SwiftTS: A Swift Selection Framework for Time Series Pre-trained Models via Multi-task Meta-Learning
Authors: Tengxue Zhang
Biao Ouyang
Yang Shu
Xinyang Chen
Chenjuan Guo
Bin Yang
Venue: ICLR 2026 Poster (2026)
Keywords: time series forecasting
model selection
transfer learning
Primary area: learning on time series and dynamical systems
TL;DR: We propose a swift selection framework for time series pre-trained models via multi-task meta-learning without fine-tuning.

Abstract: Pre-trained models exhibit strong generalization to various downstream tasks. However, given the numerous models available in the model hub, identifying the most suitable one by individually fine-tuning is time-consuming. In this paper, we propose \textbf{SwiftTS}, a swift selection framework for time series pre-trained models. To avoid expensive forward propagation through all candidates, SwiftTS adopts a learning-guided approach that leverages historical dataset-model performance pairs across diverse horizons to predict model performance on unseen datasets. It employs a lightweight dual-encoder architecture that embeds time series and candidate models with rich characteristics, computing patchwise compatibility scores between data and model embeddings for efficient selection. To further enhance the generalization across datasets and horizons, we introduce a horizon-adaptive expert composition module that dynamically adjusts expert weights, and the transferable cross-task learning with cross-dataset and cross-horizon task sampling to enhance out-of-distribution (OOD) robustness. Extensive experiments on 14 downstream datasets and 8 pre-trained models demonstrate that SwiftTS achieves state-of-the-art performance in time series pre-trained model selection. The code and datasets are available at \href{}{https://github.com/decisionintelligence/SwiftTS}.

Published as a conference paper at ICLR 2026
SWIFTTS: A SWIFT SELECTION FRAMEWORK FOR TIME SERIES PRE-TRAINED MODELS VIA MULTI- TASK META-LEARNING
Tengxue Zhang', Biao Ouyang', Yang Shu', Xinyang Chen"; Chenjuan Guo', Bin Yang! East China Normal University, HHarbin Institute of Technology (Shenzhen) ftxzhang, bouyang sstu. ecnu. edu, en, chenxinyangf@hit edu. cn (yshu, ejguo, byang) @dase. ecnu. ecnu.edu.co
ABSTRACT
Pre-trained models exhibit strong generalization to various downstream tasks. However, given the numerous models available in a model hub, identifying the most suitable one by individually fine-tuning is time-consuming. In this paper, we propose SwiftTS, swift selection framework for time series pre-trained models. To avoid expensive forward propagation through all candidates, SwiftTS adopts a learning-guin guuded approach that leverages historical dataset-model performance pairs across diverse horizons predict model performance on unseen datasets. It employs a lightweight dual-encoder architecture that embeds time series and candidate models with rich characteristics, computing patchwise compatibility scores between data and model embeddings for efficient selection. To further en- aorizon-adaptive expert
hance the generalization across datasets, we introduce composition module that dynamically adjusts expert weights, and the transferable cross-task learning with out-of-distribution (OOD) robustness. Extensive experiments datasets and 8 pre-trained models demonstrate that SwiftTS achieves state-of of-the- art performance in time series pre-trained model selection. The code and datasets are available at
and cross- pross-horizon task sampling to enhance
14 downstream
INTRODUCTION
Time series forecasting (Cirstea et al. 2002 Cheng al. 2023 Pan 2023 Chen al. 2024 is
a fundamental task with broad applications in linance, weather prediction, and transportation (uo
al.
2014 Yang al. 2023 Tian al. 2026 2025 Mei et al. 2025 Feng 2025 Wang et al.
2014
Ma et al.
et al.
2026). Inspired by the success of pre- pre-trained models in natural lan gugg
processing (Hurst et al.
2024; Yang et al. 2025) and computer vision (Dosovitkiyy et al. 202
numerous time series foundation models have been developed (Das et al. 2024) Gao et al.
