Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Authors: Zhining Liu
Ze Yang
Xiao Lin
Ruizhong Qiu
Tianxin Wei
Yada Zhu
Hendrik Hamann
Jingrui He
Hanghang Tong
Venue: ICML 2025 poster (2025)
Keywords: Time-series Forcasting
Ensemble
Adaptive Model Fusion
Primary area: applications->time_series
TL;DR: We introduce TimeFuse, an ensemble time-series forecasting framework for sample-level adaptive fusion of heterogeneous models.

Abstract: Time-series forecasting plays a critical role in many real-world applications. Although increasingly powerful models have been developed and achieved superior results on benchmark datasets, through a fine-grained sample-level inspection, we find that (i) no single model consistently outperforms others across different test samples, but instead (ii) each model excels in specific cases. These findings prompt us to explore how to adaptively leverage the distinct strengths of various forecasting models for different samples. We introduce TimeFuse, a framework for collective time-series forecasting with sample-level adaptive fusion of heterogeneous models. TimeFuse utilizes meta-features to characterize input time series and trains a learnable fusor to predict optimal model fusion weights for any given input. The fusor can leverage samples from diverse datasets for joint training, allowing it to adapt to a wide variety of temporal patterns and thus generalize to new inputs, even from unseen datasets. Extensive experiments demonstrate the effectiveness of TimeFuse in various long-/short-term forecasting tasks, achieving near-universal improvement over the state-of-the-art individual models. Code is available at https://github.com/ZhiningLiu1998/TimeFuse.

Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Zhining Liu
Ze Yang'
Xiao Lin
Ruizhong Qiu Jingrui He Hanghang Tong'
Tianxin Wei
Yada Zhu 2
Hendrik Hamann
Abstract
Percentage of Samples Where Each Model Ranks First
AutoPormer FEDFormer 2.2%
Time-series forecasting plays a critical role in many real-world applications. Although increas- ingly powerful models have been developed and achieved superior results on benchmark datasets, through a fine-grained sample-level inspection, we find that (i) single model consistently out- performs others across different test samples, but instead (ii) each model excels in specific cases. These findings prompt us to explore how to adap- tively leverage the distinct strengths of various forecasting models for different samples. We in- troduce TIMEFUSE, a framework for collective time-series forecasting with sample-level adaptive fusion of heterogeneous models. TIMEFUSE uti- lizes meta-features to characterize input time se- ries and trains a learnable fusor to predict optimal model fusion weights for any given input. The fusor can leverage samples from diverse datasets for joint training, allowing it to adapt wide variety of temporal patterns and thus generalize to new inputs, even from unseen datasets. Ex- tensive experiments demonstrate the effectiveness of TIMEFUSE in various long-fshort-term fore- casting tasks, achieving near-universal improve- ment over the state-of-the-art individual models. Code is available https: / l/gggtttt thub. com/ Zhi ni nnninngiill 998 Fusee.
(2024) 23.2%
4.2%
Mon-Stationary
(2022)
7.3%
(2023)
Time Models with Distinct Advantages
TimeMizer 10.5%
3.9%
(2023)
6.2%
Transformer 13.2%
Timestit (2023)
PatchTIST (2023)
PAtti (2024)
Imput Time-Seriie
180
Which model should be used for this input?
All of them! do adaptive ensemble!
Fused Prediction
surpess best model on up to 95. 1% samples
Figure 1. Sample-level inspection" reveals that each time series model excels in considerable fraction of test samples, highlight- ing their unique strengths for certain types of input. TIMEFUse adaptively leverages the strengths of different models for each input time series, achieving dynamically fused forecasting that outperforms the best individual model on up 95. 1% samples.
2021; Fu et al., 2025). Due to the complexity and dynamics of real-world systems, observed time series often exhibit intricate temporal characteristics arising from mixture of seasonality, trends, abrupt changes, and multi-scale depen- dencies, which in turn present significant challenges for time-series modeling (Lim & Zohren, 2021; Wang et al., 2024a). In recent years, researchers have been striving to create increasingly sophisticated models (Zhou et al., 2022; Wu et al., 2023; Wang et al., 2024c) designed to capture and predict such temporal dynamics more effectively.
1. Introduction
Time series forecasting is pivotal in a variety of real-world scenarios and has been studied with immense interest across many domains, such as finance (Sezer et al., 2020), en- ergy management (Deb et al., 2017; Hoffmann et al., 2020), traffic planning (Li et al., 2015; Yuan & Li, 2021), health- care (Ye et al., 2023), and climate science (Lim & Zohren,
Universityy of Illinois Urbana-Champaign FIBM Research 2 Stony Brook University. Correspondence to: Zhining Liu <liu326@ illinois. Hanghang Tong <htong @ illinois.cdu>>.
Despite the significant advancements in time series model- ing with increasingly better performance achieved on bench- mark datasets, a closer inspection applying a more fine-
Proceedings of the 4dnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).
RResults collected using 14 models on 7 forecasting datasets with 96 prediction steps following the optimal settings for each model reported Wu et al. (2023) and Wang et al. (2024b).

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Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
grained, sample-level lens presents quite different picture, as illustrated in Figure 1. Specifically, we analyzed the performance of popular high-performing models across 7 commonly used forecasting datasets on all test samples and presented the percentage of samples where each model ranked first. Our analysis highlights two intriguing findings: (i) there is no universal winner: even the latest models that achieve tftt---rrtt--tttt results on most benchmark datasets, were top- pop-perormmnn on only up 23.2% of test samples; (ii) each model has distinct and notable strengths: even for the bottom-ranker models, they still ranked first on non-negligible fraction of test samples. These findings un- derscore that no single model consistently outperforms the others, but instead, each model bears its unique strengths and weaknesses, often excelling in capturing specific types of temporal patterns, e.g., TimeMixer (Wang et al., 2024a) with explicit multiscale mixing is good at handling samples with high spectral complexity, while non-stationary trans- former (Liu et al., 2022) can be more suitable for handling samples with low stationarity. This highlights the potential benefits of a strategy that does not rely solely on a single model, which prompts our research question:
age of meta-features, the fusor can be jointly trained using samples from different datasets, thereby generalizing to broader range of temporal patterns and input characteris- tics, and thus achieving strong zero-shot performance on datasets unseen during meta-training. (iii) Interpretabil- ity: TIMEFUSE operates in a transparent and interpretable manner. Users can examine the fusor outputs to see how different models contribute to the fused prediction. Addi- tionally, the learned fusor weights offer insights into how specific input temporal properties (e.g., stationarity, spectral complexity) align with the strengths of different models. (iv) Performance: Extensive experiments and analysis con- firm TIMEFUSE'S efficacy in real-world forecasting tasks. By adaptively leveraging the unique strengths of different models, TIMEFUSE unlocks more accurate predictions than the state-of-the-art base model on up to 95.1% of samples, achieving near- universie performance improvements across various benchmark long/short-term forecasting tasks.
To sum up, our contributions are in threefold: (i) Novel Framework: We introduce a novel framework that tran- sitions the focus from an individual model to a sample- level adaptive ensemble approach for time series forecasting. This shift provides a fresh perspective and promotes more holistic understanding of model capabilities. (ii) Practical Algorithm: We present TIMEFUSE, a versatile solution for fine-grained adaptive time-series model fusion. It learns and selects the optimal model combination based on the char- acteristics of the input time series in an interpretable and adaptive manner, thereby unlocking more accurate predic- tions. (iii) Empirical Study: Sy Systematic experiments and analysis across diverse range of real-world tasks and state- oh-the-art models validate the effectiveness of TIMEFUSI highlighting its strong capability as versatile tool for tack- ling complex time series forecasting challenges.
How can we harness different models' diverse and comple- mentary capabilities for better time-series forecasting?
In answering this question, we introduce TIMEFUSE, novel ensemble time-series forecasting framework that en- ables sample-level adaptive fusion of heterogeneous mod- els based on the unique temporal characteristies of each input time series. Unlike traditional ensemble strategies that statically combine different models, TIMEFUSE learns dynamic fusion strategy that adaptively combines models at test time, unlocking the potential of model diversity in a highly targeted manner. Specifically, TIMEFUSE contains two core components: a meta-feature extractor that captures the temporal patterns of the input time series, and a learn- able fusor that predicts the optimal combination of model outputs for each input. We employ diverse set of meta- features to comprehensively characterize the input time se- ries, including statistical (e.g., skewness, kurtosis), temporal (e.g., stationarity, change rate), and spectral (c.g., dominant frequency, spectral entropy) descriptors. The fusor then leverages the meta-features to predict the optimal weights for combining the base models. During meta-tres veeantraining, we train the fusor to minimize the fused forecasting error across broad spectrum of samples with diverse dynamics, thus improving its adaptability to unseen temporal patterns.
2. Preliminaries
Notations We begin by defining the basic notations and concepts used in this work. For multivariate time-series forecasting with d variables, the objective is to predict the values of each variable over the next Tour time steps based on observations from the most recent Tie time steps. For- mally, let X in E R xu denote an input time series, where Tn represents the number of input time steps, and d is the number of variables or features. Formally, let Xin E Raxx denote an input time series, the forecast output is denoted as X E RT xd A base time forecasting model is rep- resented as a function f Ri + xdi mapppng the input time series to the predicted output series. Many mod- els with distinct architectural designs (Zhou et al., 2022; Wu et al., 2023; Wang et al., 2024a) have been developed to capture various temporal patterns for precise forecasting.
The design of TIMEFUSE bears several key advantages: (i) Versatility: The meta-training process of TIMEFUSE is decoupled from the training of base models, allowing us to integrate various models with diverse architectures into the model zoo and harness their distinct strengths for joint forecasting. (ii) Generalizability: Benefiting from the us-
In this work, we utilize multiple forecasting models, col- lectively forming a set F = (fi. f.). which we
2

---

Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Input Time Series Xin E
Input Sequence Meta-feature Descriptors
Model Fusor
Cross-task Meta- training Objective
Tix
Xin
R
4e(: (8): Rd
R
argmin
_ X
Update
Extractor 3()
Statistical
Temporal
Spectral
Multivariate
GoOa Data Batch Mixiing
Rure Weighe
Task Distribution Balancing
TimeMiber
Timeshet
PAttn
FEDformer
TimeXer
Patch15T
irrnnformer
Inference
Compoments
Predict
Dynamic
Forecasting Model Zoo
Model Predictions
Fusion
Adaptively Fused Prediction EX_,, (z)) o)())) ((Xm))
FF: 1.ff........
Yout Vi sssss E R KMt
Xou
Figure 2. The TIMEFUSE framework for ensemble time-series forecasting. best viewed in color.
refer to as the model zoo Each J; in F is an independently trained model, offering diverse predictions for a given in- put. As shown in Figure 1, different time series modeling techniques offer unique advantages; therefore, we aim to develop fusion mechanism to adaptively harness the di- verse and complementary capabilities of different models. Formally, we provide the problem definition as follows.
fitting: Raw features, often complex and high-dimensional. can include unnecessary information and noise, raising the likelihood of overfitting, especially with limited meta- training data. (iii) Lack of Semantic Interpretability; The complexity of raw features also makes it challenging to intuitively understand and interpret the fusor's 's behavior.
Benefits of meta-features. Drawing on existing research in Seature-based time-series analysis (Henderson & Fulcher, 2021; Barandas et al., 2020), we opt to extract key meta- features that simplify the high-dimensional data by retaining only critical statistical and temporal information. This ap- proach brings several benefits: (i) Versatility: Meta-features are task-agnostic descriptors that standardize input features across various tasks, enhancing the fusor's adaptability and aiding in generalization through cross-task training. (ii) Ro- bustness: Reducing dimensionality helps filter out noise and redundant information, minimizing overfitting risks and improving generalization new data. We now detail the meta-feature set used. (ii) Interpretability: Meta-features provide clear semantics, such as periodicity and spectral density, making it easier to analyze such features and under- stand how the fusor performs.
Problem 1 (Sample-level Adaptive Fusion for Time-Series Forecasting). Consider a model zoo F= {fi, J2.... fkk) that consists of & independently trained time-series fore- casting models fo RR. + I xd with diverse archi- tectures. The problem is to design an adaptive ensemble forecasting mechanism that for any input time series X it dynamically leverages the strengths of each model in F based on the characteristics of Xin to get the optimal fused prediction Xisse with respect to the ground truth Xout-
3. Methodology
This section presents the TIMEFUSE framework for collec- tive time-series forecasting with sample-level adaptive fu- sion. has two main components: a meta-feature extractor responsible for extracting key statistical and temporal fea- ture descriptors from the input time series, and learnable model fusor trained to predict the optimal fusion weights based on the meta-features, An overview of the proposed TIMEFUSE framework is shown in Fig. 2.
Meta-feature details. Drawing on prior research in time- series feature extraction, we meticulously crafted set of meta-features that characterize time-series properties from four distinct perspectives: (i) Statistical: Describe the dis- tribution characteristics and basic statistics of the input time series, such as the tendency, dispersion, and symmetry of the data. (ii) Temporal: Capture the time dependency and dynamic patterns of the input sequence by depicting how the input sequence evolves, such long-term trends, recur- rent cycles, and rate of change. (iii) Spectral: Derived by analyzing the time series in the frequency domain, such as power spectral density and spectral entropy. They highlight the prominence of periodic components and the complex- ity of the signal. (iv) Multivariate: Reflect the relation- ships among different dimensions in multivariate series, like
3.1. Time Series Meta-feature Extraction
We start by presenting the foundation of TIMEFUSE: char- acterizing input time series data by extracting meta-features.
Why not raw features? To achieve a dynamic ensemble based on input time-series, one could directly train a fusor using the raw features Xin Despite its simplicity, there are several fundamental drawbacks: (i) Task Dependency: Fore- casting tasks differ greatly in feature dimensions and input lengths, making the fusor task-specific brings increasing training costs while reducing flexibility. (ii) Risk of Over-
3

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Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
capabilities. Using more complex model structures does not enhance performance yet compromises the simplicity that benefits runtime efficiency and interpretability.
Table 1. Deseription of TIMEFUSE meta-features.
Frature
Dosiipia
Feearal
valas the
Stabiteel
4C-
Varubiiity safar.
(+2 m
Tasona value in the cotac
Training objective. To achieve accurate fused forecasting, we train the fusor to predict the optimal model weight vector that minimizes the forecasting error of the fused output X w.r.t the ground truth Xour Formally, given the model fusor Ve() and meta feature extraction operator (-)), the training objective of fusor T (:; +) is:
Highok valac fac
skrenees
Anyrrnury the water diorioeiis
Skapswo adia
Avenge ink- keeperal dependons
Terpori
at starienariyy
Rats of vatorary feauzes couraneddy by
ADE uue
xape.
ronused
Varubiity the shaege mat.
autoreggzonr
Sandard devistisa soall
Ereeganan
Aorrae enery the Iiqqancc docase.
P
& (X out X
Spectal
Cresgpeak
Danirax peicokiity
arg min e
E (Xn.Xa))
apectiee,
Comploiit is the fiapeccy deszan.
spectied, abbaciaa
Anyunsiyy of the spcceal dieritatis.
(I)
apectze..kuttooss
Skapsero of de distinaiion
where X xum
(()(X)))))(((()))
Varibbity the speciua over line.
E. 1: -8/-17
Molivaiee
dongreen
Avrrage whrtonday owagh
CON min
Stoeges lisur relaionili.
Weaker lnce reatrentop.
This objective encourages the model fusor to predict opti- mal weights such that the combined predictions from each model fi approximate the ground-truth output Xoar- Here the C(..) can be any loss function. In our use case, pre- dictions from different models on the same input can vary significantly due their distinct architectures, thus Huber loss (Huber, 1992) to prevent outlying individual models from affecting the stability of fusor training. The fusor is trained on the held-out validation set Dval (not used during base model training) to optimize fused forecasting performance on unseen data, this also prevents the potential overfitting of the base models from affecting the fusor's generalization capabilities.
Vasabille lasce rehainnipp.
Avrrage Arpendong brtwer Soiraes Varubiity depesdercies
cross-correlation and covariance. These features help de- scribe the dependency structures between variables. We use the average value across all input variables to compute the non- non-multivariate meta-features. These meta-features are defined and summarized in Table 1. Through ablation studies and comparative analysis, we demonstrated that these 24 features match the performance of a more complex TSFEL (Barandas et al., 2020) feature set containing 165 variables, with significant contributions from each domain to the overall forecasting performance. This indicates that our features offer a comprehensive description of the multi- faceted nature of the input time series, effectively supporting the subsequent adaptive model fusion process.
Independent meta-training dataset & pipeline. As im- plied by Equation 1, the meta training of TIMEFUSE only depends on the meta- fecturessssees (X,),, predictions from base models fo (((Xin), V1 S i S k. and the ground truth label Xout- Consequently, the fusor meta-training is decoupled from the base model training, allowing meta-training dataset to be independently collected and stored. Formally, let D' be the meta- veta-training dataset, each sample can be repre- sented by a triplet (zi,, &outs Xout), where 2; := (X,,) E Rd" is the meta-feature vector of the input time series, Xour := (X.,), f2 (2)), ... [Xm)] E gkxT.xx xd is 3 3-dimensional tensor storing the base model predictions, and Xout is the ground truth. The independence of meta- training also benefits TIMEFUSE 's extensibility: adding new models can be done by simply incorporating their pre- dictions into the tensor &ost and training a new fusor on the updated meta-training set. With the above formulations, we can now rewrite the meta-training objective as:
3.2. ddaptive Model Fusion with Learnable Fusor
With the chrattcharttt of the input time series es- tablished, we next explore how to achieve sample-level adaptive model fusion by training a learnable fusor.
Fusor architecture. Formally, let ee Rd + R be the model fusor parameterized by Ô, and 3 RTxxd + Rd be the meta feature extraction operator where d' is the number of meta-features. Given a model zoo F = J2.,,. } consisting of k models and an input time-series Xin E RTax our fusor (-) takes the meta-features xi := (XIn)) e Rdd as input and outputs a weight vector w E IR,, where each element wi represents the contribution of the i-th model f; in the final prediction. We employ softmax function to normalize w for numerical stability and facili- tate training. The final fused forecasting results X is then derived by X = E'= wi (X..). Prioritizing inter- pretability and efficiency, our fusor is single-layer neural network that learns a linear mapping O E 1dd xk between meta-features and model weights. We note that this sim- ple architecture is sufficient for effectively and accurately capturing the relationship between meta-features and model
arg ming (e X.n L (V(2), θ)T Rout Xoo) (2)
Cross-task meta-training with data mixing. Lastly, ben- efiting from the task-agnostic meta-features, the fusor can be trained jointly using diverse data from multiple forecast- ing tasks, thus better generalizing across diverse temporal
4

