CoMRes: Semi-Supervised Time Series Forecasting Utilizing Consensus Promotion of Multi-Resolution
Authors: Yunju Cho
Jay-Yoon Lee
Venue: ICLR 2025 Poster (2025)
Keywords: Time series forecasting
Multi-scale
Semi-supervised learning
Primary area: learning on time series and dynamical systems
TL;DR: we propose a novel semi-supervised time series forecasting utilizing consensus promotion learning on augmented data without requiring explicit future values.

Abstract: Long-term time series forecasting poses significant challenges due to the complex dynamics and temporal variations, particularly when dealing with unseen patterns and data scarcity. Traditional supervised learning approaches, which rely on cleaned and labeled data, struggle to capture these unseen characteristics, limiting their effectiveness in real-world applications. In this study, we propose a semi-supervised approach that leverages multi-view setting on augmented data without requiring explicit future values as labels to address these limitations. By introducing a consensus promotion framework, our method enhances agreement among multiple single-view models on unseen augmented data. This approach not only improves forecasting accuracy but also mitigates error accumulation in long-horizon predictions. Furthermore, we explore the impact of autoregressive and non-autoregressive decoding schemes on error propagation, demonstrating the robustness of our model in extending prediction horizons. Experimental results show that our proposed method not only surpasses traditional supervised models in accuracy but also exhibits greater robustness when extending the prediction horizon.

Published as a conference paper at ICLR 2025
COMRES: SEMI-SUPERVISER TIME SERIES FORECASTING UTILIZING CONSENSUS PROMOTION OF MULTI-RESOLUTION
Yunju Cho, Jay-Yoon Lee
Graduate School of Data Science Scoul National University
1 Gwanak-ro, Gwanak-gu, Scoul 08826, Korea (iyj0729, lee. jayyoon (wn.nnssnua....m...
ABSTRACT
Long-term time series forecasting poses significant challenges due to the com- plex dynamics and temporal variations, particularly when dealing with unseen patterns and data scarcity. Traditional supervised learning approaches, which rely cleaned and labeled data, struggle to capture these unseen characteristics, lim- iting their effectiveness in real-world applications. In this study, we propose a semi-supervised approach that leverages multi-view setting on augmented data without requiring explicit future values as labels to address these limitations. By introducing a consensus promotion framework, our method enhances agreement among multiple single-view models on unseen augmented data. This approach not only improves forecasting accuracy but also mitigates error accumulation long-horizon predictions. Furthermore, we explore the impact of autoregressive and non-autoregressvee decoding schemes on error propagation, demonstrating the robustness of our model in extending prediction horizons. Experimental results show that our proposed method not only surpasses traditional supervised models in accuracy but also exhibits greater robustness when extending the prediction horizon. Code is available at this repository: http:///iuubbcoomyoyccco////oooa
INTRODUCTION
Time series forecasting has seen significant advancements in recent years, with research making substantial progress in capturing the complex dynamics inherent in time-series data (Zhou al.
Nie et al. 2023 Chen et al. 2024 Liu et al. 2024a; Challu et al. 2023 Das al. 2023 Wang ct al. 2024| Zeng et al. 2023). Due to the complex and non-stationary nature real-world systems, observed time series often exhibit intricate temporal patterns, such multi-scale dependencies and diverse fluctuations. To capture the multi-scale characteristics effectively, several advanced models structurally incorporate multi-scale features(Chen et al. 2024 Shabani al. 2023] Wang et al. 2024 Challu et al., 2023). This approach generally increases model capacity, allowing for the learning of complex patterns across different scales through an increase in parameters. However, this increased capacity also increases the risk of overfitting, especially when training on small or low-diversity datasets. Addressing these challenges essential for developing stable and reliable multi-resolution forecasting models.
2022
In time series analysis, several data augmentation methods have been proposed enhance model's generalization performance (Wen et al. 2021b] Iglesias et al.] [023] Debnath et al.) [2021] Semenoglooo al. 2023). Despite their widespread use, labeling augmented data remains a significant challenge, particularly in forecasting tasks. This challenge arises because the augmented data may alter the underlying dynamics of the time series and often introduce noise. Consequently, assigning accurate labels for future predictions becomes difficult, as the augmented past values represent artificial, potentially noisy data rather than actual observations. Even slight shifts in trends or periodic patterns can lead to increased prediction errors, thereby limiting the direct applicability of augmented data in time series forecasting. However, the use of diverse and previously unseen data is essential to address the complex dynamics and time-varying heterogeneity of long-term time series data. Therefore,

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reducing the risk of model overfitting and enhancing generalization ability without manually assigning future values to augmented data is crucial for effectively utilizing data augmentation in time series forecasting.
This study investigates the use of augmented data in long-term time series forecasting through a multi-view learning approach. Multi-view data has demonstrated considerable success in various domains, such as computer vision and natural language processing (Chen et al.] 2021]] Lim et al.) 2020), by leveraging different manifestations of the same data to improve performance. In time series analysis, multi-view data can be represented by features such as varied temporal resolutions or distances, allowing for the extraction of temporal characteristics and dependencies across multiple time intervals, ultimately enhancing the accuracy and robustness of forecasts (Challu et al. [2023] Liu al. 2022, Shabani et af., 2023 Chen al. 2024). Many multi-scale modeling techniques integrate features from different time scales but are limited to labeled data. By employing semi-supervised learning, which leverages unlabeled data, we can fully utilize multi-scale features across diverse patterns.
Thus, we propose a semi-supervised approach that improves individual single-view models by enhancing consensus among them using unseen data. Inspired by traditional co-training methods (Blum& & Mitchell 1998 Lim et al. 2020). this approach leverages augmented unseen data to ensure patterns but also provide consistent predictions when
that models not only capture faced with new, unseen data. The core of this CoMRes (Consensus promotion of ) lies in maximizing agreement among multi-view models unseen data, thereby improving the overall performance and reliability of long-term time series forecasting.
In addition, we address the issue of error accumulation long-horizon forecasting. In transformer- based research for long-term time series forecasting, a common approach is the use of a non- autoregressive decoding scheme, which projects future horizons all once. [Zhang et al. (2023) were the first to conduct comparative evaluation of several models in terms of autoregressive and non-autoregressive decoding schemes. Motivated by their work, we evaluate our model with respect to both decoding styles. Specifically, we investigate how non-autoregressive models can be employed minimize error accumulation when predicting values further into the future than the forecast range on which they were trained.
In summary, our contributions are as follows:
We propose CoMRes (Consensus promotion of Multi- Resolutiooo., novel semi-supervised time series forecasting that utilizes consensus promotion of multi-resolution information and augmented data without requiring explicit future values as labels enhance long-term time series forecasting. To the best of our knowledge, this is the first work to investigate the influence of superiuee framework in the context of long-term time series forecasting.
We propose evaluating the forecasting model using both autoregressive and non- autoregressive decoding schemes. Our study focuses on how a forecasting model can extend its prediction horizon beyond the trained range while minimizing error accumulation, particularly when non-autoregressive models are used to generate autoregressive forecasts.
To further understand CoMRes, we conduct ablation study the impact of incorporating data augmentation and consensus promotion strategies in semi-supervised and supervised learning.
We evaluate the impact of our CoMRes under various training data size and analyze the effect of different data augmentation techniques to enhance model performance.
2 RELATED WORK
Long-term Time Series Forecasting Recent research has made significant progress in improving model architectures for time-series forecasting. Transformer based model such as FEDformer (Zhou et al. 2022) and Autoformer (Wu et al. 2021). apply attention mechanisms multivariate time series data. These models address the quadratic complexity of traditional attention mechanisms by introducing novel mechanisms reduce computational complexity. PatchTST (Nie et al., 2023) utilized patch-based representations to enhance local pattern recognition, while iTransformer (Liu pushed forward by capturing multivariate
et al. 2024a) and Crossformer (Zhang & Yan. 2023)
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correlations through sophisticated attention mechanisms. Meanwhile, several recent works (Das et al. (2023); Wang et al. (2023); Zeng et al. y: Wang et al. (2024) demonstrate the effectiveness of non-transformer-base methods, offering competitive alternatives.
Multi-scale Modeling for Time Series Real-world time series often exhibit diverse variations and fluctuations across different temporal scales. To address this, recent research has increasingly focused on leveraging multi-scale information to better capture these complex temporal patterns.
NHITS (Challu al., 2023) employs multi-rate data sampling and hierarchical interpolation to model features of different resolutions. Pyraformer (Liu et al. 2022) and Scaleformer (Shabani al. 2023) advanced the field with pyramidal attention mechanisms and iterative scale-refinement mechanisms, respectively, to capture multi-scale dependencies. TimeMixer (Wang et al. (024)
introduce new multi-scale mixing architecture with decomposable mixing strategy. Pathformer (Chen et al. 2024) takes more comprehensive approach by considering time series features from both different resolutions and temporal distances. Most previous methods integrate complementary forecasting capabilities through ensemble of multiple predictions that rely on labeled data. By employing cemi-supervised learning, which leverages unlabeled data, our approach effectively tackles the challenge of reconciling diverse representations, particularly in the context of unseen data.
Time Series Data Augmentation Comprehensive reviews of the most popular data augmentation approaches in time series analysis mostly focus on classification and anomaly detection tasks (Wen et al. 2021b Iglesias et al. 2023). Data augmentation is easily applicable for time series classification and anomaly detection small perturbations typically do not change the data label. Nonetheless, it is not straightforward to apply data augmentation techniques in time series forecasting as even small perturbations can lead to significant changes in the observations. Several studies (Debnath et al. 202T; Semennolou lou et al., [203]] Zhhou et al. 2023 Nochumsohn & Azencol 2025) have examined the impact of data augmentation on forecasting, consistently finding that its effectiveness depends on data characteristics. Similarly, [Wen et al. (2021a) survey time series augmentation methods, noting their benefits for classification and anomaly detection but reporting negative effects for certain data/model pairs in forecasting. Our findings (Table [] align with these observations, showing that naive augmentation often degrades performance rather than improving it. Nochhmmohnn & Azencot (2025) propose an automated augmentation approach for long-term forecasting, iteratively searching across diverse time series transformations to optimize augmentation policies using Bayesian optimization. In contrast, our study applies simple augmentation solely for consensus promotion, achieving improvements in most experiments without requiring costly search procedures or complex augmentation techniques.