2024
Wang et al. 22025] Wu et al. 2026). Pre-trained on large and diverse datasets, these models acquire transferable knowledge that can be adapted to downstream tasks through fine-tuning, eliminating the need for training from scratch (Kumar et al. 2022 Jia et al. 2022
Dettmers et al. (023).
However, single pre-trained model excels in all tasks (Li et 2025). making model selection for time series forecasting challenging. Although fine-tuning all candidate models provides model selection results, it is often computationally infeasible for large model pools. Therefore, developing efficient methods to identify the optimal pre-trained model is crucial for real-world deployment. Ex- isting approaches, primarily designed for image models, are feature-analytic methods that analyze features extracted from the target dataset using pre-trained models: some assess feature-task align- ment via statistical metrics (Nguyen et al. 2020), while others investigate intrinsie properties of the feature space (Pándy et al. 2022 Wang et al. 2023). Only a few are learning- based (Zhang et al., 2023). learning similarity functions between data and model representations for model selection. Despite recent advances, several challenges remain unresolved for time series pre-trained models:
"Corresponding authors

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Published as a conference paper at ICLR 2026
Oversight of model heterogeneity and time series data characteristics. Current time series pre-trained models are typically heterogeneous in both architecture and training objec- tives, unlike the standardized feature extractors in vision models. This diversity hinders unified fea- ture extraction and limits the applicability of many existing methods. Moreover, extracting features also requires costly forward passes through each model, leading substantial computational over- head as the model hub or datasets scale. Some learning-based methods attempt to mitigate this cost via a shared feature extractor, but often sacrifice performance, In addition, time series data exhibit temporal dependencies and sequential patterns that are critical for accurate forecasting but largely ignored in current approaches. Valuable prior knowledge and intuitive insights, such as "models generally perform better when the downstream domain aligns with the pre-training domain," are also rarely incorporated into current model selection criteria.
Challenge 1:
Challenge 2: Limited generalization in cross- domain and cross-horizon scenarios. Feature- analytic methods often fail when the target dataset diverges from the pre-training domain. In such cases, fine-tuning can induce substan- tial shifts in model parameters, making initial features poor predictors of post-tuning perfor- mance. Although few learning-basee methods assume that the learning paradigm can general- ize, they lack explicit designs to ensure robust- ness on unseen datasets. Moreover, the perfor- mance of time series pre-trained models can vary considerably across different forecasting hori- zons. A model that excels at short-term predic- tions may degrade on longer horizons. Ignoring such variability can result in misleading perfor- mance rankings that fail to reflect the dynamic, horizon-dependent nature of time series forecasting. Current methods often lack mechanisms to effectively select models tailored to specific forecasting thereby limiting their generalization across varying forecasting ranges.
Imput Data
Model
Ranking
Time Series
Heterogeneous
Horizon-qpecifle
Forecasting
Enouknanly
Efficient
H-96
H-72
Leurning guided
Deloloncelyy
Moddl Selection
Temporal
Exoee-Joenda
Cross-domain
Dependency
and broos-bborizon
Figure I: SwiftTS employs an efficient learning- guided selection framework for time series fore- casting, enabling porizon-specifii selection and improved cross-domain generalization via multi- task meta-lcarning.
horizons, in Figure I
To address Challenge 1, we propose an efficient sorming-guideed selection framework that avoids inconsistent feature extraction and reduces forward propagation costs. We collect the performance of various mataset-model pairs across different horizons as training data to learn how models per- form on unseen datasets. The framework is tailored time series characteristics and incorporates prior knowledge to enhance selection. The data encoder segments the input series into patches and generates patch-level embeddings that capture local temporal patterns and preserve sequen- tial dependencies. The model encoder incorporates meta-information, topological structure, and functionality to construct comprehensive representation of candidate models. By employing a lightweight dual-encoder architecture, our framework independently learns informative embeddings for both downstream datasets and candidate models. Finally, patch-level cross-attention assesses the fine-grained compatibility score between them, enabling accurate and efficient model selection.