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Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Table Long-term forecasting results. All results are averaged from prediction lengths (96, 336, 720) with input length 96.
lower MSE MAE indicates better prediction, we highlight the 1st and 2nd best results. See Table 11 in Appendix for the full results.
Metrie:
TFuse
TXer
TMixer
PAtnn
i1F
TNet (2023)
PIST
DLin (2023)
Fr (2023)
FEDF (2022)
NSTF
LighTTS (2022)
InF (2021)
Autof (2021)
AASE/MAR
(Ours)
(2024)
(2024)
(2024)
(2024)
(2023)
(2022)
0.430 0.433
0.444
0.465
0.450 0.440
0.464
0.453
0.521 0.489
0.460
0,455
0.452 0.451
0.460
0.457
00488 0.469
0.4390458
0.647 0.572
0.522
0.500
1.059 0.808
0.545 0.512
RT Th2
0.365 0.395
0.327 0.401
0.393 0411
0.383 0.404
0.5830.407
0.409
0.422 0.381 0.499
0.564 0.519
0.500
0.45
0.532 0.492
0.654 0.581
2.222
1.225
0.457 0.465
ETTml
0.382 0.397
0.401
0.397 0.397
0.417
0.388
0.402
0.410
0.616...22
0.530 0:473 0.421 0.421
0.845 0.668
0.517
ETTm2
0.274 0.319
0.274 0.322
0.275 0 0.323
0,286 0.331
0.339
0.298
0.333 0.289 0.334 0.355 0.402 0.350 0.390
0.208
0.351 0,518 0.139 0.362 0.409
1.224 0.849 0.337 0.368
Weather
0.240
0.241 0:277
0
0.268 0.285
0.28
0.259 0.285 0.257 0.278 0.265
01.258
0.333.0.375
0.289
0.269
0.341 0.382
Electricity
0.163
0.260
0.171 0.270
0.185 0.275
0.215 0:294
0.180
9.270
0.196
0.297 0.204 0.294 0.225 0.319 0.209 0.296 0.222 0.333
0.196 0.296
0.238 0.339
0.358
0.437 0.240 0.346
Trallic
0.419 0.272
0.466
0.287
0.513
0 306
0.555
0.358
0:422
9.262
0.624 0.351
0.482
0,308
0.673
0,419 00599 0,711 0:445 0.641
0.352
0.755 0,472
1.315 (0.652 0.402
patterns and input characteristics. However, implementing cross-task meta-training in practice faces two challenges: (i) The inconsistency in the dimensions of Xour and Xout across tasks prevents the uniform storage and mixed re- trieval of data from different tasks. (ii) Imbalanced training sample sizes across tasks can degrade the fusor's perfor- mance on tasks with fewer samples. We propose a sim- ple batch-level mixing and balancing strategy to address these issues. Specifically, given meta-training datasets (Di, .... Dr,, } derived from different forecasting tasks, we oversample all datasets to match the size of the largest task (maxosism ( (D) to balance the data distribution. All oversampled datasets collectively form the joint meta- training dataset Dj join. Further. to prevent overfitting issues that might arise from consecutive training on oversampled data from single task, we alternate training batches from each task within each training step. This dynamic training data mixing promotes the fusor's generalization across var- ious task distributions. Algorithm summarizes the main procedure of TIMEFUSE.
casting, including 16 real-world benchmarks and 13 base forecasting models. The detailed model and experiment configurations are presented in Appendix A.
Datasets. For long-term forecasting, we evaluate our method on seven widely-used benchmarks, including the ETT datasets (with 4 subsets: ETTh1, ETTh2, ETTm1, ETTm2), Weather, Electricity, and Traffic, following prior studies (Wang et al., 2024a; Wu et al., 2023; 2021). For short-term forecasting, we use PeMS (Chen et al., 2001), which encompass four public traffic network datasets (PEMS00304/07/00), along with the EPF (Lago et al., 2021a) datasets for electricity price forecasting on five major power markets (NP, PJM, BE, FR, DE) spanning six years each. detailed description of these datasets is provided in Table 7.
Base Models. To assess TIMEFUSE's ability to unlock superior forecasting performance based on state-of-the-au models, we choose 13 well-known powerful forecasting models as baselines. This includes recently developed ad- vanced forecasting models such as TimeXer (2024c) that exploits exogenous variables, TimeMixer (2024a) with de- composable multiscale mixing. and patching- based mod- els PAttn (2024) and PatchTST (2023). Other strong competitors are also compared against, including i'Trans- former (2024a), TimesNet (2023), FedFormer (2022), FreTS (2024), DLinear (2023a). Non-stationary Trans- former (2022), LightTS (2022), InFormer (2021), and Auto- Former (2021).
Algorithm TIMEFUSE
Require: model ZoO FF f2......... . sul; forecasting
dataset D: ((x(6) in x((i) 1 sn..
1: Initialize: meta-training set D* + 0.
2: for XinxXau) E DD do
3: # collect meta-training data
4: Extract meta-features in + 3(X E ERd;
5: Prediction tensor &ma + [X)() i-1 E BkxTTxdd
Setup. To ensure fair comparison, employed the TSLib (Wang et al., 2024b) toolkit implement all base models, using the optimal hyperparameters provided in the official training configurations. We trained all base models using L2 loss on the training sets of each task, and collected meta-training data on the validation sets. For each prediction length, we jointly trained a fusor using data from different tasks and reported the performance of fused predictions on the test set. More reproducibility details are in Appendix A.
6: Forecasting ground truth Xau E Blaxd
7: Update D + D* U (Iin Lour, Xout);
8: end for
9: while not converged do
10: # model fusor training
11: Update the model fusor (r; () with Eq. (2)
arg ming Eis; X DD ( O)T TJ &un, Xmn).
12: end while
13:
Return: TIMEFUSE model fusor ( +)
4.1. Main Results
Long-term forecasting. As shown in Table 2, by dy- namically leveraging and combining the strengths of dif- ferent base models, TIMEFUSE consistently outperforms the state-of-the-art individual models across all tasks, cov-
4. Experiments
We conduct extensive experiments to evaluate the effective- ness of TIMEFUSE, covering long-term and short-term fore-
5

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Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Table Short-term forecasting results on PEMS datasets, averaged from prediction lengths {6, 12, 12,24) with input length 96. Lower
MAE/RMSE/MAPE indicates better prediction, we highlight the 1st and 2nd best results. See Table 12 in Appendix for the full results.
TFuse
TXer
TMixer
PAttn (2024)
iTF
TNet
PTST
DLin
FreTS (2023)
FEDF (2022)
NSTF
LightTS
InF
AutoF
Datasets
Metric
(Ours)
(2024)
(2024)
(2024)
(2023)
(2023)
(2023)
(2022)
(2022)
(2021)
(2021)
MAE
16.005
17,900
18.283
19.232
17.420
19.349
19,499
22.028
18.634
31.446
20.337
18, 14.140
20.842
35.842
PEMS03
RMSE
24.971
27.206
28.435
30.442
27.385
30.715
30.722
35.324
29.437
44.941
31.677
27.624
32.398
52,636
MAPE
0.135
0.170
0.159
0.157
0.146
0.168
0.164
0.196
0.153
0.297
0.179
0.168
0.179
0.341
MAE
20.268
22.513
23.631
25.925
23.245
23.028
26,591
27.743
24.817
37.439
22.855
22.237
23.155
42.046
PEMS04
RMSE
32.207
34.199
36.922
40.859
36.913
36,076
40.871
42.768
38.644
53.473
35.973
34,702
37.252
59,421
МАРE
0.167
0.210
0.201
0.205
0,190
0.197
0.224
0.253
0.204
0.316
0.195
0.194
0.195
0.351
MAE
22.988
26.695
26.489
28. 946
25..934
27. 37.977
30.641
33.365
28,304
304
53.631
28. 28.978
26,005
30.211
62.726
PEMS07
RMSE
36,241
39.512
41.222
44,996
40,938
44.423
45.864
50.174
43.382
73.015
45.328
39.791
48.006
84.144
MAPE
0.110
0.142
0.129
0.138
0.126
0.138
0.157
0.176
0.139
0,278
0.145
0.131
0.148
0.348
MAE
16.468
18.613
19.114
19,920
17.978
20.367
20.623
22.513
19.172
35,569
19.712
18.103
22.870
36.078
PEMS08
RMSE
25.882
27.960
29.601
31.494
28.661
31.869
31,946
35.039
30.249
50.437
30.66 30.643
27.875
35.085
50,548
МАРЕ
0.103
0.126
0.125
0.121
0. 0.111
0.131
0.132
0.143
0.118
0.223
0.128
0.117
0.150
0,246
Table Short-term forecasting results on the EPF datasets with predict length 24 and input length 168 following Wang et al. (2024c).
Metrie:
TFuse
TXer
TMiser (2024)
PAttn (2024)
ITF
TNo
PTST
D1.in (2023)
FreT8 (2023)
FEDF
NSTV
LightTS (3022)
InF
Autol
MSR MMAR
(Ours)
(2024)
(2024)
(2023)
(2023)
(2022)
(2022)
(2021)
(2021)
NP
0.229
0.260
0.243 0.277
0.261 0.290
0.275 0.299
0.267
0.244
0.276
0.294
0.297 0,311
0,3311
0.365
0,276 0.291
0.299
0.318
0.287 0.326
0.40
PJM
0.097
194
0.118
0.315
0.097.1997
0:116
0.105 0.209
0.104
0.122...231
0.133.0.29
0.132 0.235
0,109
0.212
0.132
0.138 0:251
BE
0.378
0.241
0.379 0.222
0.415
0.76
0.396
0.261
0.404 0.277
0.401
0.274 0.404 0.261 0.459 0.315
0.437 0.311
0.474
0.332
0.396 0.253 0.664
0.297
0,369
0.481 0.311
FR
0.386
0.198
0.396 0.212222222
0.444
0.245
0.448
0.255
0,229
0:427
0.409 0.219
0.420 0.254
00.4030.235
0.456
0,465 0.240 0,473
0.258
0,479
0.559 0.292
DE
0.429
0.407
0.458
0.42
0.469
0.472
0.466 0.435
0.472.433
0.527 0:457
0.508 0.457
(05511 0.452
0.626.0.529
0.506 0:455
0.489 0.447
(.5943.0.444
(1629 0:517
ering a large variety of time series with varying fre- quencies, numbers of variables, and real-world applica- tion domains. We also note that the optimal individual model varies across different tasks and metries: while TimeXer (Wang et al., 2024a) excels in most long-term fore- casting tasks by modeling exogenous variables, other mod- els like TimeMixer (Wang et al., 2024a), iTransformer (Liu et al., 2024a), and FedFormer (Zhou et al., 2022) still emerge as top performers in certain tasks. In contrast, the proposed TIMEFUSE consistently achieves superior results across different tasks by integrating their advantages, surpassing the task-specific best models. Compared with these SOTA models, TIMEFUSE achieved an average MSE reduction of 1..6%%66.88%// 1. 1777%/...99 across seven datasets w.r.t "Krr/mmixer/PAttn/iii respectively, demonstrating the effi- cacy and versatility of the proposed TIMEFUSE framework.
via sample-level adaptive fusion. This further underscores the unique strengths of different models and the importance of combining them with adaptive model fusion.
Comparison with ensemble methods. We further com- pared the performance of TIMEFUSE with commonly used mean/median ensemble for heterogeneous model fusion. To fully unlock the potential of static ensembling, we further adopt a top-k model selection strategy based on the valida- tion performance, and test the mean/median ensemble of the top-k models. Figure 3 shows the results on long-term forecasting datasets. We observed that: (1) the adaptive fu- sion strategy of TimeFuse consistently outperformed static ensemble strategies across all tasks, even though the static ensembles also equipped a model filtering strategy based on the validation performance. (2) The optimal model set for static ensemble differs significantly across different datasets, e.g., mean ensemble achieves the best result with 10 mod- els included on the ETTh1 dataset, while only the top models are needed on the traffic dataset. In practice, find- ing the optimal model set for each dataset is cumbersome, highlighting the limitations of static ensemble strategies. In contrast, TIMEFUSE dynamically learns the optimal ensem- ble strategy for each sample (and thus dataset), which we will discuss further in the following section.
Short-term forecasting. TIMEFUSE also demonstrates superb performance in short-term forecasting tasks. As shown in Table 3, on the PEMS datasets, while iTransformer achieves the overall best performance for this task, models like TimeXer and the MI.P- LightTS also emerge as top performers in many cases. By dynamically leverag- ing their respective strengths. TIMEFUSE achieves univer- sally enhanced performance, consistently delivering optimal forecasting results across all scenarios. Compared to the top three individual models: TimeXer, iTrrasformer, and LighTTS, TIMEFUSE achieves an average MAPE reduction of 20.46%, 9,89% and 15.37%, respectively. On the EPF datasets reported in Table 4, while TimeXer exhibits sig- nificant advantages at the dataset level, TIMEFUSE still consistently achieves more accurate forecasting across all five tasks by integrating the capabilities of different models
4.2. Further Analysis
TIMEFUSE learns adaptive fusion strategies. To intu- itively grasp how TIMEFUSE learns different fusion strate- gies across various datasets and samples, Figure shows the average model fusion weights on different datasets given by TIMEFUSE, with variation bars indicating standard de-
6