METHODOLOGY
In this paper, we study the problem of long-term time-series forecasting: Given historical data of multivariate time series with a look-back window L: (It=Ly.... ,.........,,)))).. 22), where Ie denotes the observation timestamp t, our objective is to predict the future values for H timestamps (I++1; Ht+ We use similar model architecture to Pathformer, introduced by Chen et al. (2024), our base model and extend it to leverage unseen data. Our model architecture for long-term time series forecasting depicted in Figure
To effectively capture multi-scale characteristics, we employ multi-scale patch division with various patch sizes (P1, Pz..... Pm)) and dual attention transformer. The multi-scale patch division provides different views of the time series at different resolutions. These patches are fed into the transformer encoder, which comprises intra-patch attention within each divided patch and inter-patch attention across different patches. Following the transformer encoder, Hulti-Layer Perceptrons (MLPs) generate individual predictions (T;) for each patch size. These predictions are then aggregated using an equal weighted aggregation strategy, resulting in a single comprehensive prediction (f.). Unlike Chen et al. (2024), use equal weighted aggregator combine these multi-scale characteristics.
During supervised learning, we train the model to minimize the mean squared emror (MSE) between the predictions and the ground truth. Given that there + predictions, we average the errors of each prediction. The supervised loss is optimized as follows:
C. = m +1
| - -1414 1
1 - T4414+111
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Comprehensive Prediction
f.
MLP
Individual Predictions
Aggregation
Xm
MLP
MLP
Fusion
Dual Attention
Dual attention
Dual attention
Dual attention
Intra- patch
Inter- patch
Lincart Position Eibaaking
Lincart Position Embedking
Lincart Position Fimbadding
P
Multi-scale Patching (patch sizes
Figure Overall architecture of multi-rcsolution transformer, CoMRes and MRes. There are m individual blocks and aggregation block. Each individual block predict individual prediction, T. The aggregation block produce comprehensive prediction, E..
In the following sections. we provide a detailed description of consensus promotion learning on unseen data and the process of generating unseen data. Subsequently, we explain how to extend prediction horizons beyond the training ranges.
3.1 CONSENSUS PROMOTION LEARNING
Due the complex dynamics of long-term time series data, learning models from diverse and unseen data crucial for improving forecasting accuracy. However, determining the future values unseen augmented data is challenging, this data is synthetic and potentially noisy. To address this issue, propose a method inspired by standard multi-view learning approaches, which aim to jointly optimize multiple models derived from distinct perspectives, each providing complementary information. Drawing from the concept of one model teaching others, as introduced by Blum & Mitchell| (9988 and Lim et (2020), we suggest using consistency loss that encourages mutual agreement among the models. This approach leverages the unique information provided by different views to enhance comprehensive predictions (Z.) ), effectively capturing the complex, multi-resolution patterns inherent in long-tern term time series forecasting.
To achieve this, we propose that each individual-vin view model learns from the comprehensive prediction predicttinn (T,) by optimizing the following unsupervised loss:
C. m
Σ | F. Foc-i+H11
This encourages the individual-view models to align their predictions with the comprehensive prediction, thereby enhancing mutual agreement among the models. The overall objective for training the model combines the supervised loss and the unsupervised consistency loss as follows:
= L. + Warh
where w. represents the weight ot the unsupervised consistency loss C,, This joint objective ensures that the model not only minimizes the prediction aligns the individual model predictions with the comprehensive prediction(C....
with respect to the ground truth(C,) but also
The core principle of consensus promotion learning is to achieve best possible forecasting results on unseen data. By leveraging the complementary information from multiple views and aligning individual model predictions with comprehensive prediction, it reduces the variance of individual
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Extending Horion
mma
mi
of Hasie (a) Prediction emror along with the horizzon
Block-wise autoregressive forecasting
Extending
94-01
(c) Fine-grained autoregressive forocasting
Figure 2: Extending Prediction Horizons Beyond Training Ranges. Figure (a) shows eπror rising with longer horizons. Figure (b) uses block-wis forecasting for the entire horizon. while Figure (c) adopts fine-grained approach. Both methods apply autoregression with non-autoregressive trained model, but the fine-grained approach utilizes the initial prediction due its relatively small error.
predictions(see Appendix A.2), leading to more stable and reliable results on unseen data. This is because the consensus or ensemble of predictions can help mitigate the biases and errors that may be present in any single model, allowing for better generalization to new, previously unobserved patterns.
3.2 UNSEEN DATA GENERATION
We generate unseen data via augmentations (time warping, interpolation, noise injection). The objective of generating unseen data is to construct synthetic data that explores new areas of the input space. In supervised learning, data augmentation typically assumes that the relationship between the lookback period and the prediction horizon is well-defined, with known ground-truth labels. In contrast, our approach does not require defining ground truth for augmented data, offering greater flexibility for complex time series.
Time series data augmentation Debnath et al. 2021 [glesias et al. 2023 SSeeenoglou et al. 2023 Zhou et al. 2023 Nochumsohn Azencot 2025), but we focus on simpler techniques for their ease of implementation. We include three variants of CoMRes: interpolation, time warping, and noise injection. Combining multiple
forecasting has been extensively studied (Wen et al. 2021b
augmentation techniques to enhance model performance will be discussed in Section 4.3.2
Interpolation involves estimating values between known data points to produce smoother and more continuous time series. For example, linear interpolation estimates values between two known points using a straight line. In this study, adopt linear interpolation.
Time Warping includes techniques such as stretching or compressing the time window of data. Simi- lar to dynamic time warping (DTW), this method selects random time range and then compresses (down-samples) it. this study, we compress the time window by a factor of
Noise Injection adds random noise to the data introduce variability. This includes injecting Gaussian noise, spike, step-like trend, and slope-like trend, etc. In this study, Gaussian noise, which consists of random values drawn from normal distribution, is used. After normalization, add normal noise with mean of 0 and standard deviation of 0.01
3.3 EXTENDING PREDICTION HORIZONS BEYOND TRAINING RANGES
In addition to the typical evaluation forecasting performance, which involves measuring the prediction enror over H timestamps (training horizon), we also assess model's performance when
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predicting beyond this training horizon. For applications requiring long-term future predictions, such as stock prices or energy consumption, autoregressive forecasting is essential. However, autoregressive forecasting inherently suffers from error accumulation, especially when the model has not been trained autoregressively over an extended horizon, such as with teacher forcing. As depicted in Figure (a). our non-autoregressive model's prediction errors escalate the prediction horizon lengthens. Our objective is to explore methods that can extend the prediction horizon while minimizing error accumulation in autoregressive forecasting scenarios.
In this study, we evaluate the model trained with consensus promotion through two approaches: Block-wise autoregressive prediction and fine-grained autoregressive prediction. The block-wise autoregressive prediction method, illustrated in Figure extends the prediction horizon by utilizing the entire prediction range at once. contrast, step-by-step process where the output of one step serves as the input for the next step, emphasizing recurrent or sequential processing approach, as shown Figure [c). This progression demonstrates the iterative application of the model to refine predictions over multiple steps.
greggrained autoregressive prediction involves
EXPERIMENTS
4.1
TIME SERIES FORECASTING
Datasets. We evaluate model on 8 popular datasets, including 4 ETT datasets (ETTh1, ETTh2, ETTml, ETTm2), Weather, Traffic, Electricity, ILI. These datasets have been extensively utilized for benchmarking and publicly available on Wu et al. (202I) and the data statistics are shown in Appendix A.I.1
Baseline. We compare CoMRes with Pathformer Chen et al. (2024). of the state-of-the-art long- term forecasting models, which uses a multi-resolution division architecture with adaptive pathways. Pathformer outperforms most other models, such TimeMixer, NLinear, and others (as shown in Appendix Table 8). Additionally, results for another baseline model, TimeMixer, are provided in Appendix A.5 demonstrate the general application of CoMRes.
Ablations. To evaluate the impact of two core strategies- strneeicss-coneenuuus promotion and data augmenta- tion-on both labeled and unlabeled data, our proposed model (CoMRes) and its ablation models (MRes, short for We established the following three ablation models:
aggregation transformer) share the same architecture, as illustrated
Figure |
MRes (SL): MRes trained exclusively on labeled datasets using supervised learning (SL).
MRes augmentation: MRes trained on pseudo-labeled datasets augmented with Time Warping.
MRes w. consensus: MRes trained on labeled datasets with consensus promotion but without data augmentation. Predictions on labeled data are learned not only from the ground truth but also from the comprehensive prediction.
MRes with both data augmentation and consensus promotion applied to all augmented data corre- sponds CoMRes.
Experimental Setup. To assess the impact of different unseen data generation methods, we include three variants of CoMRes: interpolation, time warping, and noise injection. Each dataset was split into training, validation, and test sets. Mean squared eπror (MSE) and mean absolute error (MAE) were used as evaluation metrics, with each experiment repeated five times, and the average values reported (see Appendix [A44 for error bars). Following the setup from the Pathformer paper, all models used the same input and prediction lengths: T, = 36 for the IIII dataset and I, = 96 for the others. Prediction lengths were H e {24, 36, 48, 60) for ILI and H E {96, 192, 336, 720} for the others. More experimental details are in Appendix A.I
Results. The experimental results, summarized in Table indicate that our proposed model outper- forms the baselines on most datasets. Notably, CoMRes, which incorporates consensus promotion unseen data significantly enhanced the model's generalization ability, as evidenced by lower MSE scores on the test sets. Although MRes with consensus promotion showed good results in some datasets, these improvements were inconsistent across others. Both CoMRes and MRes with

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Multivariate time series forecasting results (MSE). The input length L 96 (L 36 for the ILI dataset). The best results are highlighted in bold, and the second-best results are underlined. The column shows the difference between CoMRes's best results and the ablation models or the baseline, with blue indicating that CoMRes outperforms and red indicating otherwise.
Table I:
Mathod
Warping
OoMRoc logeol Imere-imion
Injection
Regmentation
Mfcs
Prlhfiemer
Levengging
Epseudo l0bel)
66
IL3778
0.379
0.379
0.606
0.028
0.379
0.001
0.383
0.004
0.362
0.004
192
1.416
0.436
0,836
0.355
0101
0.836
0.000
0.479
0.000
0.840
[U00
336
0.452
0.452
0.452
0.454
0.002
720
0.474
0.094
0.007
0.479
0.005
Ang
193
0.053
336
0,316
0.346
0.036
0.006
0.368
01122
720
0.393
0.358
0.397
0.404
0.011
0.405
0.012
0.405
0.013
0.396
0.055
Ang.
0.335
0.337
0,335
0.346
0.011
0.339
0.004
0.341
0.006
0.344
0.009
50
1.311
0.111
0.31
0.330
01010
0,311
0.00
0,312
0,001
0.316
193
0.362
964
0.164
0.967
0100
0.164
0.02
0,361
.000
0.966
DBC4
396
0.556
0.566
0.987
0.834
0.018
0.185
0.000
0.981
.0005
0.366
0,000
720
01556
0.556
0,555
0.487
0.011
0,55%
0.000
9.551
0001
0.800
00004
Aug.
