254 | 0.267 | 0.429 | 0.387 | 0.592 | 0.369 |\n| Improved | **4.23%** | **5.30%** | **13.02%** | **15.05%** | **24.86%** | **24.74%** |\n| PatchMLP | 0.306 | 0.283 | 0.531 | 0.466 | 0.829 | 0.505 |\n| + SRS | 0.294 | 0.270 | 0.457 | 0.395 | 0.637 | 0.388 |\n| Improved | **3.93%** | **4.63%** | **14.09%** | **15.23%** | **23.26%** | **23.18%** |\n| xPatch | 0.269 | 0.242 | 0.593 | 0.479 | 0.849 | 0.506 |\n| + SRS | 0.258 | 0.232 | 0.521 | 0.417 | 0.701 | 0.406 |\n| Improved | **3.61%** | **4.11%** | **12.19%** | **12.87%** | **17.37%** | **19.65%** |\n| MLP | 0.303 | 0.278 | 0.523 | 0.455 | 0.826 | 0.505 |\n| + SRS | 0.283 | 0.259 | 0.439 | 0.371 | 0.611 | 0.362 |\n| Improved | **6.59%** | **6.62%** | **16.18%** | **18.46%** | **26.11%** | **28.44%** |\n\nBased on the above results, we have two main observations:\n\n1. The SRS excels at datasets with high shifting values (NASDAQ) and low seasonality values (AQWan), because there exists more special samples about changeable periods, anomalies and shifting in these cases.  The SRS can improve all patch-based models significantly by 17% — 28% on these datasets.\n2. When the datasets are closer to normal cases with higher seasonality values and lower shifting values, the performance improved by the SRS gradually decreases. On NYSE and ZafNoo, the performance is improved by 12% — 18%. Note that even on AQShunyi and PEMS08, the improvement still exists and is about 4% — 10%. This provides evidence that the SRS can handle both the normal and special cases well.\n\n**Reply to W3**\n\nThanks for the suggestion. To provide more details regarding efficiency, we conduct additional experiments. Our experiments consist of two parts:\n\n(1) The efficiency comparison between SRSNet and other baselines:\n\n|  | ETTm2 |  | Solar |  |\n| --- | --- | --- | --- | --- |\n|  | Memory | Training Time | Memory | Training Time |\n| DLinear | 573 | 6.998 | 815 | 15.6563 |\n| Amplifer | 555 | 10.82 | 715 | 14.3796 |\n| TimesNet | 2,413 | 86.553 | 13,141 | 1812.4588 |\n| FEDformer | 917 | 202.9685 | 3,751 | 227.446 |\n| Stationary | 18,373 | 147.157 | 18,529 | 156.269 |\n| Crossformer | 7,523 | 118.3208 | 16,375 | 205.602 |\n| PatchTST | 867 | 17.62 | 26,777 | 137.60377 |\n| iTransformer | 579 | 14.545 | 1,015 | 20.663125 |\n| TimeMixer | 1,099 | 20.378 | 20,602 | 107.149 |\n| TimeKAN | 1,207 | 27.108 | 13,109 | 326.378 |\n| SRSNet | 1,059 | 16.293 | 6,301 | 56.149 |\n\n(2) The complexity introduced by the SRS module:\n\n| Datasets | Variants | Memory (MB) | Params (M) | Inference Time (s/batch) | Training Time (s/batch) | MACs (G) |\n| --- | --- | --- | --- | --- | --- | --- |\n| ETTh1 | PatchTST | 2837 | 11.276 | 5.076 | 5.131 | 16.214 |\n|  | SRS | 2907 | 11.298 | 5.722 | 5.763 | 16.905 |\n|  | **Overhead** | **2.47%** | **0.19%** | **12.73%** | **12.31%** | **4.26%** |\n|  | Crossformer | 4011 | 11.101 | 27.503 | 32.613 | 56.280 |\n|  | SRS | 4159 | 11.112 | 30.311 | 35.276 | 56.625 |\n|  | **Overhead** | **3.69%** | **0.10%** | **10.21%** | **8.17%** | **0.61%** |\n| Solar | PatchTST | 27822.08 | 14.429 | 84.231 | 88.714 | 600.261 |\n|  | SRS | 29767.68 | 14.451 | 95.200 | 101.981 | 613.790 |\n|  | **Overhead** | **6.99%** | **0.15%** | **13.02%** | **14.95%** | **2.25%** |\n|  | Crossformer | 17355 | 0.711 | 79.031 | 82.472 | 61.822 |\n|  | SRS | 18978 | 0.717 | 86.674 | 90.268 | 62.174 |\n|  | **Overhead** | **9.35%** | **0.88%** | **9.67%** | **9.45%** | **0.57%** |\n\nBased on the above tables, we have two main observations:\n\n1. The SRSNet makes accuracy and efficiency meet, though not enough efficient as Linear-based models, but is more efficient than most transformer-based baselines and achieves stronger performance.\n2. It is observed that the overhead introduced by the SRS is relatively trivial. The Memory, MACs, and Params increase little. And the Training Time and Inference Time are also controllable under the end-to-end supervised cases. And the performance can be consistently improved.\n\n**Reply to W4**\n\nThanks for the question. The motivation we devise the mechanism is to keep the propagation of gradients in the Argmax operation in the equation (2) of the paper:\n\n$$\\mathcal{S} ^s = \\text{Scorer} ^s(\\mathcal{P} ^\\prime), \\mathcal{I} ^s = \\text{Argmax}(\\mathcal{S} ^s)$$\n\nSince the Argmax operation finds the patches with the max scores and return their indices, it disrupts the gradients. To avoid this phenomenon, we need to attach the gradients back to the selected patches. Note that the gradients are on the scores generated by the scorer, so we need to first retrieve the corresponding scores of the selected patches through equation (3):\n\n$$\\mathcal{S} ^s _{max} = \\mathcal{S} ^s[\\mathcal{I} ^s], \\mathcal{S} ^s _{inv} = \\text{detach}(1/\\mathcal{S} _{max} ^s)$$\n\nWe then process the scores and normalize them to 1 values, while keeping the gradients on them. The detail is that we detach the reciprocal $\\mathcal{S} ^s _{inv}$ to preserve the gradients.\n\n$$\\mathcal{P} _{max} ^s = \\mathcal{P} ^\\prime [\\mathcal{I} ^s], E ^s = \\mathcal{S} ^s _{max} \\odot \\mathcal{S} ^s _{inv}$$\nFinally, we attach the normalized scores to the patches through Hadamard product:\n$$\\tilde{\\mathcal{P}} ^s _{\\text{max}} = \\mathcal{P} _{max} ^s \\odot E ^s$$\n\n**Thanks for your sincere suggestions again! We will release the full results when the discussion phase starts. If you have any additional question, we can make further discussion!**"}]

Author rebuttal:

Meta-review: This paper proposes the Selective Representation Space (SRS) module, a plug-and-play component that adaptively selects and reorders patches for time series forecasting, addressing the rigidity of conventional adjacent patching. The strengths lie in its novel and gradient-friendly design, consistent performance improvements across benchmarks, and the ability to enhance both a simple baseline and existing patch-based models. After rebuttal, the authors further clarified implementation details, provided more experiments and addressed concerns on efficiency. All the reviewers were satisfied with the rebuttal. Therefore, I would like to recommend accepting this paper.
Decision: Accept (spotlight)