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Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Mean Ensemble
.... Median Ensemble
TimeFuse Weather
Etth1
Etth2
Ettm1
Ettm2
Electricity
Traffic
0.48
0.28
0.325
0.42
0.40
0.34
0.28
0.29
0.27
0.300
0.44
0.40
0.32
0.27
0.26
0.275
0.40
0.475
0.39
0.18
0.450
0.38
0.38
0.28
0.45
0.36
0.16
10 Top. Model
10 Top-K Model
10 Top- Model
10
Top-K Model
Top K Model
Top.K Top-K Model
Top-K Model
Figure 3.
Comparison between TIMEFUSE and static ensemble methods with validation top-k model filtering.
ETTh1
ETTh2
ETTm1
ETTm2
Weather
Electricity
Traffic
AugoE 1300 20TE
BUD 002 Thet
Terr
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
Figure 4. Visualization of the average model fusion weights by TIMEFUSE across datasets, with variation bars showing standard deviations between samples within the dataset. TIMEFUSE adaptively produces diverse ensemble strategies, effectively supporting tasks that benefit from either broad model ensemble (e.g.. ETTh1/ml) more selective integration of specific models (e.g.. Electricity/Traffic))
viations among samples within each dataset. It can be ob- served that TIMEFUSE adaptively generates diverse ensem- ble strategies. Notably, on some datasets (e.g.. ETTh1/ml TIMEFUSE opts for dynamic ensemble of a variety of mod- els, while others (e.g., Electricity/Traffic it selectively ensembles only a few specific models. This echoes the ob- servations in Figure 3, where some datasets benefit from a broad model ensemble and others from more selective integration, further demonstrating TIMEFuSE's ability to learn effective and adaptive ensemble strategies.
new models and the added diversity they bring to the model zoo, allowing for continuous performance improvement as more advanced forecasting models emerge in the future.
Zero-shot generalization to unseen datasets. As men- tioned before, TIMEFUSE operates top of task-agnostic meta-features. This allows it to be jointly trained on vari- ous datasets to enhance its generalizability, and further, to perform inference on any datasets, even unseen during meta- training (i.e., zero-shot generalization). To verify this, we evaluate zero-shot TIMEFUSE on both long- (predict length 96) and short-term (PEMS with predict length 6) forecasting tasks. For each target dataset, trained a fusor with all other datasets, and then tested it on the target dataset. As shown in Table 5, zero-shot TIMEFUSE still outperforms the best individual model in most cases, demonstrating robust zero-shot generalization performance.
Average Fused
Error
0.40
Metric
Figure 5. TIMEFUSE achieves increasingly better forecasting per- formance more base models are included in the model zoo.
0.35
MAE
26
0.30
2
8
10
12
Model Zoo Size
Table 5. Zero-shot performance of FUMEFUSE.
TIMEFUSE improves with more diverse model zoo. To assess whether TIMEFUSE can leverage emerging models to further enhance its capabilities, we check how the fused forecasting performance changes as new models are intro- duced into the model zoo. Specifically, we test TIMEFUSE on long-term forecasting datasets with a prediction length of 96, starting with a model zoo that contains only Informer and Autoformer, with newer models added sequentially per the order in Table 2 (from right to left). Figure 5 shows the average MAE and MSE on 7 datasets. We can observe that TimeFuse achieves increasingly better forecasting per- formance as more diverse base models are integrated. This indicates that TIMEFUSE benefits from the capabilities of
Normal TumeFuse
Zero-shot TIMKFUSK
Best Individual
Dataset
Model
MSE
MAE
MSE
MAE
MSE
MAE
ETThi
0.3667
0.3911
0,3707
0.3961
0.3770
0.3981
ETTh2
0.2803
0.3338
0,2817
0.3348
0.2854
0.3376
ETTm1
0.3060
0.3505
0.3078
0.3505
0.3178
0.3563
ETTm2
0.1701
0.2542
0.1721
0.2568
0.1712
0,2560
Weather
0.1546
0.2046
0,1552
0.2048
0.1574
0,2047
Electricity
0.1334
0.2312
0.1355
0.2336
0.1405
0.2406
Traffic
0,3881
0.2552
0.3907
0.2602
0.3936
0.2686
Normal
Zero-shot
Best Individual
Datasets
TIMEFUSE
TIMEFUse
Model
MAE
RMSE
MAPE
MAE
RMSE MAPE
MAE RMSE MAPE
PEMS08
14,266
22,235
0.118
14,273
22.257 0.118
14.91
23.314 0.122
PEMS04
18.936
30.338
0.154
19.023 30.467 0.154
20.073
31.934 0.168
PEMS07
21.205
33.432
0.099
21.297
33.523
0.100
22.243
34,900
0.109
PEMS08
14,930
23.570
0.090
14.933
23.571
0.090
15.661
24.577
0.095
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Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Non-stationary Transformer Contribute more on samples with stationarity.
TimeMixer
Table 6. Ablation and comparative study of meta-fcatures.
Contribute more on samples with complex frequency components.
Ablation Feature Set
Datasets
Ours
TSFEL
Statistical
Temporal Spectral Multivariate
Autohorma (2023)
Informer (2023)
ETTh1
0.3911
0.3938
0.3978
0,4007
0,4010
0.3986
(2072)
0.3
ETTh2
0.3338
0.3343
0.3406
0.3418
0.3393
0,3409
tethoomer (2822)
Non Stationery
0.2
Long term
ETTml
0.3505
0.3516
0.3552
0,3578
0.3558
0.3575
Fiets (2023)
0.1
ETTm2
0.2542
0.2550
0.2578
0.2579
0.2566
0.2553
(2023)
Weather
0.2046
0.2042
0.2074
0.2088
0.2096
0.2081
Timeshet (2023)
0.0
Electricity
0.2312
0.2327
0.2363
0.2367
0.2364
0,2361
ProchTST (2023)
Traffic
0.2552
0.2572
0.2590
0.2626
0,2661
0.2607
Thenffrmer (2024)
-0.2
Pizin (2024)
Avg.
0.2887
0.2898
0.2934
0.2952
0.2950
0.2939
TimeNlker (2024)
Timeker (2024)
0044
Short-term
PEMS03
14.266
14.270
14.521
14.584
14,593
14.547
Gevenoso
Rurboss
Auscoovaittion
statensrity
dare of charge Mean
Fresumny Maee
Freponity Peak
Speetral lrmecre
Cow aeeeeess Mast
Coratianc Old
PEMS04
18.936
18.939
19.235
19.485
19.410
19.346
Ruta change
PEMSU7
21.205
21.308
21.696
21,902
21.894
21,905
PEMSU8
14.930
14.950
15.189
15.371
15.318
15.264
Avg.
17.334
17.367
17.660
17.836
17.804
17.765
Figure 6. Visualization of the learned fusor weights. tion B.3). We also report the inference efficiency of the fusor relative to base models (Section B.1), and evaluate per- formance under up to 512 long input horizons (Section B.2). The results demonstrate that TIMFFUSE remains effective, efficient, and adaptable across diverse forecasting scenarios.
blation and comparative study of meta-features. We also conducted experiments to validate the effectiveness of the meta-features used. We compare our 24- variable meta- feature set with more complex TSFEL (Barandas et al., 2020) feature set comprising 165 variables, and perform ablation study by removing features of each domain from the meta-feature set. The MAE of long/short-term forecast- ing (with predict length 96/6) is shown in Table 6. It can be observed that our feta-feature set offers a comprehensive description of the multifaceted nature of the input time se- ries, matching the performance of the complex TSFEL set, with significant contributions from each domain.
5. Related Works
Time-series Forecasting. Time-series forecasting is piv- otal research area with rich real-world applications (Lim & Zohren, 2021). Numerous time-series modeling tech- niques have been proposed, each with its unique focus. Tra- ditional statistical methods (Anderson, 1976) can handle periodic trends but struggle with complex nonlinear dynam- ics. Later works based on recurrent (Lai et al., 2018) and convolutional (Franceschi et al., 2019) neural networks can model more complex temporal patterns but still have diffi- culty with long-range dependencies due the Markovian assumption or limited receptive field. TimesNet (Wu et al., 2023) addresses this by transforming 1D series into 2D for- mats, enhancing pattern recognition over distances. Mean- while, Transformer-based models like PatchTST (Nie et al., 2023) and iTransformer (Liu et al., 2024a) leverage self- attention model long-range dependencies. More recent studies further suggest improving forecasts by multiscale mixing (Wang al., 2024a) integrating exogenous vari- ables (Wang et al., 2024c) multimodal knowledge (Li et al., 2025). Despite these advancements, our sample-level inspection shows that no single model excels universally, prompting research into leveraging the diverse strengths of various models for enhanced joint forecasting.
Visualization of the learned fusor weights. Finally, we note that the fusor essentially learns a mapping of how spe- cific input temporal properties (e.g., stationarity, spectral complexity) correspond to the strengths of different mod- els. We visualized the learned fusor weights on long-term forecasting datasets in Figure 6 (showing subset of meta- features for clarity). Take the meta-feature "stationarity" as an example, it corresponds to large negative weights for the non-stationary transformer, suggesting that this model is weighted more heavily when inputs show lower stationarity, aligning with its ability to handle non- stationary dynamics. Similarly, TimeMixer's advantage in modeling complex fre- quency patterns through multi-scale mixing is also reflected in the learned fusor weights. We note that these advantages are relative: they indicate a model's 's relative strength in han- dling samples with specific properties compared to others in the model zoo. Nonetheless, such understanding can help users grasp the relative strengths and weaknesses of different models and provide insights for further improvement.
Ensemble Learning. Ensemble learning is a generic strat- egy to get robust predictions by aggregating outputs from multiple models (Mienye & Sun, 2022). Typical ensemble methods often employ quickly trainable weak base learners like decision trees (Sagi & Rokach, 2018). Research on time-series forecasting ensembles has been limited due to the complexity of time-series data modeling. To name a
Comparison with AutoML baselines and more analysis. We include additional experiments in Appendix B to fur- ther validate the robustness and practicality of TIMEFUSE These include comparisons with advanced ensemble strate- gies such as portfolio- portfolio-based, zero-shot, and AutoML-driven methods, as well as pretrained foundation models (Sec-
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Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
few, Kourentzes al. (2014) and Oliveira & Torgo (2015) explore the potential of mean/median and bagging ensem-
Traffic Dataset. http: / /ttp:////mmms/m// dot ca gov/.
Anderson, O. D. Time-series. 2nd edn., 1976.
bles in time series forecasting tasks. Yu et al. (2017) im- plement additive forecasting using multiple MLPs across varied feature sets, a method similar to random subspace ensembles (Ho, 1998), and Choi & Lee (2018) further inte- grates multiple LSTMs. However, these studies are confined to single-model architecture, focusing on training multi- ple same-type models based different dataset views for static homogeneous ensemble. Our work, in contrast, enables dynamic heterogeneous ensemble of models with various architectures. By employing sample-level adaptive model fusion, we dynamically integrate the strengths of different models to achieve superior joint forecasting.
Ansari, A. F., Stella, L.,, Turkmen, C., Zhang, X., Mercado, P., Shen, H., Shchur, O.. Rangapuram, S. S., Arango, S. P., Kapoor, S., et al. Chronos: Learning the language of time series. arXiv preprint arXiv:2403..m 0.811, 2024.
Ban, Y., Zou, J., Li, Z.,, Qi, Y., Fu, D., Kang, J., Tong, H., and He, J. Pagerank bandits for link prediction. In Globersons, A., Mackey, I.., Belgrave, D., Fan, A., Pa- quet, U., Tomczak, J. M., and Zhang, C. (eds.), Advances in Neural Information Processing Systems 38: Annual Conference on Neural Information Processing Systems 2024, NeurlPS 2024, Vancouver, BC, Canada, December 10 15, 2024, 2024.
6. Conclusion
We present TIMEFUSE, a versatile framework for ensemble time-series forecasting with sample-level adaptive model fusion. It learns and selects the optimal model combination based on the characteristics of the input time series in an interpretable and adaptive manner, thereby unlocking more accurate predictions. In all our experiments, TIMEFUSE consistently achieved new state-of-the-arr performance by dynamically leveraging different models' strengths test time, highlighting its strong capability as a versatile tool for tackling complex time series forecasting challenges.
Bao, W. Wei, T., Wang. H., and He, J. Adaptive test- time personalization for federated learning. Advances Neural Information Processing Systems, 36:77882- 77914, 2023.
Bao, W., Zeng, Z., Liu, Z., Tong, H., and He, J. Matcha: Mitigating graph structure shifts with test-time adaptation. The Thirteenth International Conference on Learning Representations, 2025.
Barandas, M., Folgado, D., Fernandes, L.,, Santos, S., Abreu, M., Bota, P., Liu, H., Schultz, T., and Gamboa, H. Tsfel: Time series feature extraction library. SoftwareX, 11: 100456, 2020.
Impact Statement
This paper presents novel learning-hased ensemble time- series forecasting framework, whose goal is to achieve more accurate forecasting by adaptively fusing different models for each input time series at test time. Like other research focused on time series forecasting, our work has potential so- cial impacts, but none of which we feel must highlighted here.
Caruana, R., Niculescu-Mizii A., Crew, G., and Ksikes, A. Ensemble selection from libraries of models. In Proceedings of the twenty-first international conference on Machine learning, pp. 18, 2004.
Chen, C., Petty, K. F., Skabardonis, A., Varaiya, P. P., and Jia, Z. Freeway performance measurement system: Min- ing loop detector data. Transportation Research Record, 2001.
Acknowledgements
This work is supported by NSF (2324770, 21 2117902), MIT- IBM Watson AI Lab, and IBM-Ilinois Discovery Accelera- tor Institute. The content of the information in this document does not necessarily reflect the position or the policy of the Govermment, and no official endorsement should be inferred. The U.S. Government is authorized reproduce and dis- tribute reprints for Government purposes notwithstanding any copyright notation here on.
Choi, J. Y. and Lee, B. Combining Istm network ensemble via adaptive weighting for improved time series forecast- ing. Mathematical problems in engineering, 2018(1): 2470171, 2018
Deb, C., Zhang, F. Yang, J., Lee, S. E., and Shah, K. W. A review on time series forecasting techniques for building energy consumption. Renewable and Sustainable Energy Reviews, 74:902-924 2017.
References
Fang, I.., Chen, Y., Yu, W., Liu, Y., Tang, L.-a., Torvik, V. I., and Chen, H. Tsla: A multi-task time series lan- guage model. In ICASSP 2025-2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 1-5. IEEE, 2025.
UCI Electricity Load Time Series Dataset. https: wus.ucis........ /ed..uuuiii/////////taattttttt Electricity Eleettrrdttyyiooaaaiigereee22222
9

---

Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Feng, S., Jing, B., Zhu, Y., and Tong, H. Adversarial graph contrastive learning with information regularization. In Proceedings of the ACM web conference 2022, pp. 1362- 1371, 2022.
Ho, T. K. The random subspace method for constructing decision forests. IEFE transactions on pattern analysis and machine intelligence, 20(8):832-844, 1998.
Hoffmann, M., Kotzur, L.., Stolten, D., and Robinius, M.
Feurer, M., Eggensperger, K., Falkner, S., Lindauer, M., and Hutter, F. Auto-sklearn 2.0: Hands-free automl via meta-learning. Journal of Machine Learning Re- search, 23(261):1-61, 2022. URL nttp://jmm httpppapprs//2//11p11/ htmm..
A review time series aggregation methods for energy system models. Energies, 13(3):641, 2020.
Huber, P. J. Robust estimation of location parameter. In Breakthroughs in statistics: Methodology and distribu- tion, pp. 492-518. Springer, 1992.
Franceschi, J.-Y., Dieuleveut, A., and Jaggi, M. Unsuper- vised scalable representation learning for multivariate time series. Advances in neural information processing systems, 32, 2019.
Jing, B., Tong, H., and Zhu, Y. Network of tensor time series. In Proceedings of the Web Conference 2021, pp. 2425 2437, 2021.
Jing, B., Zhang, S., Zhu, Y., Peng, B., Guan, K., Margenot, A., and Tong, H. Retrieval based time series forecasting. arXiv preprint arXiv:2209.1335 13525, 2022.
Fu, D., Fang, L., Maciejewski, R., Torvik, V. I., and He, J. Meta-learned metrics over multi-evolution temporal graphs. In KDD, 2022.
Jing. B., Gu, S., Chen, T., Yang, Z., Li, D., He, J., and Ren, K. Towards editing time series. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024a.
Fu, D., Fang, L., Li, Z., Tong, H., Torvik, V. I., and He, J. Parametric graph representations in the era of foundation models: A survey and position. CoRR, abs/2410. 12126, 2024a. doi: 1046550AARXIV.210022222 URL https: //doi. org 10. 48540/ http//ariivi.v.. 2410. 12126.
Jing, B., Wang, Y., Sui, G., Hong, J., He, J., Yang, Y., Li, D., and Ren, K. Automated contrastive learning strategy search for time series. In Proceedings of the 33rd ACM International Conference on Information and Knowledge Management, pp. 4612 4620, 2024b.
Fu, D., Hua, Z., Xie, Y., Fang, J., Zhang, S., Sancak, K., Wu, H., Malevich, A., He. J., and Long, B. Ver-graphormer: A mini-batch graph transformer via virtual connections. In ICLR, 2024b.
Jing, B., Zhou, D., Ren, K., and Yang, C. Causality- aware spatiotemporal graph neural networks for spatiotemporal time series imputation. In Proceedings of the 33rd ACM International Conference Information and Knowledge Management, pp. 1027-1037, 2024c.
Fu, D., Zhu, Y., Tong, H., Weldemariam, K., Bhardwaj. O., and He, J. Generating fine-grained causality in climate time series data for forecasting and anomaly detection. CORR, 2024c.
Fu, D., Zhu, Y., Liu, Z., Zheng, L., Lin, X., Li, Z., Fang, L., Tieu, K., Bhardwaj. O., Weldemariam, K., Tong, H., Hamann, H. F., and He, J. Climatebench-m: A multi- modal climate data benchmark with simple generative method. CORR, abs/2504.0725 0.73944 2025. doi: 10.48550/ ARX1V.2504.07399. URL https: /ttp:///oo...gg./// 48550/arXiv 2ttp0//axxiv224..... 2504. 07394.
Kingma, D. Adam: method for stochastic optimization. arXiv preprint 141.v:1412.69980 2014.
Kourentzes, N., Barrow, D. K., and Crone, S. F. Neural net- work ensemble operators for time series forecasting. Ex- pert Systems with Applications, (1(9))4435-42455 2014.
Lago, J., Marejasz, G., De Schutter, B., and Weron, R. Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open- access benchmark. Applied Energy, 293:1 16983, 20
He, X., Kang, J. Qiu, R., Wang, F., Sepulveda, J., and Tong, H. On the sensitivity of individual fairness: Measures and robust algorithms. In Proceedings of the 33rd ACM International Conference on Information and Knowledge Management, pp. 229-838,777 2024.
Lago, J., Marejasz, G., De Schutter, B., and Weron, R. Forecasting day-ahead electricity prices: A review of state-of-the of-te-of-the-rt algorithms, best practices and an open- access benchmark. Applied Energy, 293: 16983, b
He, X., Fu, D., Tong, H., Maciejewski, R., and He, J. Tem- poral heterogeneous graph generation with privacy, utility, and efficiency. In ICLR, 2025.
Lai, G., Chang, W.-C., Yang, Y., and Liu, H. Modeling long-and short-term temporal patterns with deep neural networks. In The 41st international ACM SIGIR confer- ence on research & development in information retrieval, pp. 95-104, 2018
Henderson, T. and Fulcher, B. D. An empirical evaluation of time-series feature sets. In 202/ International Conference on Data Mining Workshops (ICDMW), pp. 1032-1038. IEFE, 2021.
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Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Li, L., Su, X., Zhang, Y., Lin, Y., and Li, Z. Trend modeling for traffic time series analysis: An integrated study. IEEE Transactions on Intelligent Transportation Systems, 16 (6):3430-3433) 3439, 2015.
Liu, Z., Qiu, R., Zeng, Z., Yoo, H., Zhou, D., Xu, Z., Zhu, Y., Weldemariam, K., He, J., and Tong, H. Class-imbalanced graph learning without class rebalancing. In Forty-first International Conference on Machine Learning. 2024b.
Li, Z., Fu, D., and He, J. Everything evolves in personalized pagerank, In Ding, Y., Tang, J., Sequeda, J. F., Aroyo,
Mienye, I. D. and Sun, Y. A survey of ensemble learning: Concepts, algorithms, applications, and prospects. IEEE Access, 10:99129 11999129999149,... 2022.
L., Castillo, C., and Houben, G. (eds.), Proceedings of the ACM Web Conference 2023, WWW 2023, Austin, TX, USA, 30 April 2023 4 May 2023, pp. 3342-3352. ACM, URL https: 3583474.
Nie, Y., Nguyen, N. H., Sinthong, P., and Kalagnanam, J. A time series is worth 64 words: Long-tern forecasting with transformers. ICLR, 2023.
2023. doi: 10.1 10.1145/3543507.553447777 //doi. org 10.
Oliveira, M. and Torgo, L. Ensembles for time series fore- casting. In Asian Conference on Machine Learning, pp. 360-370. PMLR, 2015.
Li, 7., Lin, X., Liu, 7., Zou, J., Wu, 7., Zheng, I.., Fu, D., Zhu, Y., Hamann, H. F., Tong. H., and He, J. Language in the flow of time: Time-series-paired texts weaved into unified temporal narrative. CoRR, 0bs/2502.08942. 2025. doi: 104455500ARRXV.2502200022
Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., et al. Pytorch: An imperative style, high-performance deep learning library. Advances in neural information processing systems, 32, 2019.
URL https: 08942.
// //doi. . org / 10.
Lim, B. and Zohren, S. Time-series forecasting with deep learning: a survey. Philosophical Transactions of the 2021.
Royal Society A, 379(2194):202002)))
Qiu, R. and Tong, H. Gradient compressed sensing: query-efficienn gradient estimator for high- ligh-dimensional zeroth-order optimization. In Proceedings of the 41st International Conference on Machine Learning. 2024.
Lin, X., Liu, Z., Fu, D., Qiu, R., and Tong, H. Backtime: Backdoor attacks on multivariate time series forecasting. Advances in Neural Information Processing Systems, 37: 131344-131368. 2024.
Qiu, R., Sun, Z., and Yang, Y. DIMES: A differentiable meta solver for combinatorial optimization problems. In Advances in Neural Information Processing Systems, vol- ume 35, pp. 25531-255444 2022.
Lin, X., Zeng, Z., Wei, T., Liu, Z., Tong, H., et al. Cats: Mitigating correlation shift for multivariate time series classification. arXiv preprint arXiv:2504.04283, 2025.
Qiu, R., Wang, D., Ying. L., Poor, H. V., Zhang, Y., and Tong. H. Reconstructing graph diffusion history from a single snapshot. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 1978-1988, 2023.
Liu, Y., Wu, H., Wang, J., and Long, M. Non-stationary transformers: Rethinking the stationarity in time series forecasting. NeurlPS, 2022.
Liu, Y., Hu, T., Zhang, H., Wu, H., Wang, S., Ma, L., and Long, M. itransformer: Inverted transformers are effec- tive for time series forecasting. In The Twelfth Interna- tional Conference on Learning Representations, 2024a.
Qiu, R., Jang. J.-G., Lin, X., Liu, L., and Tong, H. TUCKET: A tensor time series data structure for efficient and accu- rate factor analysis over time ranges. Proceedings of the VLDB Endowment, 17(13), 2024a.
Liu, Z., Cao, W., Gao, Z., Bian, J., Chen, H., Chang, Y., and Liu, T.-Y. Self-paced ensemble for highly imbal- anced massive data classification. In 2020 IEEE 36th international conference on data engineering (ICDE), pp- 841-852. IRRF, 2020a.
Qiu, R., Xu, Z., Bao, W., and Tong, H. Ask, and it shall be given: On the Turing completeness of prompting. arXiv, 2411 2024b.
Qiu, R., Zeng, W. W., Tong, H., Ezick, J., and Lott, C. How efficient LLM-generated code? A rigorous & high standard benchmark. arXiv, 2406.06647, 2024c.
Liu, Z., Wei, P., Jiang, J., Cao, W. Bian, J., and Chang, Y. Mesa: boost ensemble imbalanced learning with meta- sampler. Advances in neural information processing sys- tems, 33: 14443144444 2020b.
Roach, S., Ni, C., Kopylov, A., Lu, T.-C., Xu, J., Zhang, S., Du, B., Zhou, D., Wu, J., Liu, L., et al. Canon: Complex analytics of network of networks for modeling adversarial activities. In 2020 IEEE International Conference on Big Data (Big Data), pp. 1634-6666660 1643. IEFE, 2020.
Liu, Z., Kang, J., Tong, H., and Chang, Y. Imbens: Ensem- ble blass-imbalanced learning in python. arXiv preprint arXiv:2 127776 2021.