0.37
0379
0.379
2000
0.522
0033
0.163
0.63
0.168
0.005
0.165
0.004
01170
0.077
192
0,00
0.38
0,009
0.369
0.390
0.021
01363
0.365
0273
0000
50
0152
00100
0.155
0104
0000
0.145
Elecalsity
336
192
0.151
0.167
0.167
0.151
0.165
0.173
0.186
0.007
0.005
0.169
0.184
0.032
0.033
0.164
8
.0002
0.000
0.167
0.156
0.001
0.005
730
0.210
12211
0.214
0221
01000
0.314
0.944
0.221
0.11
0251
0.21
Ang.
0.178
0.178
0.179
0.185
0,077
0.181
0.005
6,380
0,002
0.152
0.004
24
1987
1907
1,955
1250
0.147
1,385
0.025
1,776
0200
1357
0.320
11.
36
46
1.640
1.59
136
1535
1.514
1.09
01051
1,500
0.100
1,551
0,013
1439
0.055
0.109
1.737
1731
Ang.
1:00
Traffic
336
192
0.495
0.465
0,018
0.005
0.454
0.503
0.019
0.010
720
0.538
0.536
0,535
0.500
0.537
0.005
0.556
0.002
0.021
0.537
0.002
A0g
[L390)
1.491
0.391
030
07012
0,299
0,201
0/713
01301
50
11111
0.111
6.11
0155
0.151
0.55
0/301
0.156
Winther
336
192
I.199
0.244
0.266
(1200)
0.345
0
01200
0.248
0109
0.030
0.246
0.201
0190
0.004
0.245
8.199
01000
0,002
0.254
0.206
0107
0.000
720
0.335
0.335
0.334
0.334
0.000
0.333
0.002
0.334
0,000
0.300
0.006
Agg
07333
0235
000
0.334
0101
0231
0700
0007
consensus incorporate consensus promotion; however, CoMRes applies it unseen data, whereas MRes with consensus applies it to labeled data. This distinction is critical, as adding a consistency loss term alongside supervised loss can improve performance but also carries the risk of conflicting signals when applied to labeled data. Additionally, MRes with augmentation where augmented data artificial and potentially noisy data performs poorly. Our results indicate that CoMRes consistently outperforms the baselines across multiple datasets. The case of ILI, where CoMRes underperforms compared to Pathformer, is discussed in detail in Appendix A.9 Interestingly, MRes (SL) outper- formed Pathformer in most cases, suggesting that Pathformer's strengths lie in its ability to process multi-resolution information and its inter- and intra-attention design, rather than in the use of adaptive pathways. Among the unseen data generation techniques of CoMRes, time warping achieved slightly better performance compared to interpolation and noise injection. Overall, these findings demonstrate the efficacy of our approach in improving time series forecasting performance. Complementary results for mean absolute error(MAE) are provided in the Appendix A.3
F illustrates the mean error against the prediction horizon, demonstrating how prediction errors increase as the forecast extends further into the future from the lookback period. As shown in Figure 3 our proposed model consistently outperforms the baseline model in terms of prediction accuracy, especially over longer horizons. This comparison underscores the effectiveness of our approach in reducing errors in long-term time series forecasting.
4.2 ERROR ACCUMULATION IN AUTO-REGRESSIVE FORECASTING
Experimental Setting. In this section, we conduct experiments evaluate our proposed model (CoMRes, Time Warping) and the ablation model (MRes, SL) on test data, focusing on predictions beyond the training horizon. The datasets used are described in Section 4.1
We employ two approaches for autoregressive prediction. In both approaches, the extended prediction horizon is 96 sequences beyond the model's initial prediction horizon.
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ETT2
117r2
Colfes
Colfee They
Cailt Tiee
Mean Ervor
Gonia
667
Order Prediction Horizon
Figure 3: Prediction error along with the prediction horizon. The orange line representing the mean error of the proposed method is lower than that of MRes (SL.), the blue line.
Table 2: Auto-regressive forecasting result. MSE the extended horizon beyond the trained horizon. The best results are highlighted in bold. In both (a) and (b), CoMRes predicts more accurately than MRes. Additionally, (a) block-wise approach produces more accurate predictions compared (b) fine-grained approach.
Method
(a) Block wise Auto regressive
(b) Fine grained Auto regressive
Data
Horizon
CoMRes, Time Warp
MRes (S1.)
CoMRes, Time Warp
MRes (S1.)
96
0.477
0.490
192 96
0.476
0.490
0.481
0.499
ETTh1
0.491
0.506
720 96
0,505
0,513
0,500
0.507
96 96
0.420
0.453
0.429
0.465
ETTh2
336 96
0.4.30
0.463
0.429
0.468
720
0.437
0.469
96 96
0.412
0.414
0.424
0.442
192 96
0.416
0,418
0.421
0.429
ETTml
720 96
0.449
0.451
0.454
0.455
96 96
0.332
0,336
0.351
0.416
192 96
0.358
0.355
0.361
0.404
336 96
0.374
0.377
0.384
0.378
720++90
96 96
0,280
0.285
0,303
0.425
Weather
192 96
0.303
0.305
0.303
0.425
336 96
0.323
0.347
0.331
0.356
720+ +9
0.358
0.361
0.361
0.372
The model generates predictions for the entire extended horizon in one step. Specifically, the model uses part of its own prediction as input to produce predictions beyond this range once.
Block-wise Autoregressive Prediction:
The model generates predictions step-by-step. where each output serves the input for the next prediction step.As depicted in Figure 2(a), the initial prediction error over the prediction horizon is relatively small. Therefore, if we use the initial prediction refine the predictions over multiple steps. In this approach, we update the input with the last k=1 value using the previous prediction.
Fine-grained Autoregressive Prediction:
input extend the horizon step by step,
expect to
Auto-regressive Forecasting Results. Table 2 presents the results of our augo-segressive forecasting evaluation. Compared to the enrors shown in [ the mean errors increased due to error accu- mulation. This issue inherent in auto-regressive forecasting, particularly when the model has not been trained auto-regressively challenges, CoMRes consistently outperformed the MRes(SL) across all prediction horizons and both rugo-regressive methods, demonstrating superior predictive accuracy. The block-wise auto-regressive method generally shows smaller error accumulation compared to the fine- ane-grained auto-regressive accumulation better.
extended horizon, such with teacher forcing. Despite these
method. This suggests that the block-wise approach handles regtrrregeee
To investigate the accumulation of errors in block- Block-wise autoregressive forecasting, we compared the prediction error over the entire horizon between model trained longer forecast range and
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Mean Error
ETTML
(R)) ETTh2,
Mãae 720
(SL), ETTha, 96, Blcck-ess
(93), ETThd, 96, Blockwnne
Miaa ETTm2, 98, wtd.-weeeeeeeee
Colifes, Time ETTR3
Caldile Time Werp, ETTh0_700 Cultilas Time Warp, ETT1 Blcckwase
Collfen
CoMibio, Time ETT11, 35, Blok-etie
CoMiiies ETTm2 96, Blokkotie
Order of Prediction Horizon
Figure 4: Error Propagation. The red line(CoMRes, Time Warp. block-wist AR) shows less error accumulation in long-term forecasting compared to the orange (MRes(SS)),, 96 block-wise AR), indicating that the our proposed method more effective at mitigating error accumulation.
one using block-wiss wise autoregressive predictions made with shorter model. Figure illlssrates the performance of block-wise autoregressive forecasting with shorter predictor model, specifically one trained to predict 96 steps, which is iteratively applied times to forecast longer horizons (up to 768 time points). This approach is compared against the ablation model trained to predict 720 steps directly.
In the block-wise autoregressive setup, MRes (represented by the orange lines in the 96-step block- wise autoregressive approach) suffers from a substantial increase in error as the prediction horizon extends, especially when iterating the shorter model. This greater error accumulation in the supervised learning makes it more susceptible to compounding small errors with each iteration. On the other hand, the CoMRes (shown by the green and red lines) demonstrates stronger capacity reduce accumulation, maintaining significantly lower error rates even when using block-wise autoregressive forecasting. While error accumulation occurs in CoMRes, for some data, the block-wis autoregressive model's 's error is comparable to that of the longer horizon non non-autoregressive model. This indicates that it is feasible effectively extend the prediction horizon of CoMRes using a shorter model.
4.3 ABLATION STUDY
4.3.1
RESTURDRESOURCE SCENARIOS
Real-worid time series often exhibit complex temporal variations, making it crucial to effectively leverage training data under resource constraints. We evaluated limited-data scenarios by system- atically reducing labeled training data (20%, 50%, 80%) and comparing our CoMRes Time Warp against MRes across multiple datasets.
The results in Table demonstrate that CoMRes consistently achieves the best performance across all label sizes and prediction horizons compared the baseling" Due to temporal variations, the temporal dynamics in distant periods may differ from those in the test period, leading to irrelevant information being included and causing worse predictions even with large amount of data, Furthermore, on the ETTh2 and ETTm2 datasets, CoMRes delivers comparable performance to MRes, even at smaller label sizes.
4.3.2 COMBINING MULTIPLE UNSEEN DATA GENERATION TECHNIQUES
In this section, we evaluate the impact of combining multiple unseen data generation techniques. We examine two approaches: (I) Combining all three augmentation techniques- Time Warp. Interpola- tion, and Noise Injection- anddinnonnnnndnn (2) applying Multi Time Warp, using compression factors of 3, 5, and These methods are compared against the best results achieved by CoMRes in 4.1] primarily using Time Warp, which we refer to as Single Time Warp.
The results in Table indicate that the effectiveness of augmentation techniques depends on dataset's s characteristics. With high variability over time, such as ETTh1, combining multiple augmen- tation techniques did not lead to noticcable performance gains. However, with clear and consistent
The Traffic results obtained using H100 GPUs during the rebuttal period.