To address Challenge 2, we propose a generalizable multi-task meta-learning strategy. To equip our framework with the multi-task flexibility to accommodate varying horizons, we incorporate a horizon-adaptive expert composition. This design dynamically assigns adaptive weights to multiple experts based on the target forecasting horizon, enabling horizon-specifh ranking predictions. To further enhance generalization across both domains and horizons, we propose transferable cross- task learning improve robustness in -usttf-distiibution (OOD) scenarios. We introduce meta- learning paradigm with two task sampling strategies: (1) cross-dataset sampling, where tasks are drawn from different datasets encourage inter-domain generalization, and (2) cross-horizon sam- pling, where tasks are constructed using varying forecasting horizons to improve horizon-level adaptability. By meta-learning from tasks across diverse datasets and horizons, our framework learn transferable knowledge that captures both task-specific characteristics and shared cross-task patterns. This ultimately improves its performance in real-world applications.
To the best of our knowledge, this is the first model selection method for time series pre-trained models. The contributions are summarized as follows:
We propose a swift saaring-guided framework that leverages a dual-encoder to embed datasets and models, computing patchwise compatibility scores for model selection.
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We introduce a multi-task meta-learning strategy with horizon horizon-adaptive expert composi- tion to enhance generalization across datasets and forecasting horizons.
Extensive experiments benchmarks comprising 14 real-world downstream datasets and 8 pre-trained models show that our method achieves state-of-the-ar performance in pre- trained model selection for time series forecasting.
2 RELATED WORK
Time series Pre-trained Model. Existing models can be broadly categorized into three main archi- tectures: (1) Encoder-only models: MOIRAI (Woo et al., 2024) flattens multivariate sequences into unified sequences for Transformer pre-training. Moment Gossami et al. (024)) employs masked re- construction to train a versatile Transformer, and UniTS (Gao et al. (0224) introduces task tokeniza- tion and dynamic self-attention across temporal and variable dimensions. (2) Decoder-only models:
TimesFM Das et al. (2024) and Timer Liu et al. (2024) adopt GPT-style designs for next-token pre- diction, achieving strong zero-shot performance. (3) Encoder-decoder models: TTM Ekambaram ctt al. (2024) leverages M-x-rr blocks with multi-resolution sampling to capture cross-channel patterns. ROSE (Wang et al. 2024) enhances generalization through decomposed frequency learn- ing and time series register components. Chronos (Ansari al., (2024) adapts the T5 (Raffel et al.) 2020) language foundation model to time series by discretizing data via binning and scaling. As the number and variety of time series pre-trained models continue to grow, efficiently and accurately selecting the most suitable model from a diverse model hub remains a challenge.
Pre-trained Model Selection. Pre-trained model selection aims to quickly identify the best model for downstream tasks from model hub. Existing methods fall into two broad categories: (I) Feature-analytee methods analyze features extracted by pre-trained models from the target dataset. Early approaches, such as NCE (Tran et al., 2019) and LEEP (Nguyen et al. 2020), leverage sta- tistical metrics but depend on pre-trained classifiers, limiting their applicability self-supervised models. LogME (You et al.] 2202]) overcomes this by estimating the maximum label marginal- ized likelihood. RankME (Garrido et al. 2023) posits that models with higher feature matrix ranks exhibit superior transferability. Other methods focus class separability during the fine-tuning process. GBC (Pándy et al.) 2022) measures the degree of overlap between pairwise target classes based extracted features. SFDA (Shao et al. 2022) enhances class separability by projecting
features into a Fisher space. Etran (Gholami et al. 2023) introduces an energy-based transferability
metric, while DISCO (Zhang al. (2025) proposes framework for evaluating pre-trained models based on the distribution of spectral components, (2) Learning-based methods aim to predict model transferability through learning framework (Wu et al., 2024a b). Model Spider (Zhang
2023)
learns model representations and similarity function by aligning them with downstream task rep- resentations, enabling model selection via the learned similarity. Despite the diversity of existing methods, they often rely on costly feature extraction and generalize poorly across domains and fore- casting horizons. To address these issues, we propose SwiftTS, a swift model selection framework via multi-task meta-learning. It infuses prior knowledge and adopts a Sarning-guides paradigm, avoiding expensive feature analysis used in prior work while improving OOD robustness.