---

Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Sagi, O. and Rokach, L.. Ensemble learning: A survey. Wiley interdisciplinary reviews: data mining and knowledge discovery, 8(4): 2018.
Conference Knowledge Discovery and Data Mining, pp. 1989-1999, 2022.
Wei, T., Wu, Z., Li, R., Hu, Z., Feng, F., He, X., Sun. Y., and Wang, W. Fast adaptation for cold-start collaborative filtering with meta-learning. 2020 IEEE International Conference on Data Mining (ICDM), pp. 661-670. IEFE, 2020.
Sezer, O. B., Gudelek, M. U., and Ozbayoglu, A. M. Fi- nancial time series forecasting with deep learning: A systematic literature review: 2005-2019. Applied soft computing, 90:106181, 2020.
Shchur, O., Turkmen, A. C.,, Frickson, N., Shen, H., Shirkov, A., Hu, T., and Wang, B. Autogluon Autogluon-timeseries timeseries: Automl for probabilistic time series forecasting. In International Conference Automated Machine Learning, pp. 9-1. PMLR, 2023.
Wei, T., Feng, F., Chen, J., Wu, Z., Yi, and He, X. Model- agnostic counterfactual reasoning for eliminating popu- larity bias in recommender system. In Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining, pp. 1791-1800, 2021.
Tan, M., Merrill, M. A., Gupta, V., Althoff, T., and Hartvigsen, T. Are language models actually useful for time series forecasting? In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024.
Wei, T., You, Y., Chen, T., Shen, Y., He, J., and Wang. Augmentations in hypergraph contrastive learning: Fab- ricated and generative. Advances in neural information processing systems, 35:1909-19222 1922, 2022.
Wei, T., Jin, B., Li, R., Zeng. H., Wang. Z., Sun, J., Yin, Q., Lu, H., Wang, S., He, J., et al. Towards unified multi- modal personalization: Large vision-language models for generative recommendation and beyond. arXiv preprint arXiv:2403. 210222443..666, 2024a.
Tieu, K., Fu, D., Zhu, Y., Hamann, H. and He, Tempo- ral graph neural tangent kernel with In NeurlPS, 2024.
Tieu, K., Fu, D., Wu, J., and He, J. Invariant link selector for apatial-tempora diitt--distriuution problem. In The 28th International Conference Artificial Intelligence and Statistics, 2025.
Wei, T., Qiu, R., Chen, Y., Qi, Y., Lin, J., Xu, W., Nag. S., Li, R., Lu, H., Wang, Z., Luo, C., Liu, H., Wang, S. He, J., He, Q. and Tang, X. Robust watermark- ing for diffusion models: A unified multi-dimensional recipe, 2024b. URL https: / openreview hetpeiewwwweeeeeeeee.... net/ pdF?ic=013fIPEBS
Wang, D., Yan, Y., Qiu, R., Zhu, Y., Guan, K., Margenot, A., and Tong, H. Networked time series imputation via position-aware graph enhanced variational autoencoders. In Proceedings of the 29th ACM SIGKDD Conference Knowledge Discovery and Data Mining, pp. 2256-2268, 2023.
Wei, T., Chen, Y., He, X., and He, J. Connecting domains and contrasting samples: A ladder for domain generaliza- tion. 2025. URL https: wwl.acm... org.doiogooooooo htt//doi/100 1 1145 1445/6690622 .0208900644.779990 3709280.
Wang, L.,, Hassani, K., Zhang, S., Fu, D., Yuan, B., Cong. W., Hua, Z., Wu, H., Yao, N., and Long, B. Learning graph quantized tokenizers. In ICLR, 2025.
Wu, H., Xu, J., Wang. J., and Long, M. Autoformer: De- composition transformers with Auto-Correlation for long- term series forecasting, NewrlPS, 2021.
Wang, S., Wu, H., Shi, X., Hu, T., Luo, H., Ma, L.,, Zhang, Y., and ZHOU, J. Timemixer: Decomposable multi- scale mixing for time series forecasting. In The Twelfth International Conference on Learning Representations, 2024a.
Wu, H., Hu, T., Liu, Y., Zhou, H., Wang. J., and Long, M. TitesNet: Temporal 2d-variation modeling for general time series analysis. ICLR, 2023.
Wu, Z., Zheng, L., Yu, Y., Qiu, R., Birge, J., and He, J. Fair anomaly detection for imbalanced groups. arXiv, 2409. 10951, 2024.
Wang, Y. Wu, H., Dong, J., Liu, Y., Long, M., and Wang, Deep time series models: A comprehensive survey and benchmark. arXiv preprint arXXiv2407.13272 2024b.
Xu, H., Yan, Y., Wang, D.,, Xu, Z., Zeng, Z., Abdelzaher, T. F., Han, J., and Tong, H. Slog: An inductive spectral graph neural network beyond polynomial filter. In Forty- first International Conference on Machine Learning.
Wang, Y., Wu, H., Dong, J., Qin, G., Zhang, H., Liu, Y., Qiu, Y., Wang, J., and Long, M. Timexer: Empowering transformers for time series forecasting with exogenous variables. arXiv preprint arXiv:2402.
2024c.
Xu, Z., Hassani, K., Zhang, S., Zeng, H., Yasunaga, M., Wang, L., Fu, D., Yao, N., Long, B., and Tong. H. Lan- guage models are graph learners. CoRR, 2024a.
Wei, T. and He, J. Comprehensive fair meta-learned recom- mender system. Proceedings of the 28th ACM SIGKDD
12

---

Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Xu, Z.,, Qiu, R., Chen, Y., Chen, H., Fan, X., Pan, M., Zeng, Z., Das, M., and Tong, H. Discrete-state continuous- time diffusion for graph generation. arXiv preprint arXiv:2405.11416, 2024b.
Yoo, H., Zeng, Z., Kang, J., Qiu, R., Zhou, D., Liu, Z., Wang, F., Xu, C., Chan, E., and Tong, H. Ensuring user-side fairness in dynamic recommender systems. In Proceedings of the ACM on Web Conference 2024, pp. 3667-3678, 2024.
Yan, Y., Liu, L., Ban, Y., Jing, B., and Tong, H. Dynamic knowledge graph alignment. Proceedings of the AAAI conference on artificial intelligence, volume 35, pp. 4564- 4572, 2021a.
Yoo, H., Kang, S., Qiu, R., Xu, C., Wang, F., and Tong, H. Embracing plasticity: Balancing stability and plasticity in continual recommender systems. In Proceedings of the 48th International ACM SIGIR Conference on Research and Development in Information Retrieval, 2025a.
Yan, Y., Zhang, S., and Tong, H. Bright: A bridging algo- rithm for network alignment. In Proceedings of the web conference 2021, pp. 3907-3917, 2021b.
Yoo, H., Qiu, R., Xu, C., Wang, F., and Tong, H. Gener- alizable recommender system during temporal popular- ity distribution shifts. In Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 2025b.
Yan, Y., Zhou, Q Li, J., Abdelzaher, T., and Tong, H. Dissecting cross-layer dependency inference multi- layered inter-dependent networks. In Proceedings of the 31st ACM International Conference on Information &
Knowledge Management, pp. 2341-2351, 2022.
Yu, L.., Zhao, Y., and Tang, L. Ensemble forecasting for complex time series using sparse representation and neu- ral networks. Journal of Forecasting, 36(2):122-138, 2017.
Yan, Y. Chen, Y., Chen, H., Xu, M., Das, M., Yang. H., and Tong, H. From trainable negative depth to edge heterophily in graphs. Advances in Neural Information Processing Systems, 36:70162-70178, 2023a.
Yuan, H. and Li, G. A survey of traffic prediction: from spatio-temporal data to intelligent transportation. Data Science and Engineering, 6(1):63-85, 2021.
Yan, Y., Jing, B., Liu, L., Wang, R., Li, J., Abdelzaher, T., and Tong, H. Reconciling competing sampling strategies of network embedding. Advances in Neural Information Processing Systems, 36:6844 6861, 2023b.
Zeng, A., Chen, M., Zhang, L., and Xu, Q. Are transformers effective for time series forecasting? AAAI, 2023a.
Yan, Y., Chen, Y., Chen, H., Li, X., Xu, Z., Zeng, Z., Liu, L., Liu, Z., and Tong, H. Thegen: Temporal het- crophilic graph convolutional network. arXiv preprint a4Xiv:2412. 16435, 2024a.
Zeng. Z., Zhang, S., Xia, Y., and Tong, H. Parrot: Position- aware regularized optimal transport for network align- ment. In Proceedings of the ACM Web Conference 2023, pp. 372-382, 2023b.
Yan, Y., Hu, Y., Zhou, Q., Liu, L.,, Zeng, Z., Chen, Y., Pan, M., Chen, H., Das, M., and Tong, H. Pacer: Network embedding from positional structural. In Proceedings of the ACM Web Conference 2024, pp. 2485-24824 2296,229,.222 2024b.
Zeng, Z., Zhu, R., Xia, Y., Zeng. H., and Tong, H. Gen- erative graph dictionary learning. In International Con- ference on Machine Learning, pp. 40769-40769. PMLR, 2023c.
Yan, Y., Hu, Y., Zhou, Q., Wu, S., Wang, D., and Tong, H. Topological anonymous walk embedding: new structural node embedding approach. In Proceedings of the 33rd ACM International Conference on Information and Knowledge Management, pp.
Zeng, Z., Du, B., Zhang, S., Xia, Y., Liu, Z., and Tong, H. Hierarchical multi-marginal optimal transport for net- work alignment. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 16660-16668. 2024a.
2024c.
Ye, H., Liu, Z., Cao, W., Amiri, A. M., Bian, J., Chang, Y., Lurie, J. D., Weinstein, J., and Liu, T.-Y. Web-based long- term spine treatment outcome forecasting. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 3082-3092, 2023.
Zeng. Z., Qiu, R., Xu, Z., Liu, Z.. Yan, Y., Wei, T., Ying, L., He, J., and Tong, H. Graph mixup approximate gromov-wassersen geodesics. In Forty-firs Interna- tional Conference on Machine Learning, 2024b.
Yi, K. Zhang, Q. Fan, W., Wang. S., Wang. P., He, H., An, N., Lian, D., Cao, L., and Niu, Z. Frequency-domait mips are more effective learners in time series forecasting. Advances in Neural Information Processing Systems, 36, 2024.
Zeng, 7., Qiu, R., Bao, W., Wei, T., Lin, X., Yan, Y., Ab- delzaher, T. F., Han, J., and Tong, H. Pave your own path: Graph gradual domain adaptation on fused gromov- wasserstein geodesics. arXiv preprint arXiv:2505.1 127099, 2025.
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Regarding metrics, we utilize the mean square error (MSE) and mean absolute error (MAE) for long-term forecast- ing tasks and EPF datasets for short-term forecasting fol- lowing (Wang et al., 2024c). For the PEMS dataset, we follow the metrics of TimeMixer (Wang et al., 2024a) to report the mean absolute error (MAB), root mean squared error (RMSE), and mean absolute percentage error (MAPE) the unnormalized test set. Let x E RTux and x E xd be the ground truth and model prediction Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Zhang, T., Zhang, Y., Cao, W., Bian, J., Yi, X., Zheng. S., and Li, J. Less is more: Fast multivariate time series forecasting with light sampling-oriented mip structures. arXiv preprint arXiv:2207.01 186, 2022.
Biogeochemistry Institute in 2020. (3) Electricity (ecl) includes hourly electricity consumption data for years from 321 clients. The train/val/test is 15/3/4 months. (4) Traffic (Wu et al., 2023) records hourly road occupaney rates measured by 862 sensors of San Francisco Bay area freeways.
Zheng, L., Fu, D., Maciejewski, R., and He, J. Drgnn: Deep residual graph neural network with contrastive learning. Transactions on Machine Learning Research, 2024a.
Short-term forecasting datasets. We test the short-term forecasting performance on the PEMS (tra) dataset for traffic flow forecasting following TimeMixer (Wang et al., 2024a), and EPF (Lago et al., 2021b) datasets for electricity price prediction following TimeXer (Wang et al., 2024c). The PEMS dataset contains four public traffic network datasets (PEMS03, PEMS04, PEMS07, PEMS08) that record the traffic flow data collected by sensors spanning the freeway system in the State of California. The EPF dataset con- tains five datasets representing five different day-ahead elec- tricity markets (NP: Nord Pool; PJM: Pennsylvania-New Jersey-Maryland; BE: Belgium; FR: France; DE: German) spanning six years each.
Zheng, L., Jing, B., Li, Z.. Tong, H.,, and He, J. Hetero- geneous contrastive learning for foundation models and beyond. In Proceedings of the 30th ACM SIGKDD Con- ference on Knowledge Discovery and Data Mining, pp- 6666-6676, 2024b.
Zheng, L., Jing, B., Li, Z., Zeng, Z., Wei, T., Ai, M., He, X., Liu, L., Fu, D., You, J., Tong, H., and He, J. Pyg-ssl: A graph self-supervised learning toolkit. CoRR, abs/2412.21151, 2024c. doi: 10.48550/ARXIV. 2412.21151. URL https::t/////. //tpp::///..../// org/10. 48550/ arXiv. 2412 21151.
The detailed statistics of each dataset are given in Table 7.
Zhou, H., Zhang, S., Peng, J., Zhang. S., Li, Xiong, H.,,
and Zhang, W. Informer: Beyond efficient transformer for
A.2. Evaluation Metric Details
long sequence time-series forecasting. In Proceedings of the AAAI conference on artificial intelligence, volume 35, pp. 11106-11115, 2021.
Zhou, T., Ma, Z., Wen, Q. Wang. X., Sun, L., and Jin, R. FEDformer: Frequency enhanced decomposed trans- former for long-term series forecasting. ICML,, 2022.
Zou, J., Fu, D., Chen, S., He, X., Li, Z., Zhu, Y., Han, J., and He, J. GTR: graph-table-rag for cross-table question answering. CoRR, abs/2504.01344 2025, doi: 10.48550/ ARXIV.250H.01346. URL https: tttts://doo /ttp:///o/o./...////////
results of the i-th sample, these metrics are computed as follows:
F
MSE = (x(1)
Σ
x() out
Appendix
out
8=1
F MAE Σ
X (1)
X
(+)
A. Reproducibility Details
8=1
A.1. Dataset Descriptions
RMSE (MSE)
Long-term forecasting datasets. We conduct long-term forecasting experiments on 7 well-established real-world datasets, including: (1) ETT (Zhou et al., 2021) contains 2-year electricity transformer temperature datasets collected from two separate counties in China. It contains four subsets where ETThi and ETTh2 are hourly recorded, and ETTml and ETTm2 are recorded every 15 minutes. Each data point records the oil temperature and 6 power load features. The train/val/test is 12/4/4 months. (2) Weather (Zhou et al., 2021) records 21 meteorological factors collected every 10 minutes from the Weather Station of the Max Planck
MAPE 100
X (1)
x (1)
(5)
A.3. Implementation Details
Base Forecasting Models. To assess TIMEFuSE's abil- ity to unlock superior forecasting performance based on the state-of-the-art time-series models, we chose 13 well- known powerful forecasting models as our baselines. They include recently developed advanced forecasting models such as TimeXer (Wang al., 2024c) that exploits exoge-
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Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Table 7. Dataset detailed descriptions. The dataset size is organized in (Train, Validation, Test).
Tasks
Dataset
#Variates
Input Length
Predict Length
Dataset Size
Frequency
Deseription
ETTml
7
96
(96, 192, 336, 720)
(34465, 11521, 11521)
15 min
Electricity Transformer Temperature
ETTm2
7
96
(96, 192, 336, 720}
(34465, 11521, 11521)
15 min
Electricity Transformer Temperature
Long-term Forecasting
ETThl
7
96
(96, 192, 336, 720)
(8545, 2881, 2881)
hour
Electricity Transformer Tempersture
ETTh2
7
96
{96, 192, 336, 720}
(8545, 2881, 2881)
hour
Electricity Transformer Temperature
Electricity
321
96
(96. 192, 336, 720)
(18317. 2633, 5261)
hour
Electricity Consumption
Weather
21
96
(96. 192, 336, 720)
(36792, 5271, 10540)
10 min
Climate Feature
Traftic
862
96
{96. 192, 336, 720)
(12185. 1757. 3509)
hour
Road Occupancy Rates
PEMS03
358
96
[6. 12, 24)
(15617,5135, 5135)
5min
Traffic Flow
PEMS04
307
[6, 12, 24)
(10172, 3375)
5min
Traffic Flow
PEMS07
883
96
[6, 12, 24)
(16911, 5622)
5min
Traffic Flow
Short-term
Forecasting
PEMS08
170
96
|6, 12, 24}
(10690, 3548, 265)
5min
Traffic Flow
EPT-NP
168
24
(36500, 5219, 10460)
hour
Electricity Price
EPF-PJM
168
24
(36500, 5219, 10460)
hour
Electricity Price
EPF-BE
168
24
(36500, 5219, 10460) hour
Electricity Price
EPF-FR
168
24
(36500, 5219, 10460) hour
Electricity Price
EPF-DE
168
24
(36500, 5219, 10460) hour
Electricity Price
nous variables to enhance forecasting, TimeMixer (Wang et al., 2024a) with decomposable multiscale mixing for mod- cling distinct patterns in different sampling scales, patching- based transformer models like PAttn (Tan et al., 2024) and PatchTST (Nie al., 2023) that model the global depen- dencies over temporal tokens of time series, and iTrans- former (Liu et al., 2024a) that applies the attention on the inverted dimensions to capture multivariate correlations be- tween variate tokens. Other strong competitive models including TimesNet (Wu et al., 2023), FedFormer (Zhou et al., 2022), FreTS (Yi et al., 2024), DLinear (Zeng al., 2023a), Non-stationary Transformer (Liu et al., 2022), LightTS (Zhang et al., 2022), InFormer (Zhou al., 2021), and AutoFormer (Wu et al., 2021). To ensure fair compar- ison, we employed the TSLib (Wang et al., 2024b) toolkit' to implement all base models, the optimal hyperparameters for each model-dataset pair are used if provided in the of- ficial training sonfigurations. Unless otherwise specified in the training configuration, all models are trained for 10 epochs using an ADAM optimizer (Kingma, 2014) with L.2 loss, we also perform early stopping with a patience of 3 based on validation set loss to prevent overfitting. All ex- periments are conducted on a single NVIDIA A100 80GB
described in Section 3.2, then jointly train a single fusor and test its dynamic ensemble prediction performance on each task's test set. Similarly, we conduct joint fusor training and testing on the PEMS and EPF datasets for short-term fore- casting. The fusor is optimized using the ADAM (Kingma, 2014) optimizer and Huber loss, with batch size of 32 and learning rate of 1e-3.
B. Additional Experiments and Analysis
B.1. Inference Efficiency
We benchmark the runtime efficiency of the TIMEFUSE fusor relative to its base models. Table 8 reports batch infer- ence time (batch size 32, prediction length 96) across long- term forecasting datasets. It can be observed that thanks to its simple architecture (a single-layer neural network), the fusor introduces negligible overhead. It is significantly faster than transformer- lightweight models like DLinear. This makes TIMEFUSE practical for latency- sensitive applications and large-scale deployments.
models and is on par with
B.2. Forecasting with Extended Input Horizons
GPU.
TIMEFUSE details. We use Pytoreh (Paszke et al., 2019) to implement the fusor, which is single-layer neural net- work that learns linear mapping θ E Rd xk from meta- features to model weights. For all long-term forecasting tasks (i.e., ETTh1/h2/ml/m2, Weather, Electricity, Traffic), we collect meta-training data from their validation sets as
We assess how TIMEFUSE performs under longer input lookback lengths (L 336 and L = 512). Table 9 shows the forecasting results across seven long-term datasets. We observe that while models such as PatchTST and PAttn benefit from longer input sequences, others like TimeXer, i Trans roer, or TimesNet. show mixed or degraded performance. In contrast, TIMEFUSE consistently improve or maintain strong performance across all input lengths by dynamically leveraging each model's strengths. This
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Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Table Batch inference time (in milliseconds) of the TimeFuse fusor and each base model on long-term forecasting datasets (predict
length 96, batch size 32). All runtime results are collected from Linux server with NVIDIA V100-32G1 GPU.
TimeFuse
TXer
TMixer
PAttn
ITF
TNet
PTST
DLin
FreTS
FEDF NSTF LightTS
InF (2021)
AutoF
Datasets #Variates
(Ours)
(2024)
(2024)
(2024)
(2024)
(2023)
(2023)
(2023)
(2023)
(2022)
(2022)
(2022)
(2021)
ETTh1
7
2.37
7.77
1.72
2.25
17.30
1.96
0.80
1.41
52.52
7.05
1.29
13.04
35.07
ETTh2
7
2.41
7.18
1.58
2.42
23.11
3.13
0.53
1.11
50.86
12.68
1.20
6.83
35.41
ETTml
7
2.42
6.59
1.67
2.32
26.90
1.61
0.90
1.14
51.48
13.58
1.27
6.86
37.59
TTTm2
7
0.145
2.37
8.71
1.63
2.16
20.75
3.24
0.64
1.20
51.38
12.93
1.39
7.04
28.35
electricity
321
6.83
10.22
2.22
3.61
1237.25
3.16
0.78
1.87
51.47
65.95
1.57
13.23
39.84
weather
21
2.32
9.41
2.10
3.55
22.02
2.96
0.78
1.56
52.93
13.01
1,56
8.38
40.43
traffic
862
5.99
9.39
2.57
4.61
1034.37
3.03
0.79
1.76
53.25
14.46
1.65
8.85
41.15
demonstrates its robustness to changes in temporal context and model behaviors.
aggregate validation performance across the training dataset. While effective in capturing coarse-level model strengths, they fail to account for input-dependent variability at in- ference time. Consequently, their fusion strategies cannot adapt to diverse temporal patterns or regime shifts in test data. In contrast, TIMEFUSE dynamically adjusts fusion weights for each input instance using meta-features, en- abling finer-grained modeling and improved generalization.
B.3. Comparison with AutoML and Advanced Ensemble Baselines
To further validate the robustness of TIMEFUSE, we com- pare its performance with several strong baselines:
Advanced ensemble strategies: We include three repre- sentative methods: (1) Forward selection, a greedy Caruana- style ensemble (Caruana et al., 2004) that sequentially adds models to minimize validation loss; (2) Portfolio- based ensemble, which selects a subset of models based on overall validation performance and averages their predic- tions (Feurer et al., 2022); (3) Zero-shot ensemble, which computes similarity between input meta-features and train- ing tasks to weight base models without retraining (Feurer et al., 2022).
Limitations of zero-shot ensembling. Zero-shot ensem- ble methods attempt to address adaptivity by computing similarity between new inputs and previously seen datasets using meta-features. However, their conditioning granu- larity is limited to dataset-level similarity, rather than per- sample adaptivity, and their effectiveness depends heavily on the diversity and coverage of training tasks.
Chronos-Bolt and the challenge of generalization. Chronos-Bolt pretrained foundation model, is optimized for short-horizon univariate tasks with maximum predic- tion length of 64. While fine-tuning improves performance on some benchmarks, its architectural constraints and train- ing objectives make ill-suited for long-term or multivari- ate forecasting. In our evaluations, Chronos yields unstable degenerate predictions (e.g., extremely high MSE on ET Tm2 and Traffic) under such settings.
A fully automated ensemble system that combines 24 diverse base models using multi-layer stacking and weighted averaging, optimized through validation scores (Shchur et al., 2023). It supports probabilistic forecasting but is limited to univariate targets.
Al ensemble
Foundation model (Chronos-Bolt-Basee trained transformer model for univariate time-series fore- casting (Ansari et al., 2024). We evaluate both its zero-shot performance and fine-tuned version using the AutoGluon API. Note that Chronos is trained with short prediction horizons and does not natively support multivariate or long- range forecasting tasks.
A large pre-
AutoGluon and inference inefficiency. AutoGluon-
TimeSeries, while offering flexible ensembling over a wide model zoo, is currently restricted to univariate forecasting. Its ensemble predictions are computed independently for each variate, which leads to prohibitive computational costs in high-dimensional settings. Additionally, many of its constituent models (e.g., Prophet, ARIMA) do not support GPU acceleration, resulting in hours-long inference times for large datasets such as Elect rinctriicyyyyy (321 variates) and Traffic (862 variates). These limitations hinder its applicability in real-time or resource-constrained scenarios.
All methods are evaluated across 16 datasets from three task types: long-term multivariate, short-term multivariate, and short-term univariate forecasting. As summarized in Table 10, TIMEFUSE consistently achieves the best average performance across all three categories.
Taken together, these results highlight the advantage of TIMEFUSE as a lightweight, flexible, and input- semble framework that generalizes well across forecasting settings with varying dimensionality, horizon length, and
Static nature of traditional ensembles. Traditional en- semble strategies such as forward selection and portfolio- based ensembling determine static model weights based on
16