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Published as a conference paper at ICLR 2025
Table Result in highlighted in bold, while the best result of the remaining methods is underlined. Label size is fraction of the original training data (e.g.. 0.5 uses only the most recent half).
scenarios. The best results among the compared methods are
Method
CoMRes, Warp
Label Size
0.2
0.5
0.8
1.0
0.2
0.5
0.8
1.0
96
0.390
0.377
0.378
0,378
0.393
0.379
0.381
0.382
ETTh1
192
0.444
0.435
0.437
0.436
0.448
0.436
0,438
0,439
336
0.452
0.448
0.444
0.452
0.449
0.447
0.445
0.451
720
0.504
0.489
0.469
0.474
0.474
0.481
0.470
0.481
0.277
0.276
0:295
0.280
0.277
0,277
192
0.377
0.356
0,348
0.345
0.377
0.363
0,349
0.347
BTTh2
0.359
0.334
0.329
0.376
0.358
0.334
0.330
720
0.452
0.438
0.404
0.399
0.460
0.434
0.416
0,409
96
0.336
0,310
0.313
0,310
0.337
0.311
0,311
0,312
BTTml
0.357
336
0.401
0.378
0.390
0,386
0.399
0.378
0,384
0.381
720
0.471
0.446
0.467
0.456
0.471
0.447
0,454
0.454
0.171
0.163
0.179
0.170
0.168
0.106
ETTm2
192
0.248
0.234
0.231
0.229
0.248
0.234
0,232
0.229
0.292
720
0.409
0.400
0.386
0.383
0.408
0.401
0,386
0.383
96
0.164
0.160
0.155
0.151
0.175
0.163
0.1.5
0.152
Weather
192
0.213
0.223
0.204
0.199
0.223
0.210
0,204
0.199
336
0.265
0.257
0,250
0.244
0.258
0.257
0,250
0. 0.245
0.342
0.335
0.343
0.343
0.338
0.536
0.486
0.446
0.468
0.583
0.501
0,470
0.478
Traffic
192
0.512
0.492
0.536
0.465
0.529
0.484
0,562
0.476
336
0.566
0.501
0.526
0.493
0.550
0.503
0.589
0.501
720
0.578
0.539
0,548
0.535
0.597
0.540
0.561
0.556
periodic patterns over time, such as ETTm2, improvements were observed at certain prediction horizons, although rapid long-term trend shift caused performance declines at the 720-horizon. In the Weather dataset, which features inter-variable correlations, combining augmentation techniques resulted in performance gains. Overall, while sulliiiaggmetationn approaches do not universally improve performance, they can be beneficial for some datasets. The degree of improvement, varies according to the specific features of the dataset and the forecasting task at hand.
Table 4: Results of combining unseen data generation techniques. Performance improvements com- pared the Single Time Warp method are in blue, while declines are red.
Method
Combine three
Multi Time Warp
Single Time Warp
96
0.378
0.379
0.378
192
0.436
0.436
0.436
ETThl
336
0.452
0.452
0.452
720
0.474
0.476
0.474
96
0.164
0.163
0.163
192
0.228
0.227
0.229
ETTm2
336
0.289
0.28%
0.291
720
0.384
0.382
0.369
96
0.149
0,150
0.151
Weather
192
0.198
0.199
0.199
336
720
0.330
0.334
0.334
5 CONCLUSION
This paper introduces multi-view learning strategy for long-term time series forecasting, demon- strating superior prediction accuracy and robustness compared to traditional supervised learning approaches. This approach leverages augmented unseen data to ensure that models not only cap- ture multi-resolution patterns but also provide consistent predictions when faced with new, unseen data. Our comprehensive experiments highlight the model's ability to generalize well across various datasets and handle challenging forecasting scenarios effectively, especially in autoregressive setups, where it mitigates the issue of error accumulation.
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ACKNOWLEDGMENTS
This work was supported part by the National Research Foundation of Korea (NRF) grant (RS- 2023-00280883, RS-2023-00222663) and partially supported by New Faculty Startup Fund from Seoul National University
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with mi xup data aatgaatttuuuntttttionn
A APPENDIX
A.1 EXPERIMENTAL DETAILS
A. DATASETS
We use eight popular datasets from Wu et al. 2021 for forecasting. The ETT datase includes data from two electricity transformers at two stations, capturing metrics such as load and oil temperature. This dataset is recorded at both 15-minute and 1-hour intervals, and is labeled as ETTh1, ETTh2,
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ETTmI, and ETTm2. The Electricity datase contains hourly electricity consumption data from 321 users. The ILI datase collects weekly reports patients with influenza- illness, spanning 2002 to 2021, from the Centers for Discase Control and Prevention of the United States. The Traffic road occupancy rates from various sensors on San Francisco freeways. Finally, the
datase datass/recoodds records Weather datase comprises 21 meteorological indicators collected every 10 minutes in Germany.
Table 5: Statistics of popular datasets for benchmark.
Datasets
ETThi
ETTh2
ETTml
ETTm2
Electricity
Traffic
Weather
Features
7
7
7
321
7
862
21
Timesteps
17,420
17420
69,680
69,680
26,304
966
17,544
52,696
Split Ratio
6:2.2
6:2-2
6:2:2
6:2:2
7:1-2
7:1:2
7:1:2
7:1:2
A.1.2 DETAILS OF IMPLEMENTATION
To ensure fair comparisons, The model is trained using the Adam optimizer (Kingmal 2014) with learning rate of 10 The default loss function is I.1 Loss, and early stopping applied after 10 epochs if no improvement is observed. All experiments are implemented in Py PyToch and executed on a NVIDIA A6000 48GB GPU.
the same hyperparameters Pathformer in Chen al. (2024).
The baseline model, MRes, includes four different patch sizes, same to those used in Pathformer
repository These patch sizes selected from the following options: {2, 3, 6, 12, 16, 24, 32). Unlike Pathformer, which is composed of three multi-scale blocks, MRes does not utilize hierarchical architecture. This allows us argue that MRes achieves comparable predictive performance with fewer model parameters, offering a more efficient design.
CoMRes and MRes atgenerates one comprehensive prediction and m individual predictions, so for the final model performance evaluation, m + predictions were used in an ensemble. First, the average value of the m individual predictions was calculated, and then was averaged with the comprehensive prediction to form the final prediction.
A.2 VARIANCE OF INDIVIDUAL-VENS MODEL
The Figure 5 provides clear evidence that applying consistency loss improves consistency between individual-view models compared to MRes (SL). MRes with consensus and CoMRes exhibits consistently smoother and lower trend than MRes(SL), indicating reduced variability in predictions. This smoother trend suggests that individual models are more aligned and consistent with one another after applying the consistency loss, effectively achieving the intended effect of consensus promotion.
A.3
TIME SERIES FORECASTING
we reported the model performance using Mean Squared Error (MSE). Additionally, Table 6 presents the results based on Mean Absolute Error (MAE), providing complementary evaluation of the model's predictive accuracy.
In section
4.1
A.4 ERROR BARS
In this paper, we repeat all the experiments five times. In Table 7 report the standard deviation of our model and the baseline model. CoMRes exhibits smaller standard deviations compared to Pathformer indicating less variability in its predictions.
"https://pems.dee" http://pmmm.oo..c.aaa. wot.ca.goo//
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'e were unable to reproduce Pathformer results on the II.I dataset. Therefore, use the mean values of
the metrics as reported in the original Pathformer paper and could not ohtain the corresponding error bars.
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5033
Mino
Conpat
34
614
Mie.
0:3
6.9
4003
630
0003
0.51
20
Figure 5: Comparison of individual-view model variability between MRes(SL), MRes with consensus and CoMRes across three datasets (ETTh1, ETTh2, and Weather) with forecast horizon of h=96. MRes with consensus and CoMRes demonstrates consistently reduced variability compared to MRes(SL).
Table Multivariate time series forecasting results (MAE). The input length L = 96 (L = 36 for ILI dataset). The best results are highlighted in bold, and the second- results are underlined. The A column represents the difference between CoMRes best result and the baselines such as MRes with ablated components and Pathformer.
CoMiees (MUS)
MRes
Waaping
0:415
0.306
0.000
0.187
0.001
01420
0.14
0,415
0.000
0416
0.012
186
0.000
720
0.453
0.451
0.000
0.454
0.461
0410
0/413
0.100
0001
0.251
0001
01350
U012
66
0.377
0,327
0.327
0.312
0.005
0.39
0.000
6350
0.002
0.331
0.004
ETTh2
596
192
0.313
0.360
0.374
0.000
0.373
0.369
0.382
535
0.066
0.009
0,374
03321
0.001
0000
63173
63R5
0.002
0004
0.380
0.007
0015
720
0,422
0322
0419
0.40
0.111
0.466
0000
0.427
0.005
0.424
0,005
A52
132
01010
0.133
1000
01100
1777
0007
0.399
0100
0:341
015h
0.00
336
0.367
0.367
0.387
0.000
0390
0,000
0.354
0.007
720
0.414
04455
0.419
0000
03456
0.432
0006
Aug.
0.379
6,379
0.379
0.357
0.11
0.379
0.000
03300
0.001
0.386
0.007
96
0.245
0,355
0.46
0.250
0.246
000
0.247
00002
0.245
0,00
ETTmd
336
193
11250
0.300
0.391
0.330
0.700
0.350
0.334
0.202
0004
0.00
11289
0,230
40001
00000
6:700
0:300
0.000
0.000
0.33
0.205
0,001
0.08
720
0.37%
0.37%
0.265
00077
0.377
0.000
(189
0.01
A05
0,31
0.311
0.316
0/113
0000
0316
0,06
Eletriiity
596
192
01367
0.25
6.077
0.367
0.252
0.252
0.258
0.005
0766
0.254
0.022
0000
0.150
0.769
0/003
0.256
0.275
0.06
750
0.99
0.291
0.292
0.289
6.007
0394
0000
6.10
0,010
0.99
0017
A0g.
0.63
0.33
0.363
0.359
000%
0200
0266
00002
0.50
0000
24
D310
0321
0335
0.200
20000
03317
000
0330
0000
IL73%
40065
ILI
48
36
02066
0.755
0.764
0.999
0.788
0.077
0.549
0.741
.00044
0007
0249
-006
40022
0358
0261
0003
-0005
0.71
0.743
-0.04
0.034
0.11
0.811
0.001
0.08
00000
6:10
0.002
0.799
4,009
Ang:
Trafho
596
192
0.295
6.395
0.298
0.300
0.005
0.298
0.282
0.000
0.000
0.306
0000
0.001
0.292
0.289
0.007
0.64
720
0.324
0.324
0.334
0.335
0.089
0.323
0.001
03311
0.003
0.332
0,00
Ang.
0.204
0.294
0.204
03300
6200
0.204
00000
0.254
0.000
01200
0006
96
0.190
0.190
0.190
0.195
0.005
0.103
0.033
0.190
0.000
0.192
0.000
Weather
336
192
0.276
0.317
0.275
0.1%
0.279
0239
0.001
0.278
0.237
00000
0.376
0.3%0
0/000
0.001
11:301
0.282
0004
0.007
Agg.