PROBLEM FORMULATION
Given a model hub Z = {oh ] of K time series pre-trained models and a target dataset D (rt, yi ) with N samples, the goal is to select the model that achieves the best performance on the time series forecasting task with horizon H. Brute-force fine-tuning of all models yields the ground-truth performances {rx [r*) for the model hub, but at prohibitive computational cost. To avoid this, model selection methods estimate transferability without fine-tuning by assigning each model dy an assessment score fr. where a larger fy indicates stronger expected performance:
F& f(er, D.
The f is scoring function that measures the compatibility between the model dx and the target dataset D under the forecasting horizon H. Ideally, the predicted scores (f*] should strongly correlate with the fine-tuning results (rx 1K enabling the selection of the most transferable model.
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4 METHODS
We propose an efficient framework for pre-trained model selection in time series forecasting via multi-task meta-learning (Figure 2) The learning-guided selection framework adopts a dual- encoder architecture: a temporal-aware data encoder captures sequential patterns by segmenting time series into patches to generate data embeddings, while knowledge-infused model encoder incorporates prior knowledge about models to construct rich model embeddings. Then, we employ patch-level cross-altention evaluate fine-grained compatibility scores between them. To facilitate multi-task forecasting and enhance generalization, we further adopt a generalizable multi-task meta-learning strategy: aadapinn expert composition module adaptively assigns weights to experts based on the target horizon, and the transferable cross-task learning with cross-dataset and cross-horizon task sampling improves robustness under OOD scenarios. The framework trained on meta-dataset of N samples, Meeta = [D', Z, H' r' r' Ji=l. where the i-th sample includes a downstream dataset D', shared model hub Z, the horizon H' and the corresponding ranking scores r of the model hub. The ranking scores reflect the relative performance of models in Z on dataset D' under horizon H'. This meta-dataset allows the framework to learn how models perform on various datasets, enabling accurate performance prediction and model selection on unseen datasets.
4.1 LEARNING-GUIDED SELECTION FRAMEWORK
Temporal-Aware Data Encoder. In time series modeling, capturing temporal dependencies and sequential patterns is essential for accurate forecasting. Relying solely series makes it difficult to represent the fine-grained temporal structure. To effectively model tem- poral characteristics, we follow well-established design and divide the time series X R with L time steps across C' variates into patches of size S, yielding P P= [L/S] patches. Each patch Xp E SxC is linearly projected into a d-dimensional embedding X,, E R Rl forming patch embeddings Faacch E Pxd To preserve temporal order, the positional encodings Epus E TR Pxd following (Vaswani et al. 2017) are added: Fimp = Fepuich + E
informaifonattonnn of time
The resulting embeddings Fiup are fed into a self-attention module to capture long-range dependen- cies, where W E Rdxd, Wgge E Raxd, and We Radd are the learnable projection matrices:
Eg = SA = softmax (Emp Wa WRe) /V dy Emp W
(2)
Downstream datasets are often large, making full-dataset encoding computationally expensive and limiting the diversity of learned representations. To address this, we introduce a multiple-subset sampling strategy, where multiple subsets of B time series are sampled from the same dataset, and their attention outputs E., are aggregated into Emsb E BBx These subsets collectively offer more comprehensive representation of the overall dataset. Aggregating the compatibility across these diverse subsets, rather than relying a single random subset, more faithfully reflects the dataset-level compatibility and effectively balances intra-dataset variance. We then apply mean pooling along the batch dimension to produce compact and informative data embedding Ea Rxd, which captures shared temporal patterns within the subset while remaining robust to sample- expressive summary of downstream tasks,
level variability. Finally, the resulting F. serves allowing for compatibility scoring with model embeddings during model selection.