---

Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Table Performance of TimeFuse and base models with increasing input context length L. The results ranked //ssond waaeecoonndhiiini Ihird are highlighted. Given limited time, we run PatchTST and models newer than it except for TimeMixer, which encounters OOM on V100-32GB GPU when training with lookback length 336 or higher. Generally, longer L benefit PatchTST and PAttn on specific datasets,
but not for the rest 3 base models. TumeFuse shows consistent advantage under various L.
Lookback
TimeFuse
PST
TimeXer
PAtin
iTransformer MAE
TimesNet
Dataset
Length (1)
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MSE
MAE
ETThl
0.367
0.391 8*
0.379
0.400
0.382
0.403
0.390
0.405
0.447
0,444
0.389
0.412
ETTh2
0,280
0.334
0.292
0.345
0.285
0.338
0.299
0.345
0.300
0.350
0.337
0.371
ETTml
0.306
0.350
0.327
0.366
0.318
0.356*
0,336
0.365
0.356
0.381
0.334
0.375
ETTm2
0,170**
0.254
0.186
0.269
0.171
0.256*
0.180
0.267
0.186
0.272
0.189
0.266
L 96
weather
0.155
0.205 t
0.172
0.213
0.157
0.205*
0.189
0.226
0.175
0.216
0.169
0.219
electricity
0.133
0.231
0,180
0.273
0.140*
0.242
0.196
0.276
0.149
0,241
0.168
0.272
traffic
0
0.255
0,458
0.298
0.429
0,271
0.551
0.362
0.394
0.269*
0,590
0.314
Average
0.257
0.289***
0.285
0.309
0.269
0.296
0.306
0.321
0.287
0.310
0.311
0.319
E
0.370
0.
0.403
0.417
0.397
0.413
0.386*
0.404
0.435
0.441
0.438
0.450
ETTh2
0,274
0.333
0.286
0.345
0.297
0.353
0.288
0.344
0.307
0.364
0.367
0.417
ETTml
0.279
0.331
0.295
0,350
0.306
0.356
0.298
0.345*
0.315
0.363
0.319
0.367
ETTm2
0.155
0.245 90
0.173
0.261
0.169*
0.261
0.170
0.258
0.179
0.273
0.187
0.275
L = 336
weather
0.140
0.191 $015
0.154
0.204
0.158
0.209
0.158
0.206
0.171
0.223
0.164
0.220
electricity
0.228 0.130
0.147
0.251
0,153
0.258
0.143
0,239
0.169
0.274
0.191
0,297
traffic
0,387
0.267
0,405
0.291
0.412
0.297
0.404
0,282
0,442
0.330
0.605
0.345
Average
0.248
0.284
0.266
0.303
0.270
0.307
0.264
0.297
0.288
0.324
0.324
0.339
E
0.364 "
0.393 9*
0.381 e
0.404
0.389
0,413
0.381
0,407
0.435
0.444
0.434
0.450
ETTh2
0.274
0.332
0,290
0.348
0.286
0.349
0.287
0.347
0.309
0.371
0.390
0.424
ETTml
0,282**
0.334
0.296
0,350
0.307
0.358
0,301
0.347
0.321
0.367
0.337
0.379
ETTm2 0.157
0.248
0.169
0,260
0.171
0.260
0.171
0.260
0.180
0.273
0.191
0.278
1= 512
weather
0.138
0.190
0.151 *
0.203
0.157
0.208
0.153
0.202
0.166
0.220
0.157
0.215
electricity
0.127
0.225
0.144
0.249
0.148
0.255
0.138
0.236*
0.165
0.270
0.196
0.302
traffic
0
0.262
0.397
0,289
0.399
0.290
0.392
0.277
0.434
0.325
0.597
0.329
Average
0,245**
0.283**
0,260
0.301
0.265
0.305
0.260*
0.296
0.287
0.324
0.329
0.340
temporal complexity.
served that some base models perform strongly on the meta- training set but yield different behavior on the test set, which may affect fusion decisions. In some cases, excluding such models from the model zoo has been observed to improve results. Future work may investigate data augmentation (Lin et al., 2024; He et al., 2025; 2024; Li et al., 2025; Yan et al., 2023a; 2024b;c; Xu et al.; Zheng et al., 2024b; Feng et al.. 2022; Jing et al., 2024b; Zeng et al., 2024b; Wei et al., 2025;
C. Full Results
Due to space constraints, report the average performance scores across all prediction lengths for long-term forecasting datasets and short-term forecasting PEMS datasets in the main content. Detailed experimental results are provided in Tables 11 and 12, which show that TIMEFUSE consistently delivers robust performance at various prediction lengths and consistently outperforms the task-specific best individ- ual models across different datasets and metrics.
2022), adaptation (Yoo et al., 2025a;b; 2024; Zeng et al.,
2025; Wu et al., 2024; Bao et al., 2023; Wei al., 2020). and generation (Jing al., 2024a; Xu et al., 2024b; Qiu et al., 2024c;b; Wei et al., 2024b;a) techniques to enrich meta-training distributions and support better adaptation un- der potential distribution shifts (Fu et al., 2022; Bao et al., 2025; Lin et al., 2025; Qiu et al., 2024a; Qiu & Tong, 2024; Tieu et al., 2025; Wei et al., 2021; Wei & He, 2022).
D. Discussion on Limitations and Future Directions
While TIMEFUSE demonstrates strong performance across diverse forecasting tasks, several limitations remain that point to promising directions for future work.
Fusor Expressiveness. The current fusor architecture is designed to be simple for general applicability and com- putational efficiency. As the diversity of tasks increases, exploring more expressive fusor models that can capture complex meta-level patterns becomes an appealing direc- tion. Careful design is needed to balance model complexity and generalization, particularly when meta-training data is
Distribution Shift. TIMEFUSE relies on meta-training data to learn its sample-wise fusion strategy, and its per- formance can be influenced by distribution shifts between meta-train (validation) and meta-test (test) sets. We ob-
17

---

Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
limited.
Task Contribution Balance. To address the imbalance in the number of training samples across tasks, we currently adopt a straightforward oversampling strategy. While effec- tive in some settings, this approach may not always capture the optimal balance across tasks with differing sample sizes. Alternative resampling strategies (Liu al., 2020b;a; 2021; 2024b; Yan et al., 2023b) from the imbalanced classifica- tion literature may offer more flexible and adaptive way to enhance training efficiency and model robustness across tasks.
Incorporating Spatial or Graph Structure. Many multi- variate time series are associated with spatial structure, such as traffic weather sensors distributed over geographic regions, where nearby sensors often record similar measure- ments. These spatial dependencies are often represented using graph structures (Fu et al., 2024a; Ban et al., 2024; Zou et al., 2025) and analyzed using graph mining tech- niques (Yan et al., (0;;b;a;20 2022; Li et al., 2023; Lin et al., 2024; Roach et al., 2020; Jing et al., 2022) or learning on graphs (Fu et al., 2024b; Tieu et al., 2024; Zheng et al.,
2024a; Qiu al., 2023; 2022; Xu et al., 2024a; Zheng al.,
2024c; Wang et al., 2025; Jing et al., 2021; 2024c; Zeng et al., 2023b;c; 2024a). Extending the TIMEFUSE frame- work to explicitly incorporate such spatial or graph-based information could enable more adaptive fusion strategies, particularly for applications where spatial relationships play central role (Wang et al., 2023; Yan al., 2024a; Fu al., 2024c; Fang al., 2025).
These challenges present opportunities to further enhance the robustness, adaptability, and efficiency of TIMEFUSE in future iterations.
18

---

Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Table 10. Performance comparison between TimeFuse and (i) advanced ensemble solutions, (ii) AutoML ensemble AutoGluon
(with 'high "high.qualis quality'l' presets), and (iii) pretrained time series model Chronos Bolt-Base (finetune/influence with the AutoGluon API). We test the prediction length of 96/24 for long/short-term forecasting due to limited time. The results ranked / Ithid are highlighted.
Ours
Advanced Ensemble
AutoML Ensemble
Foundation Model
Task
Dataset
Metric
Forward Selection
Portfolio Ensemble
ZeroShot Ensemble
AutoGluon (24 models)
ChronosBolt Finetuned
ChronosBolt Zeroshot
TueeFuse
MSE
0.367
0.380
0.381
0.373
0,422
0.414
0.490
ETTh1
MAE
0.39 **
0.399
0,400
0,397
0,437
0.397
0.403
MSE
0
0.284
0.284
0.298
0,309
1.405
1411793,08$
ETTh2
MAE
0
0.34
0.341
0,361
0.356
0.385
68.569
Long-term Forecasting
MSE
0.306 *F
0.309
0.308
0.328
42,945
0.930
8927.445
ETTml
MAE
0
0.358
0.357
0.372
0,492
0.488
1,505
Multivariate
MSE
0.170
0.173
0.173
0.177
3412923.439
2.037
5908821.4 .446
ETTm2
MAE
0.254
0.261
0.262
0,271
219.784
1.035
289. 118
MSE
0.133
0.137
0.136
0.150
OOT
0.353
13507. ,261
electricity
MAE
0.23
0,240
0.240
0.255
OOT
0.280
2.041
MSE
0.155
0.167
0.159
0.164
0.211
0.219
0.218
weather
МАE
0.205 9
0.233
0.218
0.219
0.263
0.258
0.256
MSE
0 W
0.405
0.397
0,467
OOT
0.904
24684.661
traffic
MAE
0.255
0.267
0.262
0.299
OOT
0.340
2.048
MSE
0.257
0.265
0.263
0.279
682593.465
11.609
1052533.515
Avg.
MAE
0.289*#
0.300
0.297
0.311
44.266
0.598
51.992
MAE
18.551 th
19.226
18,886
19.669
37,392
44.713
45,925
PFMS03
RMSE
28.966
29.867
29.398*
30.700
58.613
72.054
73.835
MAPE
0.158
0.163
0.159
0.164
0.235
0.306
0.384
Short-term Forecasting
MAE
23.643
22.900
24.985
33.367
32.949
37.422
PEMS04
RMSE
35
36.889
36.098*
38.930
50.031
50.661
55.908
MAPE
0.189#
0.207
0.192
0.204
0,262
0.278
0.355
Multivariat
MAE
26.105
27.755
27.434
29.487
61.004
61.704
64.239
PEMS07
RMSE
4
42.742
42.382
44,976
90.104
94.850
98.631
MAPE
0.128
0.142
0.137
0.148
0.289
0.334
0.370
MAE
19.125
20.225
19.924
21.150
40.538
26.423
29,556
PEMSO8
RMSE
29.748*a
31.326
30.696*
32.709
52.422
39.718
43.971
MAPE
0.123
0.133
0.133
0.137
0,216
0.168
0.199
MAE 21.598*a
22.712
22.286*
23.823
43.075
41.447
44,285
Avg.
RMSE
3
35,206
34.643*
36,829
62,792
64.321
68.086
МАPE
0.149
0.161
0.155
0.163
0.250
0.271
0.327
MSE
0.229**
0.235
0.234
0.245
0.235
0.255
0.264
NP
MAE
0
0.277
0.277
0.279
0.267*
0.275
0.279
Short-term term Forcasting
MSE
0
0.086
0.086
0.087
0.084**
0.090
0.092
PJM
MAE
0
0.191
0.189
0.191
0.182**
0.187
0.191
Univariate
MSE
0
0.397
0.400
0.403
0.407
0,373
0,428
BE
MAE
0
0,254
0.255
0.260
0.270
0,248
0,262
MSE
0.386
0.391
0.392
0.399
0.379*
0.376
0,434
FR
MAE
0.198**
0.209
0.208
0.207
0.220
0.211
0,225
MSE
0.429
0.455
0.451
0.452
0.437*
0.503
0,553
DE
MAE
0.407
0.438
0.435
0.434
0.389**
0.424
0.455
MSE
0.301
0.313
0.312
0.318
0.308
0.319
0.354
Avg.
MAE
0.258
0.274
0.273
0.274
0.265
0,269
0.282
OOT: Out-of-time, AutoGluon inference predict each of the 321/862 variates on the electricity/trattie dataset. (ii) The predict length significantly influences the inference time of some AutoGiloon base mudels. large part AutoGluon
hours. This is duc
AutoGluon for univariate forecasting and repeatedly
models cammol
by GPU.
long-term forecast tasks: We carcfully checked pipeline and confirmed these rosults. believe this because Chronos canpot handle long-term teme forecasting that extends over its predict length (64) used in pretraining
Antoooo// abnormally high