A.5 ADDITIONAL APPLICATION OF COMRES TO TIMEMIXER
To examine the general applicability of the proposed CoMRes, we explore the applicability of consen- sus promotion on augmented data to other architectures, particularly TimeMixer Wang et al. 2024). Tablee&ddeonsstaati that applying consensus promotion on augmented data enhances TimeMixer's forecasting accuracy in most cases. The berf-performing CoMRes results (across different augmen- tations) are compared against the reproduced TimeMixer results in the A column. In the majority of datasets, TimeMixer + CoMRes achieves lower MSE than the reproduced TimeMixer, indicat- ing improved forecasting performance. While CoMRes generally contributes to better results, its effectiveness varies depending on the dataset and forecasting horizon.
In our adaptation of TimeMixer, we treat downpooled series as individual views. TimeMixer derives its final prediction by summing single-scale predictions, whereas Pathformer generates its final
15

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Published as a conference paper at ICLR 2025
Table 7: We provide standard deviation for our method and the MRes baselines over 5 independent runs. The asterisk (*) denotes statistically significant differences at the 95% confidence level.
Method
Time Warping
CuMRes (ours)
Interpolaton
Nevws Injection
w. augennellaiion
W. W.EIOOOIIN
Mikes (SL)
Pathfonmer
Conseriou Promotion
T Lveeraging Angmented Data
(pesics-Shelsd)
96
0.578+0.001
0.379+0.00
0.379+00001
0
0.379-0.001
0.382+0001
0.382-00002
192
0.36++0.002
0,436+00.001
0,436+00.001
0.455=0.006
0.436=0.001
0,492=0.001
0:440=0.001*
0.452:0.001
0.452+00001
0.452+0.001
0.452:0.001
0,451=0.001
0.444=0.002*
720
0.474
0.4781000033
0.478100.033
0.1751000001
0.00
0.001
0.479
96
0:275=00:002
0,275=00002
0,275=0:022
0
0.275
0
0.279=00.005
ETTb2
336
192
0.326+0.001
0.347
0.346200.02
0.328+00.05
0.34620.001
0.326+0.001
0.05520.0009
0.34620.003
0.330+0.004
0.34810.001
0.33240.008
0.348-0.005*
0,349
720
0.393=00.002
0.398:00.009
0.397=00.009
0.404
0 000
0.406=00009
0.398=00.012
96
0.310=000011
0.311=0000
0.311=00000
0.326=0002-
0
0.51250.001
0,316:20.002
BT7ml
192
0.362+0.001
0.364+0.001
0.364-0.001
0.067-0.002
0.363-0.000
0.361+00.002
0 0.366--0.022
0.386=00.00
0.386=00:001
0.387=0.001
0,404=0.004
0.386+00.00
0.381+0:001
0.386=0.003
720
0.456:0.001
0.456::0.002
0.456:00.001
0.007
0.456
0.45
0.460:000003
96
0 0:16++0.000
0.163+0.000
0.163+0.0001
0.168-0001
0.106--0.001
0.167=0001
D. 0.170-0.0011
BTTm2
192
0.291
0.229=0.001
0.229=00001
0.229=000001
0.2921000011
0.230=00.000
0.292-0.002
0.229=00.001
0.231
0.29210.001
0.293=100003
0.23
720
0.36910.003
0.369100003
0.36910.003
0.385
0.282_0.002"
0.36910.003
0,290.10,001
95
0.152:00.004
0.153=00000
0.153:00005
0.162500000
0.15
0.150:0:00
0.045:000006
Electricity
192
0.167+00000
0.167+0.001
1.16--00002
0.173+00001
0.1
0.164+000003
0.167-0.101
336
0.181+00007
0:18-=00007
0.181+00006
720
0.210=00.022
0.2
0.214=00003
0.218
0.004
0.223+0.005
0.231
24
957700.072
1.907+0.002
1556-00000
1,760-00667
186--0.112
1.976+00.051
1.587
11.1
36
1.529=0.097
640==0.036
L511=+00055
1.599=0.076
1.38
1.90==0.101
1.51440.
1.56==0.07
1.540-0.558
1.551+0.137
1.429
60
1699310.091
L.739100004
1.71510.019
1.22740.047
L679
1.71450.018
1.731
96
0.466+0.000
0.
0.470=00005
0.475
0.479=000033
0.478+0.003
0.479=0.007
Traflic
192
0.465
0.493,00009
0.466:10.001
0.094100007
0.0941000007
0.466=20.002
0.5111000006
0.482
0.479=00000
0.50110.006
0.50110.006
0,476200003
0.484:10.004
0.503-10.004
720
0.535+00.002
0.535==0.002
0.535=00.00
0.540=+0.005
0.537=00.005
0.556+00000
0.537=40.004
95
0.151:00.000
0.151=0:000
0.151:00000
0.155
0.154
0.152:0.001
0.156:0.0002
Weather
192
0.199+0.001
0.200+00.00
0.200+00005
0.203+00001
0.201
0.199-0.001
0.206--0.002
192
0.246+00002
0.246+00022
0.248+0.002
0.346+0.000
0.245+0.001
0.254-0.602
192
0.33550.004
0.33510.004
0.33420.004
0.334
0.333-10.002
0.33420.004
0.340:0.0003
prediction through an additional projection layer after aggregating individual predictions. To facilitate complementary learning at the individual prediction level while avoiding conflicting ground truth signals, we apply the supervised loss only to TimeMixer's final prediction, rather than enforcing an ensemble-supervised loss on individual predictions.
The reported TimeMixer results could not be fully replicated with the hyperparameters provided in For a fair comparison, we performed a
the official code (https://github.c http:///ggguuub.co/uuuuiiie hyperparameter search to reproduce TimeMixer baseline and applied the same hyperparameter (e.g., learning rate, batch size) for expanding TimeMixer with CoMRes's consensus promotion on augmented data, maintaining consistency in experimental conditions. As our reporeduced results slightly lower than the reported TimeMixer results, we also display the originally reported results in the last column a reference.
A.6 ADDITIONAL BASELINES
To provide additional evaluation results and contextualize current progress in long-term time series forecasting, we include several advanced basclines in Table 9 Pathformer (Chen et al. 2024).
PatchTST NNe et al. 2023). TimeMixer (Wang et al., 2024), NLinear (Zeng et al. 2023), Scaleformer (Shabani et al. 2023). and TiDE (Das et al. 2023). All models use the same input length (H- 36 for the ILI dataset and H 96 for others) and prediction lengths (F' E (24, 36, 48, 60) for the ILI dataset and F E {96, 192, 336, 720) for others). We evaluate model performance using two common metrics in time series forecasting: Mean Absolute Error (MAE) and Mean Squared Error (MSE). The results for TimeMixer are taken from Wang et al. (2024), those for PSt are sourced from Nic ct al. (2023). and the remaining results are obtained from Chen et al. (2024).
A.7 LIMITED-RESOURES SCENARIOS
As noted in Section 4.3.I CoMRes consistently outperforms MRes across all label sizes and prediction horizons in limited resource scenarios. Not only does CoMRes achieve the best scores, as presented
16

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Published as a conference paper at ICLR 2025
Table 8: Results of Applying Consensus Promotion on Augmented Data TimeMixer. The reported MimeMixer results are taken from the original paper, while the reproduced results are obtained through our replication. The A column shows the difference between CoMRes's best results and Mixe. with blue indicating that CoMRes outperforms and red indicating otherwise.
TimeMixer + CoMRes (ours)
TimeMixer
Method
Time Warping
Interpolation
Noise Injection
Reproduced
Reported
0.379
0,376
0.376
0.377
0.001
0.375
-0.001
192
0.436
0.431
0.430
0.431
0.001
0.429
-0.001
ETTh1
01.844
0.485
0.001
0.484
0.000
720
0.499
0.489
0.489
0.498
0.009
0.498
0.009
Avg.
0,450
0.445
0.445
0.448
0.003
0.447
0.002
96
0.294
0.294
0.294
0.295
0.001
0.289
-0.005
192
0.374
0,374
0.374
0.375
0.001
0.372
-0.002
ETTh2
336
0.388
0,388
0.388
0.388
0.000
0,386
-0.002
720
0.419
0.419
0.419
0.422
0.003
0.412
-0.007
Avg.
0.369
0.369
0.369
0.370
0.001
0.365
4..04
0.322
0.331
0.331
0.331
0.009
0.320
00002
0.364
0.369
0.006
0.361
-0.003
ETTml
0.398
0.396
0.397
0.398
0.002
0.390
-0.006
720
0.465
0.458
0.460
0.461
0.004
0.454
-0.004
Avg.
0.387
0.387
0.388
0.390
0,003
0.381
-0.00
96
0.175
0.174
0.174
0.175
0.001
0.175
0.001
192
0.239
0.240
0.240
0.242
0.003
0.237
-0.002
ETTm2
336
0.294
0.295
0.295
0.294
0.000
0.298
0.004
720
0.390
0.389
0.389
0.393
0.003
0.391
0.002
Avg.
0,274
0,275
0.275
0.276
0.002
0.275
0.001
0.164
0.165
0.165
0.165
0.001
0.163
-0.001
0.209
0.209
0.209
0.000
+0.001
Weather
336
0.262
0.264
0.264
0.263
0.001
0.251
-0.111
720
0.341
0.342
0.342
0.341
0.000
0.339
-0.002
Avg.
0.244
0.245
0.245
0.244
0,000
0.240
-0004
96
0.462
0.461
0.459
0.477
0.018
0,462
0.003
192
0.453
0.456
0,458
0.496
0.043
0,473
0.020
Traffic
336
0.475
0.475
0.461
0.516
0.054
0.498
0.037
0.502
0.502
0.505
0.538
0.036
0.506
0.004
avg.
0.473
0.473
0.471
0.507
0.036
0.484
0.013
Table but also demonstrates higher prediction accuracy when trained on the same amount of labeled data. This suggests that CoMRes possesses generalization ability.
The table I0 shows the results training with distant data from the test period. Compared to Table 3 the overall best scores have changed due to intricate temporal variations. This suggests that the relevance of the data more important than the amount of data used. As the same as result of the recent data, CoMRes consistently achieves the best performance across all label sizes and prediction horizons compared to the baseline.
A.8 DISCUSSION MORE RELATED WORKS
Semi-supervised learning in other domain Semi-supervised learning have been extensively studied
in domains such as natural language processing (NLP) (Lim et al. 2020 Chen al. 2020 Sawhney
et al. 2021 Park & Caragea 2024) and image classification (Laine & Aila 2017] Xie et al. 2020 Zhang al. [222]] Chen al. 2023). In these fields, acquiring unlabeled data relatively straightforward due to the availability of large-scale datasets comprising sentences or images from the web. Ensemble-hand loss functions, which effectively leverage unlabeled data, have been shown to enhance model performance by capitalizing this abundance. Moreover, data augmentation offers a computationally efficient and accessible approach in resource-constraine scenarios. Techniques such augmentation with pseudo-labels have been particularly effective in expanding training sets for classification tasks, further boosting model performance.