Enowledge-Infused Model Encoder. Directly embedding model with millions of parameters and a complex structure is challenging. To characterize a pre-trained model Φx. we infuse three key components: meta-information, topological structure, and functionality. This design aligns with hu- man intuition in model selection (e.g.. "choose a larger model for complex tasks"), " which has been largely overlooked in existing methods. The mefa-information embedding oe e R. xd, encodes prior knowledge from the pre-training to guide model selection. We consider: (1) Model architec- ture: Categorized into encoder-only, decoder-only, and encoder-decoder, reflecting structural design and training characteristics. (2) Model capacity: Estimated by parameter count, indicating ability to capture complex patterns. (3) Model complexity: Measured in Giga Multiply-Accumile
R1xd,
op-
erations (GMACs). Generally, higher complexity allows the model to capture richer patterns. (4) Model dimension: The hidden dimension size across inputs, states, and outputs. Larger dimen- sions enable the model to learn more expressive and detailed information. (5) Pre-trained domain: Models pre-trained on similar domains typically transfer better. More details of these five types of inta-information for each model are provided in Appendix A.5
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Training Tasks
Task
Support
Query
Learning-Guiled Selection
Teut
Liseen
Cross-lick Learning
Datnvr
Ranking
Aggregator
Concat
K
Expert
Expert 2
Expert G
Horizon-kdaptive Expert Composition
Mett Information
Functionality
Router
Patchmise Cross-Aftention
Horizon
Linear
Mode' compleoyyy
Data Embrdding
Model Embreding
Prearalse dowala
randoon rigut
Mcan Pooling
Topolrgical Structure
Encoder
Model Encoder
GraphZvee
Self-Atteation
Datasets
DAG
Patck
A,
Figure 2: The framework of SwiftTS, consisting of (I) temporal-aware data encoder, (2) knowledge-infused model encoder, (3) patchwise cross-attention, (4) horizon-adaptiie expert com- position module, and (5) the transferable cross-task learning.
The topological structure provides detailed view of model's architecture and inductive biases. Structural information, such as layer depth, data flow, and connectivity reveals how models process inputs, extract features, and make predictions. We first represent the architecture of the model Øs as a directed acyclic graph (DAG), denoted by G3 Ev, Ag), ), where V₁, and Eg denote vertices and edges, and Ag represents the node attributes. By leveraging the chain rule and gradient propagation maps, we trace how data flows through the network, thereby identifying the operations applied to the data and the directed paths along which the data travels. In this DAG, each node corresponds to computational operation performed within the network (e.g., normalization, activation). The edges correspond to the directed paths along which the data are propagated, reflecting the computational dependencies and information flow within the model. Once the DAG is constructed, we employ graph2vec (Narayanan et al. 2017 Rozemberezki et al. 2020). unsupervised graph embedding method inspired by doc2vee (Le & Mikolov 2014) to obtain the topological embedding vf RIxd.