---

Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Table II. Full long-term forecasting results.
Forcast MSE:
TFuse (Ours)
TXer
TMiser (2024)
PAtin (2024)
iTF
'NNet
PIST
DLin
FreTS (2023)
FEDF
NSTF
Ligh(TS
IuF'
AutoF'
(2024)
(2024)
(2023)
(2023)
(2023)
(2022)
(2022)
(2022)
(2021)
(2821)
96
0.367
0.382
0,378
0.390
0.447
0.389
0.379
0.396
0.400
0.377
0.510
0:135
0.963
0.524
192
0.415
0,429
0.441
0.437
0,519
0.439
0.427
0.445
0,451
0.420
0.635
0.494
1,020
0.557
01452
0.467
0.500
0.498
0.554
0.494
0.478
0.487
0.509
0.45%
0.781
0.549
1,030
0.555
720
0.476
0.499
0.479
0,533
0.563
0,516
0.522
0.513
0.563
0.502
0.632
0.612
1,222
0.545
Avg.
0.4.0
0.414
0.450
0.461
0.521
0.460
0.452
0.460
0.781
0:439
0.617
0.522
1,059
0.515
9/
0.220
0.285
0.290
0.299
0.300
0.357
0.252
0.341
0.342
0.348
0.397
0:435
1.764
0.385
Weather ETTmz RTIml ETTh2
192
0.355
0.363
0.387
0,381
0,382
0,405
0.381
0.482
0.440
0.424
0.532
0.561
2.201
0.451
336
0.,04
0.412
0.427
0.423
0.424
0.459
0.418
0.593
0.538
0.457
0.569
0.683
2.173
0.490
0.417
0.448
0.469
0,428
0.426
0:434
0.433
0.840
0.796
0.476
0.631
0.937
2.750
0.504
Avg.
0.365
0,377
0.393
0.383
0.383
0.409
0.381
0,564
0.329
0.426
0.532
0:654
2.222
0:457
0.306
0.318
0.336
0,336
0.356
0.334
0.327
0.316
0.310
0.539
0.406
0.369
0.740
0.522
192
0.346
0.362
0.363
0.376
0.399
0.408
0.370
0.382
0,383
0.535
0,517
0.399
0.761
0.617
0.380
0.395
0.790
0,407
0,433
0.413
0.398
0.115
0.420
0.681
0.583
0:430
0.872
0.640
720
0.443
0.452
0.456
0.467
0.501
0.486
0.458
0.473
0.497
0.709
0.614
0:488
0.998
0.557
Avg.
0.366
0,302
0.386
0,397
0.422
0.410
0.388
0.404
0,410
0.616
0.530
0:421
0.843
0.5K4
96
0.170
0.771
0.175
0.180
0.186
0.189
0.186
0.193
0.195
0.211
0.307
0.209
0.744
0.306
0.233
0.236
0.236
0,246
0.263
0.246
0.285
0.277
0.271
0.591
0.300
0,937
0.283
336
0
0.295
0.297
0.308
0.315
0.320
0.310
0.385
0.370
0.328
0.497
0.393
1.278
0.330
0.392
0.394
0.394
0,40X
0.421
0.415
0.556
0.560
0.420
0.679
0.545
1,938
0.428
Avg.
0.274
0.274
0.275
0.286
0.292
0.25%
0.289
0.355
0,350
0.308
0.518
0.362
1.224
0.337
0.1155
0:757
0.161
0,189
0.175
0.172
0.196
0.184
0,280
0.175
0.196
0.519
0.244
192
0.203
0.204
0.207
0.234
0.225
0.225
0.220
0.239
0.223
0.330
0.235
0.242
0,577
0.500
336
0.260
0.261
0,263
0.287
0.280
0,281
0.279
0.281
0.272
0.328
0.335
0.290
0.971
0.353
720
0.34T
0.340
0,344
0.362
0.361
0.359
0.355
0.345
0.351
0.391
0.112
0.350
1.266
0.426
Avg.
0.240
0.24]
0.244
0,268
0.260
0,259
0.257
0.265
0.258
0.333
0.289
0.269
0.834
0.341
Electricity
96
0,133
0.740
0.156
0.196
0.149
0.168
0.180
0.210
0.189
0.198
0.171
0.213
0.350
0.201
192
0.151
0.157
0.170
0.197
0.164
0.187
0.187
0.210
0.192
0.202
0.184
0.222
0.357
0.221
336
0.168
0.177
0,187
0.212
0.178
0.204
0.201
0.223
0.207
0.229
0.203
0,242
0,352
0,252
720
0.199
0:211
0.228
0,254
0.227
0.225
0.246
0.258
0.247
0,762
0.225
0.277
0.394
0.287
Avg.
0.163
0.171
0.185
0.215
0.180
0.196
0.201
0.225
0,209
0.223
0.196
0,238
0.358
0.240
96
0,388
0,429
0.474
0.551
0.394
0.590
0.458
0.697
0.565
0.654
0.615
0,769
1.156
0.673
Traffic
192
0.409
0.418
0,501
0.539
0.412
0.615
0.169
0.647
0.568
0.660
0.650
0.728
1.307
0.632
336
0.421
0.472
0.528
0,549
0.423
0.635
0.483
0.653
0,600
0,740
0.641
0.737
1,416
0.632
0..457
0.515
0.548
0.581
0.458
0.656
0.517
0.694
0.661
0.792
0.658
0.785
1,480
0.675
Avg.
0.419
0.466
0.313
0.555
0.422
0.624
0.482
0.673
0.599
0.711
0.641
0.755
1315
0.652
Forcust MAR
TFuse
TXer
TMixer
PAttn
TNet
PIST
DLin
FreTS
FEDF
NSTF
LighTTS
InF
AntoF
(Ours)
(2024)
(2024)
(2024)
(2024)
(2023)
(2023)
(2023)
(2023)
(2022)
(2022)
(2022)
(2021)
(2021)
0.391
0.403
0.298
0,405
0.412
0,400
0.411
0.412
0.418
0.502
0.444
0.780
0.495
192
0.420
0.435
0.430
0.439
0.483
0.442
0.432
0.440
0.443
0.444
0.565
0.478
0.794
0.517
0.444
0:419
0.160
0,170
0.502
0.471
0.161
0.165
0.181
0.167
0.652
0.510
0.780
0.514
720
0.477
0.493
0.472
0.499
0.525
0.494
0,506
0,310
0,340
0,503
0.570
0.569
0.880
0.523
Avg.
0.433
0.415
0.440
0.453
0.189
0.455
0.151
0.157
0.169
0.158
0.572
0.500
0,808
0.512
96
0.334
0,338
0.341
0.345
0.350
0,371
0.345
0.395
0.397
0.391
0.420
0.473
1.074
0.417
0.384
0.389
0:101
0,395
0.400
0.115
0.101
0.179
0.119
0.137
0.187
0.538
1,202
0.453
336
0.431
0.424
0:435
0,430
0.432
0.454
0.435
0.542
0,309
0,468
0.514
0.598
1,230
0.486
720
0.439
0.453
0.489
0.444
0,445
0.448
0.452
0.661
0.644
0.486
0.548
0.714
1,386
0.503
Avg.
0,393
0.401
0.411
0.404
0.407
0.422
0.409
0.319
0.500
0.445
0.492
0.581
1.233
0.465
0.350
07115
0.375
0,465
0.381
0.375
0.366
0.374
0.375
0.490
0.409
0.301
0.620
0.485
Weather RTTmZ k1
192
0.372
0,589
0.384
0,383
0,402
0.414
0,390
0.391
0.398
0.494
0.457
0:406
0.627
0.529
336
0.395
0.407
0.404
0,000
0.424
0.421
0.408
0.415
0.425
0.548
0.493
0.436
0.688
0.541
720
0,434
0.441
0.445
0,438
0.462
0.461
0.444
0.451
0.474
0.562
0.531
0.462
0.738
0.513
Avg.
0.353
0.397
0.101
0.397
0.17
0.418
0.102
0.108
0.118
0.521
0,473
0.121
0.608
0.577
96
0.354
0.256
0.258
0.267
0.272
0.266
0.269
0.293
0.285
0.294
0.338
0.308
0.631
0.344
192
0.297
0.299
0.298
0,308
0,312
0,312
0,306
0.361
0.35L
0.329
0.467
0.375
0.746
0.341
336
0.335
0.338
0.339
0.347
0.353
0.348
0.349
0.429
0.404
0.364
0.435
0.435
0.889
0.365
720
0.392
0.394
0.399
0.403
0.406
0.406
0.411
0.523
0.519
0.116
0.518
0.519
1.131
0.422
Avg.
0.319
0.322
0.323
0.331
0.336
0.355
0.334
0.402
0.390
0.351
0.439
0.409
0.849
0.368
96
0.385
0,205
0.208
0,226
0,216
0.219
0.213
0.256
0.239
0.349
0.227
0.255
0.515
0.348
192
0.247
0.247
0.251
0.264
0.258
0.264
0.256
0.299
0.274
0.384
0.277
0.299
0.539
0.361
336
0,287
0,290
0.292
0,301
0.298
0.304
0.298
0.331
0.318
0,366
0.343
0.337
0.734
0.388
720
0.342
0.340
0.344
0.349
0.351
0.354
0.347
0.382
0.387
0.399
0.390
0,383
0,883
0.432
Avg.
0.270
0,271
0.273
0,285
0.281
0.285
0.278
0.317
0.304
0.375
0.309
0.318
0.668
0.382
Elccricity
0.231
0.242
0.248
0.276
0.241
0.272
0.273
0.302
0.277
0.309
0.272
0.316
0,415
0.318
192
0.247
0,256
0.261
0.279
0.256
0.289
0.280
0.305
0.279
0.315
0,284
0.325
0.439
0.330
0.364
0.275
0.277
0.294
0.271
0.305
0.296
0.319
0.297
0.342
0.302
0.344
0,436
0.355
720
0.296
0,306
0:313
0.327
0.311
0.323
0.328
0.350
0.333
0.365
0.324
0.371
0.457
0.382
Avg.
0.366
0.270
0.275
0.294
0.270
0.297
0.204
0.319
0.296
0.333
0.296
0.339
0.437
0.346
96
0.255
0.271
0.295
0.362
0.269
0.314
0.208
0,429
0.368
0,420
0.342
0.477
0.598
0.403
Traffic
0.366
0.282
0.302
0,350
0.277
0.324
0.301
0.407
0.365
0.418
0.359
0.463
0.713
0.396
336
0.274
0.289
0.308
0.352
0.283
0.338
0.307
0.410
0.374
0.457
0.355
0.464
0.788
0.396
0.292
0.307
0.323
0,369
0.300
0.347
11398
0,184
0.555
0.185
0.812
0.115
Avg.
0.272
0.287
0.306
0.358
0.282
0.331
0.308
0.419
0.376
0.445
0.352
0.472
0.728
0.402
20

---

Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
Table 12. Full short-term forecasting results.
Metric
TFuse (Ours)
TXer (2024)
TMixer (2024)
PAttn
ITF
TNet
PTST
DL.n
Fr
FEDF
NSTF
LightTS (2022)
InF
AutoF
MAE
(2024)
(2024)
(2023)
(2023)
(2023)
(2023)
(2022)
(2022)
(2021)
(2021)
PEMS03
14,266
15.883
15.811
15,529
14.94/
17.665
16,319
17.085
15,709
31,027
16.918
15.429
20.130
23. 23.146
12
15.197
17.469
15,910
18.443
16.947
18.784
19.216
20.927
18.079
33.682
23.130
17.821
20.280
35.126
24
18.551
20.349
23.130
23.694
20.372
21.599
22.962
28.073
22.113
29.629
20.963
21.169
22.115
49.254
Avg.
16,005
17,900
18.283
19.222
17,420
19.349
19,499
22.028
18.634
31,446
20.337
18,140
20.842
35.842
PEMS04
18,936
21.105
21.373
21.092
20.128
21.695
21.726
21.818
21.011
40.668
21.227
20.073
22.521
27.033
12
19,259
22.019
19.572
24.621
22.390
22.668
25.555
26.567
23.872
37.758
22,952
21.478
22.779
39.194
24
22.610
24.416
29.948
32.061
27.217
24.722
32.492
34.845
29.569
33.891
24.387
25.161
24.166
59.911
Avg.
20.268
22,513
23.631
25.925
23.245
23.028
26,591
27.743
24.817
37.439
22.855
22.237
23.155
42,046
PEMS07
6
21,205
26.042
23.542
23.228
22.243
26.487
25.604
25.027
23.077
56.636
28.244
22.694
29.543
48.333
12
21.654
25.627
22.
27.409
25.061
27.380
28.721
31,468
27.044
$7.879
28,580
25.365
29.789
63.533
24
26.105
28:416
33.799
36.199
30.498
30.064
37.596
43,600
34.793
46,379
30.111
29.955
31,301
76.314
Avg.
22.988
26.695
26,489
28.946
25.934
27.977
30.641
33.365
28,304
53,631
28.978
26.005
30.211
62,726
PEMS08
6
14,930
16,740
16.637
16.456
15.661
18.946
16.639
18.028
16.439
40,313
17.693
15.751
20.979
26.978
12
15.348
18.163
15.687
18.872
17.215
19.943
20.023
21.191
18,378
36.794
19.814
17.467
22.934
36,776
24
19.125
20.937
25.019
24.430
21.057
22.213
25,207
28.321
22.699
29.598
21.629
21.090
24.698
44.481
Avg.
16.468
18.613
19.114
19.920
17.978
20.367
20.623
22.513
19.172
35.569
19.712
18.103
22.870
36.078
Metric
TFuse (Ours)
TXer
TMixer
PAtin
iTF
TNel
PTST
FreTS
FEDF
NSTF
LighTTS
DLin
InF
AutoF
RMSE
(2024)
(2024)
(2024)
(2024)
(2023)
(2023)
(2023)
(2022)
(2022)
(2022)
(2022)
(2021)
(2021)
PEMS03
6
22.235
23.876
24.497
24.313
23.314
28.235
25.664
27.315
24.730
44.
26.435
23.861
31.024
33.683
12
23.711
26.522
24.578
29.237
26.724
29.713
29.729
33,507
28,502
48.111
35.845
27.169
31.499
50,224
24
28.966
31.220
36,229
37.774
32.117
34.198
36.772
45.149
35.078
42.545
32.752
31.840
34,672
74,000
Avg.
24.971
27.206
28,435
30.442
27.385
30.715
30.722
35.324
29.437
44.941
31.677
27.624
32.398
52.636
PEMSI1
30.338
31.934
33,606
33.612
32.180
34.250
33,790
34.495
33,210
58,083
33.788
32.030
36.552
40.349
12
30,929
33.554
31,238
38.856
35.739
35.574
39.076
40,904
37.265
53,603
36.031
33,865
36.780
55.733
24
35,355
37.109
45.923
50.108
42.821
38.403
49.747
52,904
45,463
48.733
38.099
38.212
38.422
82.180
Avg.
32,207
.9.119
36.922
40.859
36.913
36.076
40.871
42.768
38.646
53,473
35.973
34,702
37.252
59.421
PEMS07
33.432
37,931
36.471
36.319
34,950
41,903
37,786
38.507
35,841
76.475
43,350
35,161
47,256
64,889
12
34.528
309
35,089
42.679
39.564
43.602
43.247
47.167
41.573
78.103
44,804
38.917
47.676
83.471
24
40.763
42.496
52.107
55.990
48.301
47.763
56.559
64,849
52.731
64.466
47,829
45,295
49.086
104.071
Avg.
36,241
39.512
41.222
44,996
40.938
44.423
45.864
50.174
43,382
73.015
45.328
39.791
48.006
144
PEMS08
6
23.570
24.859
25.930
26,133
24.869
29.863
16.181
28.614
26.140
56,395
27.592
24.577
32.029
38.493
12
24.328
27.116
24.738
29.882
27.467
31.215
30.742
32,961
29.110
52,460
30.628
27.043
35.299
50.732
24
29,748
31.906
38,135
38.467
33.646
34.530
38.916
43.542
35.498
42.456
33.707
32,004
37.927
62.418
Avg.
25.882
27.960
29.601
31.494
28.661
31.869
31.946
35.039
30.249
50.437
30.643
27,875
35.085
$0.548
Metric
TFuse
TXer
TMixer
PAttn
iTF
TNet
PTST
FreTS
FEDF
NSTF
LighTTS
DL.n
InF
AutoF
MAPE
(Ours)
(2024)
(2024)
(2024)
(2024)
(2023)
(2023)
(2023)
(2022)
(2022)
(2022)
(2022)
(2021)
(2021)
PEMSO3
6
0.118
0,153
0.139
0.126
0.122
0,151
0.134
0.144
0.127
0.296
0.145
0,132
0,176
0.230
12
0.130
0.165
0,142
0.150
0,142
0,162
0.169
0.187
0.147
0.307
0,203
0,164
0,175
0.316
24
0.158
0.193
0,197
0.195
0.173
0.191
0.190
0.256
0.184
0.287
0.189
0,208
0,187
0.477
Avg.
0.135
0.170
0.159
0.157
0.146
0.168
0.164
0.196
0.153
0:297
0.179
0.168
0.179
0.341
PEMSI1
0.154
0.201
0.186
0.171
0.169
0,183
0.181
0.195
0.174
0.323
0.180
0.168
0.189
0.243
12
0.160
0.206
0.169
0.192
0.181
0.193
0.220
0.248
0.197
0.324
0.197
0.181
0.193
0.332
24
0.189
0.223
0.247
0.253
0.221
0.215
0.270
0.316
0.241
0.302
0.209
0.232
0.202
0.478
Avg.
0.167
0.210
0.201
0.205
0.190
0.197
0.224
0.253
0.204
0.316
0.195
0.194
0.195
0.351
PENIO07
0.099
0.135
0.113
0.109
0.109
0.130
0.130
0.121
0.112
0.282
0.143
0.110
0.144
0.279
12
0.104
0.138
0.108
0.129
0.122
0.134
0.144
0.169
0.132
0.305
0.140
0.128
0.145
0.373
0.128
0.154
0.166
0.175
0.146
0.150
0.197
0.238
0.172
0.247
0.151
0.144
0.154
0.391
Avg.
0.110
0.142
0.129
0.138
0.126
0.138
0.157
0.176
0.139
0.278
0.145
0.131
0.148
0.348
PEMSO8
6
0,090
0.112
0,104
0.097
0.095
0.120
0,101
0.109
0.098
0.243
0.112
0.098
0,139
0.181
12
0.097
0.124
0.102
0.115
0.106
0.129
0.132
0.135
0.113
0.225
0.127
0.113
0.150
0.254
24
0.123
0.142
0.170
0.150
0.132
0.146
0.162
0.186
0.143
0.202
0.145
0,140
0.161
0.301
Avg.
0.103
0.126
0.125
0.121
0.111
0.131
0.132
0.143
0.118
0.223
0.128
0.117
0.150
0.246
21