However, extending these approaches to time series forecasting introduces unique challenges. Unlike NLP or image classification, time series data often lacks the diversity and abundance of high- quality unlabeled data. Additionally, the temporal and continuous nature of time series data makes
17

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Published as a conference paper at ICLR 2025
Table 9: Multivariate time series forecasting results for additional baselines. The input length L 96 (L = 36 for the ILI dataset). The best results are highlighted in bold. CoMRes's 's performance represents the average values over 5 runs. The results for TimeMixer are taken from Wang et al.]
(2024), the results for PatchTST are sourced from Nie et al. (2023), and the remaining results are obtained from Chen et al. (2024).
Method Metric
CaMRes
Pathformer
PatchTST
TimeMixer
Nlinear
Scaleformer
MSB
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSB
MAE
MSE
MAE
MSE
MAE
96
0.378
0.386
0.382
0,400
0.394
0.408
0.375
0.400
0.386
0.392
0.396
0.440
0.427
0,450
192
0.436
0.415
0.440
0.427
0.446
0.438
0.429
0.421
0.440
0.430
0.434
0.460
0.472
0.486
ETTh1
336
0,452
0.421
0.454
0.432
0,485
0.550
0.484
0.458
0,480
0.443
0.462
0.476
0.527
0.527
720
0.474
0.483
0.479
0.461
0.495
0.474
0.498
0.482
0.486
0.472
0.494
0.500
0.644
0.605
Avg.
0.435
0.419
0.439
0.430
0.455
0.468
0.447
0.440
0.448
0.434
0.447
0.469
0.518
0.517
96
0.275
0.327
0.279
0.331
0.294
0.345
0,289
0.341
0.290
0.339
0.364
0.407
0.304
0.359
192
0.346
0.373
0.349
0.380
0.378
0.394
0.372
0.392
0.379
0.395
0.466
0,458
0.394
0.422
BTTh2
336
0.326
0.369
0.348
0.382
0.382
0.410
0.386
0.414
0.421
0.431
0.479
0.476
0.385
0.421
720
0.393
0.419
0.398
0.424
0.412
0.433
0.412
0.434
0.436
0.453
0.487
0.492
0.463
0.475
Avg.
0.335
0.372
0.344
0.379
0.367
0.395
0.365
0.395
0.582
0.405
0.449
0.458
0.387
0.419
96
0.310
0.339
0.316
0.346
0.324
0.36]
0.320
0.357
0.339
0.369
0.355
0.398
0.356
0.381
192
0.362
0.365
0.366
0.370
0.362
0.383
0.361
0.381
0.379
0.386
0.428
0.455
0.391
0.399
ETTml
336
0.386
0.387
0.386
0.394
0.39
0.402
0.390
0.404
0.411
0.407
0.524
0.487
0.424
0.423
720
0.456
0.424
0,460
0.432
0.461
0.438
0.454
0.441
0.478
0.442
0.558
0.517
0.48
0.456
Avg.
0.379
0.379
0.382
0,386
0.384
0.396
0.381
0.396
0.402
0.401
0.466
0.464
0,413
0.415
96
0.163
0.245
0.170
0.248
0.177
0.260
0.175
0.258
0.177
0.257
0.182
0.275
0.182
0.264
192
0.229
0.290
0.238
0.295
0,248
0.306
0.237
0.299
0.241
0.297
0.251
0.318
0.256
0.323
ETTm2
336
0.291
0.330
0.293
0.331
0.304
0.342
0.298
0.340
0.302
0.337
0.34
0.375
0.313
0.354
720
0.369
0.378
0.390
0.389
0,403
0.397
0.391
0.396
0.405
0.396
0.435
0.433
0.419
0.410
Avg.
0.263
0.311
0,273
0.316
0,283
0.326
0.275
0.323
0.281
0.322
0.302
0,350
0.293
0.338
96
0.152
0.239
0.145
0.236
0.18
0.264
0.153
0.247
0.185
0.266
0.182
0.297
0.194
0.277
192
0.166
0.252
0.167
0.256
0.188
0.275
0.166
0.256
0.189
0.276
0.188
0.300
0.193
0.280
Electricity
336
0,181
0.267
0.186
0.275
0,206
0.291
0.185
0.277
0.204
0.289
0,210
0.324
0,206
0.296
720
0,210
0.292
0,231
0.309
0.247
0.328
0.225
0.310
0.245
0.319
0.232
0.339
0.242
0.328
Avg.
0.177
0.263
0.182
0,265
0,205
0.290
0.182
0.273
0.206
0.288
0.203
0.315
0.2019
0.295
96
1.907
0.830
1,587
0.758
1,724
0.843
2.725
1.069
0.232
0.339
2.154
0.992
192
1.538
0.755
1.429
0.711
1,536
0.752
2.530
1.032
2.745
1.075
2,436
1.042
ILI
336
1,490
0.766
1.505
0.742
1.821
0.832
2.510
1.031
2.748
1.072
2.532
1.051
720
1.693
0.811
1.731
0.799
1,923
0.842
2.492
1.026
2.793
1,059
2.748
1.142
Avg.
L.657
0.791
1,563
0.753
1.751
0.817
2.564
L.040
2.130
0.836
2.468
1.057
96
0.468
0.270
0,479
0.283
0.492
0.324
0.462
0.285
0.645
0.358
2.678
1.071
0.568
0.352
192
0.465
0.285
0.484
0.292
0.487
0.303
0.473
0.296
0.599
0.365
0.564
0,351
0.612
0.371
Traffic
336
0.493
0.295
0.503
0.299
0.505
0.317
0.498
0.296
0.606
0.367
0.57
0.349
0.605
0.374
720
0.535
0.324
0,537
0.322
0.542
0.337
0.506
0.313
0.645
0.388
0.576
0.349
0.647
0,410
Avg.
0.490
0.294
0.501
0.299
0.307
0.320
0.485
0.298
0.624
0.377
1.097
0.330
0.508
0,377
96
0.151
0.19
0.156
0.192
0.177
0.218
0.163
0.209
0.168
0.208
0.288
0.365
0.202
0.261
192
0.199
0,236
0.206
0.24
0.224
0.258
0.208
0.250
0.217
0.255
0.368
0.425
0.242
0.298
Weather
336
0.244
0.275
0,254
0,282
0,277
0.297
0.251
0.287
0.267
0.292
0.447
0.469
0.287
0.335
720
0.334
0.331
0.340
0.336
0.35
0,345
0.339
0.341
0.351
0.346
0.640
0.574
0.351
0,386
Avg.
0.232
0.258
0,239
0.263
0,257
0,280
0.240
0.272
0.251
0.755
0.436
0,458
0.271
0.320
it difficult to generate meaningful augmented data. These challenges necessitate tailored strategies to successfully adopt semi-supervised learning and data augmentation in the context of time series forecasting.
Semi-supervised learning for Time Series Classification The concepts of consensus promotion with pseudo-labeling have also been explored in the context of semi-supervised learning for time series classification (Jawed et al.
2020 Liu et al. 20233 Shin et al. 2023 Bac et al. (2024] Liu et al. 2024b).
For instance, Dawed et al. (2020) leverage features learned from self-supervised tasks on unlabeled
data, while Shin et al. (2023) propose context-attached augmentation to generate augmented instances
with varying contexts that preserve the target instance. [iu al. (2024b) introduce the Scale-Tease Teaching paradigm, which captures discriminative patterns in time series while mitigating noisy labels. Bae jet al. (2024) explore consistency regularization by artificially downsampling high- gigh-sampling-ratt time series to generate augmented versions. These studies demonstrate the effectiveness of leveraging augmented data with pscudo labeling in time series classification.
Despite these advances, the application of semi-supervised learning and consensus promotion to time series forecasting remains underexplored. In this work, we argue that forecasting poses unique challenges distinct from classification tasks, such the prediction of continuous outputs rather than discrete labels. Additional complexities include long-term temporal dependencies, seasonality, and error propagation in autoregressive settings. These factors make direct application of pseudo-labeling
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Published as a conference paper at ICLR 2025
2TTh1, prediction horiran=96
FT1h1. preditdion horizan:96
FTTh.. prediction heriesn=96
FTThL, predicdiin horionn96
0440
0.452
0:506
connees
Whes IS0
0.60
Mites (SU
0.432
sites ISU)
0.500
Mites ISU
0.433
0:466
0664
0.449
0.344
0.422
0.440
0:485
0.117
0.30-
5400
4.500
0408
0413
0378
0496
0470
0.5
1.0
02
0.8
02
0.
02
0.5
1abcl-Abe
sbed size
labelAkee
2TTh2 prediction 50rizon=:66
eTTh2 prediction herizon=966
ETTh2 prediction horieon=96
ETTh2 predicdion horizon:96
0.233
custees time worl
ISL)
0.375
cuentes Trme worp
Caspes Tine-war
curtee wamewarp Wheee
0370
0.292
0.56-
0.44
1 0.333
0.500
0.35
0.43
0.50-
0.2-
0.290
0.34
041
0.75
0.345
0.33
0.0
1.0
02
02
<1Tml. predicaion 90
2TTm]. prediction horizon
ETTml. predicdion horizonu99
ETTmL. predicdion horizon:99
0.33
CUMRes, Hhos (SL
Mhtee ISL)
4.00
Mitee ISL)
0470
Mitce iSL)
0.500
0.305
0.433
03675
0.300
03600
0.435
03635
03600
0.450
0.00
0.330
03375
0.445
0.
0.6
2.6
0.5
0.
0.5
0.0
label
labelatee
ldbel sooe
Idded sooe
ETTm2 predicaion h5r
ETTmZ, prediction horizon-96
ETTm2, predicdion horizon-99
ETTm2, predicdion horizon-90
0.37
CoMtes Tare Who (SL)
02475
coMtee Time warp Mhea
comfees Time warp Mitae
curmes Time worp Mitea
0.36
02450
0310
0.003
0334-
0.305
0.400
0332
0370
83375
0.85
02350
0.300
0.289
82325
0200
6364
02300
Weather. prediction hor
Weather, predicdion horizon-s9
Weather, predicdion horizonu99
Weether, predicdion herlzon-90
0.35
0366
Hho (SL)
5350-
Mitic (SL)
Milica (SL)
0330
0200
0.3475
5315
0.285
8230
5.256
0.3425
0.80
0335
8200-
0250
0.357
8200-
Hihen
0245
6350
0.5
0.5
66
0.5
0.5
0.5
0.0
1abel 10z
Iabel 121
Iabel 10
Iabel 1000
Figure 6: Comparison figures between CoMRes and MRes, evaluated using the same label sizes and dataset
and traditional augmentation techniques problematic, as evidenced by conflicting signals in the lookback context observed during our experiments [..