The functionality reflects how pre-trained parameters encapsulate the biases and knowledge ac- quired during pre-training. Since directly embedding millions of parameters infeasible, we adopt functional embedding inspired by model distillation, which characterizes model through its input-output behavior. The intuition simple: models with different architectures or parameters implement distinct functions and thus expected to produce distinguishable outputs identical inputs. Although using real or synthetic time-series inputs can reflect how a model responds to the real-world time series, it causes the resulting functional embedding inadvertently inherit biases or domain-specific priors from the chosen probing data. For example, model would yield a more fa- vorable embedding than others simply because the probing inputs are similar its pre-trained data, which is unfair to other models. In contrast, random Gaussian noise serves as a neutral stimulus, which enables us to observe the model's intrinsic input-output behavior without imposing external assumptions. Therefore, we feed a fixed set of Gaussian random noise inputs ~ N/O,, I) into each model db and record the outputs 2a (c) as its functional embedding, where oft IR xde
Finally, we integrate the meta- ietta-informtiion embeddings v, E Rxd,, the topological embeddings v. I Kx,, and the functional embeddings v, E R xde of the model hub by concatenation, then project the result through linear transformation W., Idx(d,+ to generate the final model embedding E, R Kxd,
and nonlinear activation
E,n = a ((v,, vc J. w.)W"
Patchwise Compatibility Score. To facilitate fine- mane-grained and context-aw comparison between downstream datasets and pre-trained models, we compute compatibility score using patchwise
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cross-attention (CA). Unlike global similarity measures, patchwise cross- cross-attention captures local- ized correspondences by assessing each data patch's contribution to overall compatibility. Specifi- cally, the model embedding E. the query, and the data embedding Ea as the key and value:
Eça CA(Em Ea) softmax (En (EaWx)" /Vdx E
(4)
where W Rdddd Wx Rdddd We Raxd are projection matrices. This mechanism enables the model to focus semantically meaningful patches in the data that are most relevant to the char- acteristics of the model. Finally, a multi-layer perceptron (MLP) produces the ranking prediction, where & E RK denotes the predicted ranking scores for K candidate pre-trained models:
MLP(EE.)
(5)
Learn-to-select Optimization. During training, we adopt a joint objective combining ranking reg- ularization and prediction accuracy. The ranking loss enforces correct relative orderings among pre-trained models, while the prediction loss (MSE) ensures precise performance estimation:
K
Liotal
(f) log (x)r +
| fx
(6)
km
ranking loss
prediction loss
where á and denote the predicted and ground-truth ranking scores, (f) and (x(r)) their softmax-normalized forms of the k-th model, and fy. Tk are the corresponding individual scores.
4.2 GENERALIZABLE MULTI-TASK META-LEARNING
Horizon-Adaptive Expert Composition. Time series models often perform inconsistently across forecasting horizons, leading varying rankings. To equip framework with the multi-task flexibility to accommodate varying horizons, we propose a horizon-adaptive expert composition module that dynamically integrates specialized experts for different horizons. A lightweight router network assigns boftmax-normalle weights to G experts based on the target horizon H:
softmax (Router( H; 02))
where 9. denotes the parameters of the router, and I the expert weights. Each expert, implemented as an MLP, processes the cross-attention output E. to generate the final prediction through a linear combination of the expert outputs to replace Equation (5)
Wg MLP (LPg(EEa)
This design flexibly adapts to diverse horizons without the need for retraining, enhancing both pa- rameter sharing across tasks and improving computational efficiency.
Transferable Cross-Tase Learning. Existing methods often struggle to generalize when faced with datasets that deviate significantly from the pre-training distribution. This presents major challenge in real-world applications, where data distribution can vary widely across different domains. This issue is particularly pronounced in time series forecasting, where model performance is not only influenced by the nature of the dataset but is also highly sensitive to the forecasting horizon. To achieve robust and flexible model ranking and selection, we focus on two types of OOD scenarios: (1) generalizing model rankings from previously seen datasets to unseen datasets, which requires learning transferable features that capture the essential characteristics governing model performance; and (2) transferring performance prediction across different horizons, which demands understanding how model capabilities evolve with forecasting horizons.
To enable transferable cross-task learning and enhance the model's ability to adapt to diverse sce- narios, we incorporate meta- learning (Finn et al., (017)) into our framework. Given the constructed meta-dataset Dmeta {D', Z, H' 1==1 sample set of diverse tasks T {T1, Tz. ..., Tn where each task is divided into a support set and a query set. During training, as shown Figure the support set is used to simulate fast adaptation new conditions without updating the parameters,

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referred to as the inner-loop update. Subsequently, the query set evaluates the model's performance after adaptation and involves actual parameter updates, constituting the outer-loop update.