Reviews:
[{"review_id": "eDWnRpbETr", "reviewer": "Reviewer_F3V1", "summary": "This paper proposes TIMEFUSE, a framework designed to improve time-series forecasting accuracy by adaptively fusing the predictions of multiple (pre-)trained forecasting models. The core idea is to train a “fusor” model that predicts a suitable set of fusion weights based on a set of expert-designed meta-features extracted from each input time series. By leveraging statistical, temporal, and spectral descriptors to characterize each input sample, TIMEFUSE dynamically weights and combines the outputs of different base models, thereby taking advantages of each base model’s complementary strengths. Experimental evaluations on standard long-term (e.g., ETT, Electricity, Weather, Traffic) and short-term (e.g., PEMS traffic, EPF electricity price) forecasting benchmarks show improvements over state-of-the-art individual models. TIMEFUSE also empirically demonstrates its task-agnostic ability to zero-shot generalize to completely unseen datasets.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Thank you for the thoughtful review and constructive feedback! With our best efforts, we conducted numerous additional analyses to address your concerns. Full results: https://anonymous.4open.science/api/repo/ICML25Reb-034C/file/Results.pdf?v=b00206ad. Please understand that due to the 5000-character limit, we can only summarize the most critical insights in the rebuttal :)**\n\n# W1: Why not TSFEL\n\nWe propose a compact meta-feature set alongside TSFEL for three main reasons:\n\n1. **Unexpected NaN values in TSFEL**: We observed that TSFEL often outputs a large number of NaN values, e.g., 15,876 NaNs on the weather testset. **Table 5** in the full results shows NaN counts across datasets. These NaNs scattered across different samples and features. TSFEL’s documentation offers no clear explanation or fix. In our implementation, we impute NaNs with the feature-wise mean.\n2. **Lack of multivariate features in TSFEL**: TSFEL computes features only on single variable. We believe that for multivariate time series, inter-variable relationships are important. Therefore, we constructed a smaller meta-feature set that explicitly includes such information.\n3. **Demonstrating TimeFuse’s flexibility**: We see TimeFuse’s ability to work with different meta-feature sets as an advantage: with a well-engineered implementation, TSFEL and other existing sets (e.g., catch22) can all be seemlessly intergrated into TimeFuse. Users can also design their own feature sets based on domain needs or interpretability considerations.\n\n# W2: Training objective and other details\n\n- **Training objective:** Explicitly computing optimal model weights for each sample requires *solving a least squares problem for each sample*, which is computationally expensive and unnecessary. In practice, our training objective in Eq (1) can directly optimizes the fusor via backpropagation.\n- **How to ensemble:** Our goal is to learn the best weighted sum of base models. This has several advantages over selecting the best single model: (i) **no need to break ties** since we’re not picking just one model; (ii) **more flexible integration**: for example, if one model overestimates and another underestimates, their combination can outperform either model alone. In cases where all models over-/underestimate, our approach can fall back to single-model selection. In practice, such cases can be also mitigated by including more diverse models in the zoo.\n\nWe will carefully revise the paper to better clarify these details.\n\n# C1: Sample-level breakdown analysis\n\n**Great suggestion! Please see Table 3 in the full results, where we report the sample-level win rate and average rank for all 13 base models and TimeFuse, using the same settings as Fig 1.**\n\nOverall, TimeFuse achieves a **46.11%** win rate with base models range **0.12%-9.89%**. For average rank, TimeFuse scores **2.37**, compared to **13.83–4.09** for base models, significantly outperforming any single model at the sample level. For cases where TimeFuse doesn’t outperform all base models, your point about “all models over/underestimating” is likely a cause. This might be addressed by adding a prefiltering step to select which models participate in the ensemble.\n\n\n# C2: Update Figure 4\n\nPlease see **Figure 1** in the full results for an updated version, where we order the base models by performance. Generally, TimeFuse tends to assign higher weights to more accurate base models.\n\n# C3: Clarification on Figure 6\n\nThank you for the suggestion. We note that Fig. 6 shows the fusor weights jointly trained across all long-term forecasting datasets. Its goal is to reveal the relationship between model weights and **input sample** properties, so the characteristics of a single dataset should not affect the results in Fig. 6.\n\n# Q1: On large MTSF models\n\n**We believe ensemble methods can complement large MTSF models rather than compete with them.** In fact, existing AutoML frameworks like AutoGluon already use pretrained MTSF models as base models in ensembles and achieve improved performance.\n\nAdditionally, current large MTSF models still have notable limitations: for example, we found that Chronos (a pretrained MTSF model) struggles with long-term or multivariate forecasting due to its univariate-centric design. Please kindly refer to our response to Reviewer oty5 Q1 for more details.\n\n\n# W0: Accuracy-time tradeoff\n\n**Since TimeFuse's fusor has a very simple architecture, its computational cost is minimal compared to the base model.** As shown in the **Table 2** of full results, the batch inference time of TimeFuse is nearly identical to that of the base model, indicating negligible overhead. We will include a detailed discussion in the paper.\n\n**We want to thank you again for the thoughtful review. We’ve dedicated over 60 hours to get the new results and will include them to enhance the paper’s quality. We hope our responses address your concerns and are happy to discuss if you have any further questions!**", "claims_and_evidence": "The main claims of the paper are (1). no single model can predict all data instances well, and (2). it is possible to train a simple model based on a set of expert-designed meta features to predict the combination weights for all model to get a adaptive predictions. Both claims seem intuitively reasonable and are backed up well with motivation examples and empirical results.", "methods_and_evaluation_criteria": "The methods follows the main claims well.\n\nThe datasets, the experimental settings (look-back length and forecasting length) and the main evaluation metrics (MSE and MAE, etc.) follow the common practice in MTSF.", "theoretical_claims": "To my understanding, there are no theoretical claims in this paper.", "experimental_designs_or_analyses": "The experiment designs, i.e., main results, ablation studies, sensitivity of the model zone size, seem reasonably complete and can empirically back up the advantage of the proposed method.\n\nHowever, using multiple models instead of one single model will require more resource and time for both training and inference. The tradeoffs between the forecasting accuracy and the (a). training time and (2). inference time for different model zoo sizes should also be reported to the readers.", "relation_to_broader_scientific_literature": "To my understanding, there are no clear relations to a potential broader scientific literature, besides MTSF and its applications.", "essential_references_not_discussed": "To my knowledge, this paper refers to a reasonably good number of references.", "other_strengths_and_weaknesses": "S1. The paper is largely well-written and easy to follow.\n\nBesides the experimental designs (forecasting accuracy vs. training and inference time under different model zoo sizes) to be clarified, some other weaknesses include:\n\nW1. It seems the TSFEL feature set is pretty comprehensive and shows similar performance, why not just use it? What is the specific technical novelty of the TIMEFUSE meta-features compared with TSFEL?\n\nW2. The training objective is not clear. Specifically, what is the optimal combination weight, and how to get it? Shall we choose the best single model, or should we choose a best weighted sum of the models, even though all models might be either overestimated and underestimated? How to break tie? Please clarify the details and justify the design choices.", "other_comments_or_suggestions": "C1. Although TIMEFUSE demonstrates good average forecasting accuracy, it would be very useful if the authors can provide a per-instance breakdown of the best models, as in Figure 1. This can demonstrate how much TIMEFUSE is away from the ideal case, and relevant discussions about what might be missing can be very beneficial to understand the questions.\n\nC2. I like Figure 4. Besides the weights, can you also combine the forecasting accuracies of each model in Figure 4, such that it would be very easy to see if TIMEFUSE assigns higher weights on more accurate models?\n\nC3. I like Figure 6, too. Can the authors also combine the domain and properties of each dataset in this figure, to further enhance the interpretability of TIMEFUSE?", "questions_for_authors": "Q1. Ensemble learning has been a popular learning paradigm to enhance accuracy before the foundation model era. However, with the emergence of foundation models, a popular understanding is that large models after a certain scales can be much more powerful than ensembles of smaller models. Can the authors envision the possibility of large model for MTSF (actually there are already quite some explorations), and whether or how TIMEFUSE can still be useful with large MTSF models?", "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": {"ethical_review_concerns": "N/A"}}, {"review_id": "oQuBvudXa4", "reviewer": "Reviewer_tYpH", "summary": "The manuscript introduces TimeFuse, a fusion model for time series fusion model. Specifically, TimeFuse uses the outputs of a model zoo and uses meta features of input time series to train a fusion model that predicts the ensemble weights of the individual models from the model zoo. The meta feature set uses various feature sets (statistical, temporal, spectral, multivariate). The authors evaluate their method on 16 datasets and compare the results of TimeFuse with simple mean/median ensemble strategies, along with other further analysis (size of the model zoo, ablation of the meta features, zero-shot performance).", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Great thanks for your thoughtful review and constructive feedback! With our best efforts, we conducted numerous additional analyses to address your concerns. Full results: https://anonymous.4open.science/api/repo/ICML25Reb-034C/file/Results.pdf?v=b00206ad. Please understand that due to the 5000-character limit, we can only summarize the most critical findings in the rebuttal :)**\n\n# Q1: Experiment with long input length\n\n**Following your suggestion, we trained multiple base models and TimeFuse with longer input context lengths $L$ (both 336 and 512) on 7 long-term forecasting datasets.** Given limited time, we trained PatchTST and models newer than it except for TimeMixer, which encounters OOM on V100-32GB GPU when training with L=336 or higher.\n\nWe report the averaged MSE for $L=96/336/512$ below (with 1st*/2nd best highlighted), please see full results for each dataset and metrics in **Table 4** in the link.\n\n|InputLen (L)|TimeFuse|PatchTST|TimeXer|PAttn|iTransformer|TimesNet|\n|-|-|-|-|-|-|-|\n|L=96|**0.257***|0.285|**0.269**|0.306|0.287|0.311|\n|L=336|**0.248***|0.266|0.270|**0.264**|0.288|0.324|\n|L=512|**0.245***|0.260|0.265|**0.260**|0.287|0.329|\n\n## Key findings\n1. **Across different $L$, TimeFuse consistently outperforms individual models by dynamically fusing their predictions.**\n2. **Both PatchTST and PAttn benefit from longer input lengths.** At L=336/512, PAttn replaces TimeXer as the best model, with PatchTST showing comparable performance.\n3. **TimeXer and iTransformer are insensitive to input length, while TimesNet degrades as input length increases.** Despite these mixed trends, TimeFuse effectively learns each model’s strengths across samples to produce more accurate predictions.\n\nAdditionally, we want to highlight that we use TSLib for implementing all models with unified APIs and recommended hyperparameters. While there may be slight differences from the original PatchTST implementation, we confirm that **our PatchTST results align with (often better than) those reported in recent papers (e.g., TimeMixer)**.\n\n\n# Q2 & M1: Results and clarification on TSFEL feature set\n\nPlease see **Table 6** in the full results for more results with the TSFEL feature set.\n\n**We want to clarify that our goal in proposing a new meta-feature set was NOT to outperform TSFEL (nor do we claim this as a core contribution)**, but rather to (i) avoid TSFEL's engineering issues and (ii) demonstrate that TimeFuse can integrate with various meta-feature sets and still perform well.\n\nMore specifically, we propose the compact set alongside TSFEL for three main reasons:\n\n1. **Unexpected NaN values in TSFEL**: We observed that TSFEL often outputs a large number of NaN values, e.g., 15,876 NaNs on the weather testset. **Table 5** in the full results shows NaN counts across datasets. TSFEL’s documentation offers no clear explanation or fix. In our implementation, we impute NaNs with the feature-wise mean.\n2. **Lack of multivariate features in TSFEL**: TSFEL computes features based on single variable. We believe that inter-variable relationships are also important. Therefore, we constructed a smaller meta-feature set that explicitly includes such information.\n3. **Demonstrating TimeFuse’s flexibility**: We see TimeFuse’s ability to work with different meta-feature sets as an advantage: with a well-engineered implementation, TSFEL and other existing sets (e.g., catch22) can all be seemlessly intergrated into TimeFuse. Users can also design their own feature sets based on domain needs or interpretability considerations.\n\n# Q3 & Q4 & M2: Comparison with AutoGluon, stronger ensemble algorithms, and foundation time-series model.\n\nPlease see **Table 1** in the full results for a comprehensive comparison with the suggested baselines. **Due to space constraints, we kindly refer you to our response to Reviewer oty5 Q1 for detailed analysis.**\n\n**In short, TimeFuse outperforms the ensemble baselines with its test-time adaptive ensembling capability. AutoGluon and Chronos are limited by their univariate-centric design and short pretrain predict length, leading to especially poor performance on long-term or multivariate forecasting tasks.**\n\n# M3: Performance with raw features\n\n**Please see Table 6 in full results for the performance of using raw features.**\nUsing either ours or TSFEL feature sets consistently outperforms the result with raw features by a significant margin.\n\n\n# D1: Discuss on the evaluation datasets\n\n**We greatly appreciate you pointing out the related works on the limitations of long-term time series benchmarks.** We have carefully read the literature and found them very insightful, relevant discussion will be included in the paper.\n\n**We want to thank you again for the thoughtful review. We’ve dedicated over 60 hours to get the new results and will include them to enhance the paper’s quality. We hope our responses address your concerns and are happy to discuss if you have any further questions!**", "claims_and_evidence": "One major claim of the paper is that TimeFuse as an ensemble method outperforms individual models and other ensemble models (top-k mean/median). Another major claim of the paper is that this can be effectively achieved by the presented meta-feature set. Overall, the evidence presented in the paper is through empirical evaluation on the evaluated datasets that beyond mere error reduction provides insight into the fusion weights, size of the model zoo, and learned fusor weights. While the overall evaluation is sound, there are some specific shortcomings of the evaluation that I will address in the next section.", "methods_and_evaluation_criteria": "### Datasets\n\nThe authors use the widely used long-term forecasting benchmark along with the PEMS and EPF benchmark. Since the evaluation covers several benchmarks, I think it the manuscript offers a sound empirical evaluation of their method. However, the long-term time series benchmark has limitations. These have been explored in recent position papers (https://arxiv.org/abs/2502.14045) and in the NeurIPS 2024 time series workshop (https://neurips.cc/virtual/2024/workshop/84712#wse-detail-108471, see Christoph Bergmeir's talk). I think it is important for the time series forecasting filed to move towards more extensive evaluation which is proposed in several recent papers (Gifteval: https://arxiv.org/abs/2410.10393; FEV (from the Chronos paper): https://openreview.net/forum?id=gerNCVqqtR). \n\nIn addition, the evaluation presented here has specific issues that I further elaborate in the \"Experimental Designs Or Analyses\" section.\n\n### Baselines \nThe authors use the individual models in the model zoo as baselines along with mean/median top-k ensembles. While these baselines are sound, I think additional baselines need to be added to effectively support the claims of this work. \n\n1/ Table 6 shows the ablation and comparison to TSFEL features. Since one of the contributions of this paper is the meta feature set, I think the TSFEL results should be added to the main results section with all evaluated forecasting horizons. The improvements by the introduced meta feature set are small, so I'm wondering if the improvement holds up for the entire benchmark. \n\n2/ I think the mean/median ensembles are too simplistic to serve as a baseline for other ensemble approaches and I also think the the comparison to other ensemble-based approaches is missing. I would suggest to compare their method against AutoGluon-TimeSeries as an alternative AutoML package that implements an ensemble/meta method for time series forecasting. I appreciate that the model zoo might be rather different, but it would give a meaningful evaluation against other established AutoML/ensemble packages in that domain.\n\n Additionally, I would suggest that the authors evaluate their method against the ensemble method implement in AutoGluon (https://openreview.net/forum?id=XHIY3cQ8Tew) with their model zoo (forward selection algorithm) \n\nCaruana, R., Niculescu-Mizil, A., Crew, G., and Ksikes, A. (2004). Ensemble selection from libraries of models. In Proceedings of the twenty-first international conference on Machine learning, page 18.\n\nThese comparison would substantiate the claims in the paper and demonstrate improvements against stronger baselines/ensembling methods. \n\n3/ The authors mention that raw features would not work as well as the proposed ensemble approach. However, I would kindly ask the authors to substantiate the claim by showing benchmark results with raw features.", "theoretical_claims": "There are no theoretical claims in this work.", "experimental_designs_or_analyses": "One specific issue with the specific setup in this paper is that the historical window length is fixed to 96 time steps. One issue that this is introduces is that some of the baseline methods perform much worse in the benchmark presented in this work compared to their original paper. For example, I compared the results in Table 2 in this work with the original PatchTST paper (and with this recent position paper: https://arxiv.org/abs/2502.14045) and found that the error for PatchTST in this work is consistently higher. This is likely attributed to the 96 historical window length As such, the improvement that is showed in this paper is only true relative to some baselines that have been run under suboptimal conditions (96 instead of 512 historical window length). This likely also affects the baseline results TSMixer. I appreciate that there has been earlier work that indicated that the performance of some of the transformer variants does not improve with longer input length. But I think the suboptimal conditions chosen here for PatchTST and TSMixer impact the findings. I would suggest the authors to compare against the baseline models when run against longer input windows.", "relation_to_broader_scientific_literature": "As mentioned before previously, this work does not compare against other AutoML/ensemble methods like AutoGluon-TimeSeries and does not compare against strong ensemble baselines such as forward selection. Additionally, for the zero-shot results the paper does not mention and/or compare against recent zero-shot pretrained time series models (TimesFM, Chronos, or even TabPFN-v2). Thus, it is unclear whether the presented method improves over other AutoML packages or ensemble methods or the zero-shot results present improvements over pre-trained models.", "essential_references_not_discussed": "As mentioned throughout the review, these essential references are missing either in discussion and/or evaluation \n\nAutoGluon-TimeSeries: (O. Shchur, A. C. Turkmen, N. Erickson, H. Shen, A. Shirkov, T. Hu, and B. Wang. AutoGluon-Timeseries: Automl for probabilistic time series forecasting. In International Conference on Automated Machine Learning, pages 9–1. PMLR, 2023.)\n\nCaruana, R., Niculescu-Mizil, A., Crew, G., and Ksikes, A. (2004). Ensemble selection from libraries of models. In Proceedings of the twenty-first international conference on Machine learning, page 18.\n\nPretrained time series models should also be discussed as they would be an alternative way to obtain zero-shot results.", "other_strengths_and_weaknesses": "The paper is clearly written and the empirical study is presented well. I appreciate the simplicity of the approach and I think that the work here gives good suggestions the training methodology through oversampling and alternating batching. As discussed, the weaknesses are mostly with specific issues in the experimental setup and choice of baselines.", "other_comments_or_suggestions": "n/a", "questions_for_authors": "I summarize my main questions to the authors here: \n\n1/ How would the individual model results change if the input context length is increased to 336 or 512 as proposed by earlier work (for example PatchTST)? Would TimeFuse still improve over the baselines? If I compare to the results of the original PatchTST paper, I suspect that the improvement over PatchTST might be much smaller when ran with longer input length, at least for the long-term benchmark dataset. \n\n2/ What would the full results look like for the TSFEL feature set? What improvement has TimeFuse over this feature set? \n\n3/ Does TimeFuse improve over other AutoML/ensemble baselines?\n\n4/ Would the TimeFuse ensemble method improve over stronger ensemble baselines (like forward selection)? \n\nI would consider raising my score if the authors address these points.", "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": "DhVOnJflIE", "reviewer": "Reviewer_VM6w", "summary": "This paper introduces TIMEFUSE, a novel framework designed for adaptive fusion of multiple heterogeneous forecasting models to enhance time series forecasting. Key findings indicate that no single model consistently outperforms others across all samples; each excels in specific scenarios. The method addresses this by adaptively fusing model outputs based on input meta-features (statistical, temporal, spectral). A learnable fusor dynamically determines optimal weights for each model. Extensive experiments show that TIMEFUSE outperforms individual state-of-the-art models, achieving improved accuracy on up to 95.1% of test samples.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Thank you for your recognition and thoughtful review! We've conducted extensive analyses to address your concerns. Full results: https://anonymous.4open.science/api/repo/ICML25Reb-034C/file/Results.pdf?v=b00206ad. Please understand that due to the 5000-character limit, we can only summarize key findings here.**\n\n# E1: Training objective of base models\n\n**Base models are trained using their standard prediction losses; the overall (fused) forecasting loss in Eq (1) and (2) is only for training the fusor.** In other words, the base models’ training and inference remain entirely standard—we do not modify their input format, loss functions, or inference procedures. Please refer to Appendix A.3 Implementation Details – Base Forecasting Models for more details.\n\n# E2: Compare with advanced ensemble/MoE algorithms\n\n**Thank you for the great suggestion. We test 4 more advanced ensemble methods from AutoSklearn2 and AutoGluon:**\n\n1. **Forward Selection**: Builds an ensemble by iteratively adding the model that most improves current predictions on a validation set.\n2. **Portfolio**: Optimizes the model weights to directly minimize validation loss, similar to risk minimization.\n3. **Zero-Shot**: Computes the agreement/similarity among model predictions and assigns higher weights to models that have more agreement with others.\n4. **AutoGluon**: (AutoML) learns the optimal ensemble of 24 base models (with `high_quality` presets).\n\nThey are trained and evaluated on all 16 datasets:\n- **Long-term Multivariate (LM)**: ETTh1/h2/m1/m2, Weather, Electricity, Traffic\n- **Short-term Multivariate (SM)**: PEMS03/04/07/08\n- **Short-term Univariate (SU)**: EPF (NP/PJM/BE/FR/DE)\n\nWe report the averaged MAE for each task type below (with **1st***/**2nd** best highlighted), please see full results for each dataset and metrics in **Table 1** in the link.\n\n|Task Type|TimeFuse|ForwardEns|PortfolioEns|ZeroShotEns|AutoGluon|\n|-|-|-|-|-|-|\nLM|**0.289***|*0.300*|**0.297**|0.311|44.266|\nSM|**21.598***|*22.712*|**22.286**|23.823|43.075|\nSU|**0.258***|0.274|0.273|0.274|**0.265**|*\n\n## Key Findings\n\n1. **TimeFuse consistently outperforms others across diverse task types.**\n2. **Caruana, portfolio, and zero-shot ensembles optimize fusion weights at the dataset level, but still statistic at test time and thus underperform TimeFuse's sample-level adaptive ensemble.**\n3. **AutoGluon is limited to univariate forecasting and is extremely slow for long-multivariate tasks, due to per-variate inference and lack of GPU support in many base models.**\n\nWe note that we also evaluated the pretrained foundation time-series model Chronos. Due to space constraints, please kindly refer to our response to **Reviewer oty5 Q1** for more details.\n\n# R1: Related work\n\n**Thank you for pointing out this related work. We have carefully reviewed the paper and its references and will include a detailed discussion in our revised version.**\n\n# W1 & W2: Clarification on expanding model zoo and oversampling\n\nWe appreciate the weaknesses you pointed out and would like to clarify two points:\n\n1. **Retraining the fusor incurs minimal computational cost**—usually just a few minutes. This allows easy integration of new models by simply adding their predictions to the meta-training data and retraining the fuser.\n2. **We use oversampling to balance the data distribution and prevent the pattern of minority datasets from being overwhelmed by larger ones.** We understand concerns about its impact on data representation quality, a potential solution is to adopt more advanced data augmentation techniques to achieve distributional balance.\n\n# Q1: Input format of base models\n\n**Yes, all forecasting base models accept the same input format.** As mentioned in our response to E1, the base models’ training and inference remain entirely standard, with no additional processing required.\n\n# Q2: Why not raw features?\n\n**Sorry for the confusion. We’d like to clarify that using raw features directly as meta features results in higher-dimensional meta features, rather than more samples.** For example, consider a input time series sample $X$ with $D$ variates and length $L$. Using raw features means treating $X\\in R^{(L,D)}$ as a single input sample (instead of $D$ samples) to the fusor. In contrast, meta features compress information from $X$ into a lower-dimensional space, reducing the risk of overfitting when learning from complex, high-dimensional raw features. We also ran additional experiments using raw features to validate this point, please see **Table 6** in the full results. **Results show that using meta features consistently outperforms raw features by a significant margin across all datasets.**\n\n**Thank you again for your recognition :) We’ve devoted over 60 hours to get the new results and analysis, which we believe significantly strengthen the paper. We hope our responses have addressed your concerns and would be glad to discuss any further questions.**", "claims_and_evidence": "Yes, the authors’ claims: that (1) no universal model winner and (2) the effectiveness of adaptive fusion have been validated by empirical results.", "methods_and_evaluation_criteria": "The proposed methods and evaluation criteria presented in the paper are well-suited for addressing the problem at hand. Given the key insight that no single forecasting model excels universally, it is natural to combine the strengths of multiple base forecasting models to achieve consistently strong performance across all tasks. Moreover, extracting multiple meta-features is a reasonable approach that standardizes the input for each forecasting model without requiring separate processing to meet each model’s specific requirements.", "theoretical_claims": "There are no theoretical claims.", "experimental_designs_or_analyses": "The experimental designs and analyses are mostly sound. The choice of baseline models includes a diverse set of recent state-of-the-art models, and the datasets used are standard benchmarks widely recognized in forecasting research.\n\nHowever, two things are not very clear: \n\n(1) It seems that the fusor is trained on a hold-out validation set and directly minimizes the overall forecasting loss; then what is the training objective of the individual base model? Do they minimize the overall forecasting loss or its own specific loss?\n\n(2) The authors only compare the proposed approach with static ensemble methods and single base models, while there could probably be many other dynamic ensemble methods that produce (soft) combination of models, or MoE that combine predictions from multiple experts. The authors should have a discussion on this aspect.", "relation_to_broader_scientific_literature": "Unlike traditional static ensemble methods (Kourentzes et al., 2014; Oliveira & Torgo, 2015), TIMEFUSE dynamically integrates diverse models using interpretable meta-features inspired by prior research on feature extraction (Barandas et al., 2020). It extends earlier ensemble ideas (Yu et al., 2017; Choi & Lee, 2018) by enabling heterogeneous models and dynamic sample-level weighting, thus bridging the gap between ensemble methods and state-of-the-art single-model forecasting techniques (Wang et al., 2024; Wu et al., 2023).", "essential_references_not_discussed": "Yes, the author missed discussing a related work. Although the following work didn't employ that many base models and extract different meta-features, the overall problem it frames is very similar:\n\nHan et al., (ICDM 2022), Dynamic Combination of Heterogeneous Models for Hierarchical Time Series", "other_strengths_and_weaknesses": "Weakness:\n\n1. The framework requires specifying a fixed set of predictors. If there are new available models one needs to retrain the fuser to obtain the updated set of weights.\n\n2. In line 234, oversampling all datasets to match the size of the largest task may break the internal structure of that dataset; particularly for time series with strong temporal dependency.", "other_comments_or_suggestions": "None", "questions_for_authors": "1. Do all forecasting base models accept the same input format? Should there be an extra processing step to obtain model-specific input?\n\n2. It is still not clear to me why training on raw features will lead to overfitting. The number of samples that raw features provide should be much more than aggregated values from meta-features.", "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": "zM1pFPNoNg", "reviewer": "Reviewer_oty5", "summary": "The paper proposes an approach to learn the weights of an ensemble of forecasting models based on meta-features of datasets. The approach first featurizes a time-series dataset then predicts optimal weights of models and average them to obtain predictions. The model is trained with a collection of datasets to learn the optimal weight combinations conditioned on the meta-features to a dataset. Experiments are conducted on real-world datasets against time-series base models.\n\n## update after rebuttal\n\nBased on the rebuttal, I decided to increase my score. I still think the paper will need another submission as the changes will be consequential.\n\n**Results comparison.** I reviewed the results provided by the author and think they will greatly improve the paper, they provide much better baselines than the initial ones.\n\nHowever, I cannot provide a full assessment as those results would need a major revision of the paper and another full round of review to carefully verify the fully redacted experimental protocol. For instance, how the ensemble are selected (validation error), why AG / Chronos provides large numbers (could be that the method fail catastrophically but it needs some justification given the high scores in public leaderboards), …\n\n>    In contrast, TimeFuse can adaptively predict the optimal weights for each test sample.\n\nI totally see that this could explain the performance improvement, the only caveat is that I think the evaluation setup is a bit restricted, see my comment bellow on the evaluation protocol.\n\n**Evaluation protocol.** I appreciate the clarification on zero-shot results: you perform inference on a dataset that was not seen during training which is what I understood when reading your paper.\n\nMy point is that most experiments are not done in this setup (only Tab 5 does it) and even in this setup, lots of datasets are highly similar (eg training on PEMS04/07/08 and evaluating on PEMS03).\n\nHowever, other methods such as Chronos Bolt are really in this setup where they are evaluated on time series that were not seen. I believe the experimental protocol will carry more weight if most of the pretraining was done on a set of datasets and evaluation was performed on a distinct one (for instance say using gift-eval training split and evaluating on their test datasets).\n\nBased on the rebuttal, I decided to increase my score. I still think the paper will need another submission as the changes will be consequential.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Thank you for the thoughtful review and constructive feedback! With our best efforts, we conducted numerous additional analyses to address your concerns. The full results are at https://anonymous.4open.science/api/repo/ICML25Reb-034C/file/Results.pdf?v=b00206ad. Please understand that due to the strict 5000-character limit, we can only summarize the most critical results and insights in the rebuttal :)**\n\n# Q1: Compare with AutoGluon/AutoSklearn2 ensemble and Chronos-Bolt\n\nWe implement and test the following approaches following your suggestions:\n\n- **Ensemble**: forward selection (Caruana), portfolio, and zero-shot techniques from  AutoGluon and AutoSklearn2.\n- **Foundation Model**: Chronos-Bolt-Base, both zero-shot and finetuned.\n- **AutoML Ensemble**: AutoGluon-timeseries with all 24 available base models (with `high_quality` presets).\n\nThey are trained and evaluated on all 16 datasets, which are categorized into 3 task types:\n- **Long-term Multivariate**: ETTh1/h2/m1/m2, Weather, Electricity, Traffic\n- **Short-term Multivariate**: PEMS03/04/07/08\n- **Short-term Univariate**: EPF (NP/PJM/BE/FR/DE)\n\nWe report the averaged MAE for each task type below (with **1st***/**2nd**/*3rd* best highlighted), please see full results for each dataset and metrics in **Table 1** in the link.\n\n|Task Type|TimeFuse|ForwardEns|PortfolioEns|ZeroShotEns|AutoGluon|ChronosBoltFT|ChronosBolt|\n|-|-|-|-|-|-|-|-|\nLong-Multi|**0.289***|*0.300*|**0.297**|0.311|44.266|0.598|51.992|\nShort-Multi|**21.598***|*22.712*|**22.286**|23.823|43.075|41.447|44.285|\nShort-Uni|**0.258***|0.274|0.273|0.274|**0.265**|*0.269*|0.282|\n\n## Key Findings\n\n1. **TimeFuse shows a clear advantage across various task types, and we summarize the reason below.**\n2. **Caruana/portfolio/zero-shot ensemble search the optimal fusion weights at dataset-level, but still statistic at test time.** In contrast, TimeFuse can adaptively predict the optimal weights for each test sample.\n3. **Chronos is limited to univariate forecasting only and is pretrained with a short predict length (64)**. In Chronos's paper, evaluations are also limited to univariate short-term (4-56) tasks. Our experiments reveal that Chronos suffers in long-term OR multivariate forecasting tasks. While fine-tuning offers improvements, its performance on such tasks is still far from optimal.\n4. **AutoGluon shares similar limitations with Chronos as it also only supports univariate prediction, and Chronos is one of its main base models.** Additionally, AutoGluon inference is notably slow on long-multi tasks (e.g., needs ~20 hours for predict on traffic dataset with 862 variates), primarily due to (i) the need for independent inference per variate, and (ii) many AutoGluon base models lacking GPU acceleration and running solely on CPUs.\n\n# Q2: Clarification on the evaluation protocol\n\nWe appreciate your point on the necessity of testing meta-learning methods on unseen datasets, but we would like to clarify two aspects:\n\n1. **Table 5 presents valid zero-shot results**: TimeFuse does not train on data from the target dataset in any predict length for zero-shot results. For instance, the results for ETTh1 are obtained with the fusor trained solely on 6 other long-term forecasting datasets. Similarly, results for PEMS03 involve training the fusor exclusively with data from PEMS04/07/08.\n2. **TimeFuse is not a \"pure\" meta-learning approach**: We note that TimeFuse is a model fusion framework, it cannot directly predict new datasets without training base models on the new data first. \n\n**Therefore, we opted to compare TimeFuse with other methods (e.g., Caruana/portfolio/Chronos) that also access new data for fine-tuning/searching optimal weights to answer Q1, following your suggestion.**\n\n# Q3: Discussion of related works\n\nWe greatly appreciate the suggested papers. We have read these articles and the references cited therein, gaining significant insights from them. We will revise our paper to more accurately reflect our position. Specifically, we believe that compared with existing works, **TimeFuse's core novelty and contribution lie in introducing a methodology for instance-level dynamic ensembling based on the input sample's meta-features, and demonstrating its broad effectiveness in practical applications**. We will discuss these additional related works in the paper to more accurately and comprehensively articulate TimeFuse's relationship with existing research and its position within the literature.\n\n**Finally, we want to thank you again for the thoughtful review, they have been very helpful in improving this paper. We’ve dedicated over 60 hours to implementing the new algorithms, training models, testing, and organizing results, and we will continue expanding those results to further enhance the paper’s quality. We hope these responses address your concerns and would be glad to continue the discussion if you have any further questions!**", "claims_and_evidence": "Most of your results are reported on the datasets used for training your meta-learning model. However, the standard practice is to report on hold-out datasets as the performance can be inflated otherwise (see [Auto-Sklearn 2.0: Hands-free AutoML via Meta-Learning](https://www.jmlr.org/papers/v23/21-0992.html) for instance). If you would report performance on those datasets, then you should compare with methods that are also trained on those datasets, for instance some foundational models such as Chronos-bold fine-tuned on those datasets and the performance will be likely quite better. In Tab 5, you report performance on “unseen” datasets but those are mostly the same as it is just the prediction length that is being changed, you just have PEMS which is a true old out dataset.", "methods_and_evaluation_criteria": "In addition to discuss more recent prior work on ensembling done for time-series, the paper should also consider non naive-ensembling baselines. Taking only the mean and median in particular is a really weak baseline and it is the only one considered. At the very least, I would recommend to compare with Caruana approach used in AutoGluon-timeseries and AutoSklearn2. I would also recommend to look at portfolio/zeroshot configurations as a second non-naive baseline (described here for instance [Auto-Sklearn 2.0: Hands-free AutoML via Meta-Learning](https://www.jmlr.org/papers/v23/21-0992.html)).", "theoretical_claims": "NA", "experimental_designs_or_analyses": "Yes, they currently suffer from two limitations:\n* the performances are mostly reported on the datasets used for training as opposed to what is frequently being done in meta-learning\n* only very naive baselines are considered for the ensembling", "relation_to_broader_scientific_literature": "The forecasting part is well addressed but the part discussing ensembling is very limited and does not include recent work on ensembling for time-series.", "essential_references_not_discussed": "The paper seems to claim that it is the first to consider ensemble across different models/architectures:\n\n> these studies are confined to a single-model architecture, focusing on training multiple same-type models based on different dataset views for a static homogeneous ensemble. Our work, in contrast enables dynamic heterogeneous ensemble of models with various architectures\n\nAt least, it provides no previous reference whereas considering ensemble across models is an obvious approach and has been discussed for instance in those two papers: [AutoGluon-TimeSeries: AutoML for Probabilistic Time Series Forecasting](https://arxiv.org/abs/2308.05566) and [Multi-Objective Model Selection for Time Series Forecasting](https://arxiv.org/pdf/2202.08485) to mention just two (there are also many references outside of time-series, for instance AutoGluon-Tabular or AutoSklearn2 that I mentioned above). I would also recommend referring to [hasson23a](https://proceedings.mlr.press/v202/hasson23a/hasson23a.pdf) for a discussion on ensembling where the conditioning is done on items, timestamps and forecasting horizon.", "other_strengths_and_weaknesses": "Strength:\n* The paper is well written and easy to read.\n* The approach proposed is sound and conditioning on meta-features could improve the final performance of ensembles\n\nWeaknesses:\n* Very weak baselines considered\n* Performance is mostly reported in the training (meta) dataset\n* Discussion in related work of ensemble for time-series forecasting mostly missing", "other_comments_or_suggestions": "NA", "questions_for_authors": "I would recommend to perform all evaluations on unseen datasets using leave-one-out between one of the 16 datasets and also to compare with non-naive ensembling methods such as Caruana or portfolio configurations.", "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:

Meta-review: This paper introduces TIMEFUSE, a framework designed to improve time series forecasting by dynamically fusing predictions from a diverse set of pre-trained base models ("model zoo"). The core idea is to extract a set of meta-features (statistical, temporal, spectral, multivariate) from each input time series sample and use these features to train a lightweight "fusor" model. This fusor predicts instance-specific optimal weights for combining the outputs of the base models, aiming to leverage the complementary strengths of different forecasters. Initial reviews acknowledged the novelty and soundness of the approach, its clarity, and good motivation. However, significant concerns were raised regarding the evaluation methodology, particularly the weakness of the initial ensemble baselines (simple mean/median), the lack of comparison to established AutoML frameworks (like AutoGluon) or stronger ensemble techniques (like Caruana selection), and the absence of comparison to recent large pre-trained time series models (like Chronos), especially concerning the zero-shot claims. Questions were also raised about the experimental setup (e.g., using a short, fixed input length for base models) and the evaluation protocol (reporting results primarily on datasets used for fusor training).

In response, the authors conducted a substantial rebuttal effort, including over 60 hours of additional experiments. They introduced comparisons against strong baselines including AutoGluon-TimeSeries, Chronos (zero-shot and fine-tuned), Caruana selection, portfolio optimization, and zero-shot ensembles across all 16 datasets. They also reran experiments with longer input lengths for base models. The new results showed TIMEFUSE consistently outperforming these enhanced baselines, with the authors providing justifications for the observed poorer performance of AutoGluon/Chronos on long-term multivariate tasks (univariate design, pretraining limitations). They clarified aspects of their methodology, including the training objectives, the rationale for their proposed meta-features versus TSFEL (NaN issues, lack of multivariate features in TSFEL) and raw features, and provided analysis on computational overhead (minimal). This extensive rebuttal was well-received: all three reviewers who had initially provided scores (ranging from Weak Reject to Weak Accept) explicitly raised their scores in light of the new evidence and clarifications.
Decision: Accept (poster)