To address these challenges, we propose a novel approach that emphasizes consensus promotion on augmented data without relying on pseudo-labels. While our framework may initially seem straightfforward, it addresses the non- non-trivial challenge of integrating ideas from two different fields: semi-supervised learning and time series forecasting. By integrating ideas from semi-supervised lear-
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Table 10: Results in Rissure-Resuuree Scenarios: When using the oldest data. The best results among the compared methods are highlighted in bold, while the best result of the remaining methods is underlined. The label size represented as a ratio of the original training data. For example, a value of 0.5 indicates that only the first half of the original data was used for training, meaning that the most oldest portion the training data was used.
Method
SSL. Time Warp (ours)
SL. Baseline
Label Size
0.2
0.5
0.8
1.0
0.2
0.5
0.8
T.0
96
0.412
0.398
0.378
0.378
0.409
0.396
0.381
0.382
ETTh
192
0.486
0.455
0.433
0.436
0.482
0.456
0.438
0.439
336
0.533
0.478
0.454
0.452
0.523
0.479
0.452
0.451
720
0.579
0.502
0.481
0.474
0.544
0.506
0.484
0.481
96
0.270
0.275
0.279
0.271
ETTh2
192
0.357
0.353
0,343
0.345
0.361
0.357
0.347
0.347
336
0.343
0.334
0.333
0.329
0,346
0.338
0.333
0.330
720
0.453
0,385
0.389
0.399
0.434
0.388
0.395
0,409
96
0.383
0.387
0.312
0.310
0.381
0.382
0.318
0.312
BTTml
0.412
0.416
0.368
0.362
0.412
0.416
336
0.436
0.438
0.392
0,386
0.436
0.436
0.397
0.381
720
0.513
0.511
0.458
0,456
0,514
0.508
0.466
0.454
96
0.130
0.172
0.166
0.163
0.180
0.170
0.168
0.160
ETTm2
192
0.242
0.233
0.231
0.229
0.243
0.234
0.232
0.229
336
0.306
0.297
0.292
0.291
0.305
0.294
0.292
0.292
720
0.409
0.390
0.386
0.383
0.406
0.389
0.384
0.383
ing and time series forecasting, our framework effectively balances the complexities of forecasting with the benefits of consensus promotion, offering a meaningful contribution.
A.9 DISCUSSION RESULT ON ILI DATASET
The ILI dataset presents unique challenges due to its highly non-stationary patterns, which make accurate prediction particularly difficult. While CoMRes demonstrates strong performance across most datasets, its performance on the ILI dataset is less competitive compared Pathformer, es- pecially when f = 24 and h = 36, as shown in Table | Notably, we were unable to reproduce Pathformer's 's reported performance on the ILI dataset; however, crediting the authors, Table I includes the performance metrics as reported in the original Pathformer paper.
The ILI dataset is characterized by a rapid long-term uptrend, which poses significant challenges for forecasting models. Recent advanced models, such as those proposed by Shabani et al. (2023) and Nie et al. 2023), exhibit high prediction errors (MSE above 2), while others, such as Wang et al.) (2024) and Das et al. (2023), exclude the IIII dataset from their experiments, further reflecting its inherent difficulty.
We hypothesize that the rapid long-term uptrend in the ILI dataset limits the advantages of multi-scale modeling, as long-term dependency patterns may not effectively leverage multi-resolution features. Nonetheless, experimental results show that CoMRes improves prediction accuracy compared to MRes (SL). This suggests that the unsupervised consistency promotion mechanism in CoMRes has a positive impact on enhancing model generalization, even in challenging scenarios like the ILI dataset.
A. DISCUSSION COMPARISON ON A PER-AUGMENTATION BASIS
To better understand the impact of different augmentation strategies, we conducted a per-augmentation analysis, comparing the performance of CoMRes with MRes across three augmentation techniques: Time Warping, Interpolation, and Noise Injection in Table [I]
The results indicate that the effectiveness of each augmentation depends on both the characteristics of the data and the context in which the augmentation is applied. Augmentations in supervised learning scenario (e.g., MRes w. augmentation) tend to degrade performance, likely due to overfitting or mismatched data distributions. In contrast, CoMRes utilizes augmented data within semi- supervised learning framework, which mitigates overfitting and enhances generalization. This distinction is evidenced by CoMRes consistently achieving better results across all tested scenarios.
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In conclusion, the pergentmnnntio analysis highlights the robustness of CoMRes across various augmentation strategies, while demonstrating the critical role of applying augmentations within a semi-supervised framework to achieve consistent and significant improvements over MRes.
Table 11: Results of per- per-augmentation analysis.
Method
CoMRes
Time Warping
Mices
CoMREs
Interpolation
MIKes
CoMRess
Noise Injection MRCs
MR
Consensus Promocion
Loveraingg Augmental Pats
unlabe
psanlislibel
uniahel
pacnd-lihhl
unbikel
ponalo-Shhl
0.378
0,406
0.028
0.379
0.414
0.038
0.379
0.410
0,037
0,382
192
0.46
0.455
0019
0.36
0.499
0.023
0.466
0.44
0.04
0.490
ETTh
336
0.452
0,422
0130
0452
0.448
.0004
0452
0.446
40,006
0.451
720
0.474
0.75
0.01
0.78
0.433
-0.05
0478
0.447
0.031
0441
0003
0,290
0.277
0.347
0008
0.36
0355
0000
0.346
0.352
0.006
0.348
BTT12
336
0.326
0.346
0020
0.328
0335
0000
0.336
0.336
0010
0.333
720
0.395
0.401
0011
0.398
0
0000
0.397
0.402
0.005
0.406
0.335
0.346
0011
0.357
03445
0.336
0.343
1007
0.341
0.364
0,420
0.436
ETTml
0018
0.386
0,456
0.518
0.131
0.581
720
0.456
0.467
0011
0.256
0,306
0.466
0,532
0.076
0.454
Avg:
0.379
0.301
0015
0.179
04452
001
0.350
0:476
0/07
0.377
0.163
0.103
01005
0.163
01775
0.163
0.176
0003
0.167
BTTm2
0.201
0.044
0.308
0.292
0016
0.369
0.405
0.369
Avg.
01263
0.270
0007
0.283
02282
01019
0.261
0.252
0018
0.265
95
0:151
0.135
01004
0151
0.159
0.131
0.163
0012
0.152
192.
0.199
0.303
0.004
0.200
0.205
0.005
0.300
0.208
0.088
0.199
Weather
336
0.246
0.248
0.004
0.246
0.25
0.001
0.246
0.252
0.245
-1.011
Avg.
0.013
0.333
0,240
A.11 DISCUSSION COMPUTATION COST
In this section, we analyze the computational efficiency of CoMRes in comparison to Pathformer, with focus both the training and inference stages.
Training Time Pathformer's s training involves operations such as temporal decomposition using the Discrete Fourier Transform (DFT) and weight generation with two learnable parameters. In contrast, CoMRes utilizes M + 1 Multi-Layer Perceptrons (MLPs) and integrates data augmentation its design. Although CoMRes introduces additional parameters
as a fundamental component due to the extra MLPs, the capabilities of modern GPUs effectively mitigate potential performance limitations, ensuring the computational requirements remain practical. Runtime metrics confirm that the increased burden is manageable (see Table T2). Notably, the longer training time observed for CoMRes is primarily due to the overhead associated with on-the on-the-fly data augmentation. This additional cost can be reduced by employing precomputed augmentations optimizing the pipeline through parallelization.
Table 12:
Quantitative comparison of training and inference times for CoMRes and Pathformer. Results are based on lookback window (L= 96), prediction horizon (h 96), M =4 views, and identical configurations (e.g., patch sizes) for both models.
#purameters
Train (seconds per epoch)
Inference(sevonds test sumple)
CoMRes
pathformer
batch size
CoMRes
puthformer
#iest samples
CoMRes
pathlormer
ETThl
379,054
231.222
512
4.17
3.56
2,785
1.89
1.67
ETTm2
2,752,162
2,161,962
512
18.81
12.47
11,425
5.64
4.45
Weather
627.408
332,120
47.57
33.40
10,444
7.43
7.35
Traffic
3,212,905
2,622,705
478.51
269.08
3.413
37.83
32.23
Inference Time During inference, Pathformer performs a top-k weighted sum operation followed by an MLP to produce its final predictions. In comparison, CoMRes employs an equal-weight sum, which computationally simpler, followed by MLP. The computational overhead for CoMRes during inference minimal, and the additional complexity introduced by its design does not significantly impact overall performance. CoMRes has the flexibility the comprehensive prediction directly
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the final output, bypassing the need for M individual MLP computations for each view. This approach further reduces the computational burden in practical scenarios, making CoMRes efficient for inference.
To provide empirical context, we measured the training and inference times for both models under a standardized experimental setup an NVIDIA A6000 GPU. The results in Table [2 indicate that while computational differences between CoMRes and Pathformer exist, they are manageable and be further optimized in practical scenarios.
A.12 VISUALIZATION
We visualize the prediction results of CoMRes and Pathformer on ETTh1, Weather, Traffic dataset. As shown in Figures 7 and the prediction curve closely aligns with the ground truth, demonstrating the excellent predictive performance of CoMRes. Additionally, present the prediction results of CoMRes, MRes, and Pathformer in an autoregressive forecasting scenario. Figure i0llusstraes that CoMRes effectively mitigates error accumulation.
ETTh1
ETTh1
V
-3-
Pathformr
200
(a) Prediciton Horizon 96
(b) Prediciton Horizon H 192
ETTh1
Quttiis ground nuth Refhfomer
CotMfics oroundruuh
Pethfformr
200
(c) Prediciton Horizon H 336
(d) Prediciton Horizon H 720
Figure 7: Visualization of CoMRes's and Pathformer's prediction results ETTh1. The input length
96
A.13 LIMITATIONS AND FUTURE WORK
CoMRes has demonstrated favorable performance in long-term time series forecasting: however, there room for further exploration and refinement of its design options. First, our framework assumes a Euclidean distance to measure consensus between the aggregated prediction and each view. While this approach is straightforward and widely used, it may not be optimal for all scenarios. Alternative metrics, such soft-DTT (Dynamic Time Warping, Cuturi & Blondel (017)). which better capture
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ETTh2
Perifomer
3.0-
CoMiaaa
-0.-
150
(a) Prediciton Horizon H 96
Prediciton Horizon H 192
ETTh2
ETTh2
Groundiruth
1.-
-0.-
-05
-1.0
-10
-15-
OroandPruth Rathformer
Contiee
100
200
400
2000
300
400
500
800
700
a0o
(c) Prediciton Horizon = 336
(d) Prediciton Horizon H 720
Figure 8: Visualization of CoMRes's and Pathformer's prediction results ETTh2. The input length
H 96
temporal aligmment and dependencies, or differentiable loss functions, could be investigated to improve performance. Additionally, this study focuses three basic augmentation strategies -timettimee warping, noise injection, and interpolation. Although these techniques are effective and simple to implement, they may not fully leverage the potential of more complex augmentation methods. As demonstrated in Section 4.3.2 the effectiveness of augmentation techniques varies depending on the dataset's characteristics. Future work could explore the performance of our framework with advanced augmentation strategies, such as learned augmentations or domain-specific transformations, to provide deeper insights and enhance the applicability and robustness of the proposed approach. Lastly, we employ multi-scale patch division with various patch sizes, which is similar to the model architecture used in Pathformer (Chen et al., (024). contrast, other multi-scale models, such as TimeMixer( ManeereaaWanggggg et al.) 2024) and Scaleformer Shabani et al.) 2023). generate multi-scale time series through pooling. Incorporating consensus mechanisms between these pooled series could be promising direction for extending framework.
For future research, we aim to explore further improvements non-Markovian frameworks, where the model would benefit from considering the entire history rather than relying limited past observations. Another promising direction is investigating how to ensure consistency multi-scaling predictions across different time horizons, enhancing the overall reliability of forecasts. These studies could further strengthen the capability of our multi-view learning strategy as a tool for long-term time series forecasting across diverse applications.
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weather
weather
04
GroenThuh
Calibee
00
0.2
0.0
-03
-04
-041
-0.
-36
M
-10
300
350
200
250
(a) Prediciton Horizon H 96
(b) Prediciton Horizon H 192
weather
weather
Graundhuuh
0.50
W
0.5
WM
M
25
-1.00
-10
100
700
400
10.0
3000
-000
500
6003
200
803
(c) Prediciton Horizon = 336
(d) Prediciton Horizon H 720
Figure Visualization of CoMRes's and Pathformer's prediction results on Weather, The input length H = 96
ETThl
(b) 151122
Figure 10: Visualization of CoMRes's, MRes's and Pathformer's autoregressive prediction results on ETTh1, ETTh2 and Weather.
24


Reviews:
[{"review_id": "EB7JkV1SWm", "reviewer": "Reviewer_2k6g", "summary": "This paper addresses challenges in long-term time series forecasting, particularly in managing unseen patterns and data scarcity. The authors propose CoMRes, a semi-supervised, multi-view approach to enhance forecasting by promoting consensus among multiple models on augmented, unseen data. This method aims to improve prediction accuracy and reduce error accumulation over extended horizons. Additionally, the study examines both autoregressive and non-autoregressive decoding schemes, emphasizing the robustness of non-autoregressive decoding in minimizing long-term error propagation. Experimental results highlight CoMRes's superior performance and stability compared to traditional supervised models.", "questions": "- Could the authors add error bars?\n- What are the author's plans wrt. the release of code?\n\nEdit: the authors have addressed the questions and points I raised to a level that I find satisfactory. I am raising my score as a result.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The strengths are as follows:\n\n- The paper is clear, well-written and presented.\n- The authors cover most of the commonly used datasets in the field, and some relevant baselines: the empirical constributions appear sound as a result.\n- Results indicate the method does indeed provide some life over the baselines.", "weaknesses": "The weaknesses are as follows:\n\n- Absence of submitted code making reproducibility more difficult.\n- The paper could benefit from more detailed comparisons with other time-series forecarsting methods.\n- It would be interesting to include error bars on the results table, especially given the proximity of different methods.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "iI7xlVG9pG", "reviewer": "Reviewer_GeBU", "summary": "The authors propose CoMRes, a long-term forecasting architecture based on Pathformer, which leverages a consensus promotion mechanism for multi-resolution views. The core idea is to align the supervised predictions of multiple resolutions with the aggregated prediction. Furthermore, they use augmentation strategies (Time Warping, Interpolation and Noise Injection) to construct the different views.  The work also presents an evaluation using autoregressive and non-autoregressive decoding schemes, aiming to show the robustness of the forecasts in longer prediction horizons. The authors claim that CoMRes outperforms traditional supervised models, exhibiting greater robustness and accuracy on multiple popular datasets.", "questions": "1. In line 032, the paper cites Wang et al., suggesting multi-resolution methods \"overlook consistency.\" Could you provide specific details about what was missed in the multi-resolution reconciliation methods used by Wang et al.?\n\n2. In Section 3, you mention that augmentations are less effective in forecasting compared to classification and anomaly detection. Could you elaborate on why this is the case? Specifically, how does your chosen augmentations differ?\n\n3. Why do you assume a Euclidean distance to measure consensus between the aggregated prediction and each view? Would other measures, such as soft-DTW, work better?\n\n4. Does your framework also work with more \"complex\" augmentation strategies beyond the three mentioned (time warping, noise injection, interpolation)? Maybe discussing the limitations is a valuable contribution.\n\n5. Could you clarify whether MRes is your method (with ablated components)? I would not count that as a baseline.\n\n6. I'm a bit confused, at what points do you use augmentations, and at what different resolutions (scales)? Could you describe this process in more detail?\n\n7. The paper claims superior robustness compared to traditional supervised learning approaches. Could you clarify how exactly robustness was demonstrated?", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- The paper introduces an interesting concept of promoting consistency among multi-resolution views, which has potential in capturing complex temporal relationships.\n\n- The amount of datasets used in the experimental section is exhaustive, which adds impact to the of the experimental results.\n\n- The addition of limited-resource scenarios is valuable, as this is often the case in time series applications.\n\n- In general i think the writing of the paper is good and understandable.\n\n- The discussed related work seems to be exhaustive.", "weaknesses": "- The title and abstract do not clearly explain why the proposed approach is semi-supervised. It is challenging to understand how forecasting can be performed in a \"semi-supervised\" manner, given that \"labels\" can be constructed by shifting the time window. It would be helpful to provide more concrete explanations on this aspect, particularly regarding the proposed use of augmented data and the challenges with temporal dynamics.\n\n- In lines 031-033, the statement about the superiority of transformers in forecasting is misleading. Multiple recent works (Das et al., 2023; Wang et al., 2024; Zeng et al., 2023) have shown that transformers are not always state-of-the-art. This statement should be reconsidered or at least clarified with respect to specific contexts or benchmarks.\n\n- The comparison against relevant baselines is lacking. The paper does not include benchmarks like TimeMixer, TiDE, PatchTST, D/NLinear, and other advanced transformer-based models (e.g., iTransformer). Including these baselines would significantly strengthen the evaluation and provide a better context for the proposed model.\n\n- The tables, particularly Table 1, are difficult to read. I'm not sure what red or blue means at least its not stated in the caption.\n\n- The baseline method achieves the best result multiple times without the proposed augmentations, which weakens the argument for using the augmentations. In general I'm pretty confused about what the idea of multiple resolutions vs augmentations is in this work.\n\n- While the limited-resource scenario is a useful addition, it does not effectively demonstrate how the method performs on datasets with many variables (e.g., Traffic or Electricity). This should at least be stated in the limitations/conclusion section.\n\n## Refs\nDas et al., Long-term forecasting with TiDE: Time-series dense encoder. (TMLR 2023)\n\nWang et al., TimeMixer: Decomposable multiscale mixing for time series forecasting. (ICLR 2024)\n\nZeng et al., Are transformers effective for time series forecasting? (AAAI 2023)", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "yNWCmHcS8N", "reviewer": "Reviewer_iocg", "summary": "This paper proposes a \"consensus promotion\" learning objective to enhance the consistency of multi-scale time series data predictions. Additionally, given this learning objective is well-suited for semi-supervised learning, the authors introduce data augmentation strategies aligned with the proposed framework to further improve model generalizability. Extensive experiments are conducted on various datasets and ablation settings.", "questions": "N/A", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "(1) This paper proposes and investigates a novel perspective on improving time-series prediction tasks: the consistency of predictions across different patch sizes of time-series data, which represents an interesting and promising research direction.", "weaknesses": "The main weakness of this paper lies in its evaluation. \n\n(1) The variance of model performance and metrics is not reported for any experimental results, making it difficult for readers to assess whether the minor improvements are consistent and significant or simply due to stochastic gradient descent. The authors are encouraged to report variances for all results and conduct comprehensive statistical tests to demonstrate whether the improvements are statistically significant.\n\n(2) There is no experimental evidence to demonstrate whether the proposed consensus promotion is actually beneficial. For example, what is the exact prediction MSE for each \"individual-view model\"? Do they actually become more consistent after applying the unsupervised consistency loss? Additionally, in Table 1, if I understand correctly, the only difference between \"MRes (SL)\" and \"MRes w. consensus\" is that \"MRes w. consensus\" includes additional consensus promotion learning objectives. However, there are no consistent patterns indicating which model's MSE is generally smaller. The authors are encouraged to design clear experiments that demonstrate whether the proposed consensus promotion works as expected and whether it is beneficial for the prediction task.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "BmLaygnhM7", "reviewer": "Reviewer_GunG", "summary": "This paper discusses multi-resolution long-term time-series forecasting (LTSF). This work extends the Pathformer architecture with two components: data augmentation, and consensus-based training loss for multiple MLP outputs. Comparison between the ablated components and Pathformer is held on widely used time-series prediction benchmarks. Proposed CoMRes improves over the baselines.  Further analysis is done on resource-efficient case.", "questions": "See weaknesses.", "limitations": "", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1) The multi-resolution time-series forecasting task is an important direction.\n\n2) Authors have done an in-depth study on the ablation study.", "weaknesses": "1) I am uncertain about the novelty of the proposed paper. This paper borrows most of the architecture from the Pathformer, except the MLP for the individual component output and the aggregation layer. Furthermore, the consensus-based loss that minimizes the relative difference can be naturally formulated while utilizing the ensemble. I feel like this paper is a sheer extension of the Pathformer and the previous methods that utilize data augmentation. \n\n2) The experiment results do not convince the efficacy of the method. MRes with consensus training often underperform over the MRes baseline. Furthermore, performance differences between the data augmentations are small. This questions the efficacy of each component as a general method. Finally, ComRes drastically underperforms Pathformer in one dataset, which questions the efficacy of the whole algorithm in general.\n\n3) The extra MLP layer may induce an extra computation burden on the training and inference stage, especially since (M+1) calculations are all required for the final computation. Maybe further analysis of the computation efficiency will further help to understand the limitations.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)