We introduce two task sampling strategies to explicitly encourage effective cross-domain and cross-horizon generalization: (1) cross-dataset sampling, where tasks and their support and query sets are drawn from different datasets to promote generalization across domains. (2) cross-horizon sampling, where tasks and their support and query sets are constructed from varying forecasting horizons to enhance adaptability at the horizon level. By exposing the model to these heterogeneous conditions during meta-training, it is encouraged to identify both shared and domain-specific patterns, recognize the underlying structures that govern pre- trained model performance, and improve model selection across diverse forecasting scenarios. In practice, downstream datasets and target fore- casting horizons often exhibit greater diversity. To simulate more realistic and challenging con- ditions, we combine the above two strategies into a unified sampling approach. Specifically, within single meta- training task, the support set and the query set are randomly sampled from disjoint collections of datasets and forecasting horizons, ensuring that there is no distribution leakage and minimizing task redundancy.
A L
Mata kommly
Deman
1.2
Loa Adiptatio
Domais
05
1 1
Horvee
Themais
0g4
D Baok
Doeman 3
Suppor
Query
Training Tasks
To formalize the cross-task learning process, we treat each sampled task an independent learn- ing episode during training. In each episode, the model first adapts to a support set, simulating rapid adjustment to a new domain or forecast- ing horizon. The adapted parameters are then evaluated on query set, and the meta-gradients are computed based on the performance this query set. These gradients subsequently used to update the initial model parameters in direc- tion that improves generalization across tasks. Formally, let represent the initial parameters of the model. For a given task Tú, we compute the task-specific parameters 0g via few gradient steps on the support set: set:
Support
Query
Task N
Counges
-
Modiel Ranking on Unsern distect
Test
horison-specilee prefiction
Figure 3: Parameter update process in cross-task learning (top-left), and sampling strategies for cross-horizon and cross-dataset tasks (bottom).
(9) where is the inner-loop learning rate and Lsupa (Ts; 0) denotes the loss function evaluated on the support set of task T. as defined in Equation 6 The adapted parameters 8 are then evaluated on the query set to compute the meta-objective that measures how well the model generalizes after adaptation: Lquery (Ti; 0'). This loss is also computed as defined in Equation (6). Finally, the model parameters are updated using the meta-gradient across all tasks:
0' = - a V Suup (T:; 0)
レ 0 - v Σ querry (Tr; 8)),
(10)
where y is the outer-loop learning rate. By repeatedly performing the two-step optimization process, which consists of lnner-loop adaptation and outer-loop generalization, the model learns parameters that enable rapid adaptation to new domains or forecasting horizons with minimal data and compu- tational resources. Please refer to Algorithm| for the overall algorithmic process.
EXPERIMENTS
5.1 EXPERIMENTAL DESIGN
Datasets. We evaluate SwiftTS on 14 public time series forecasting datasets across diverse do- mains, including electricity (ETThI/ETTh2 (Zhou et al.] 2021). ETTm//ETTm2 (Zhou et al.] 2021), Electricity (Trindade 2015)). energy (Solar (Lai et al. 2018). Wind (Li et al. 2022 traffic (PEMS08 (Song et al., 2020)) Traffic (Wu et al. 2021)). environment (Weather ( (Wu et al. 2021). AQShunyi (Zhang al. 2017)), natural (ZatNoo (Poyatos al. 2021), Czelann (Poyatos et al.
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Table 1: Method comparison of the weighted Kendall's Tu across 14 datasets and their average. The best and recond-best results are in bold and underlined. Our method achieves the best overall Tw-
Horizon
RankME
LogME
Regression
Eiran
DISCO
AutoForecast
Model spider
zero shol
SwiRTS
Hw9h
0.257
0.287
0:213
0.224
0.309
0.464
[I=192
0.182
0.014
0.104
0.147
0.059
0.233
0.386
.0.058
0.479
kTTh
H=336
-0.036
0.232
0.436
H=720
0.086
0.196
0.108
0.147
0.019
0.329
0.354
0.241
0,543
H=36
0.256
0.156
0.29%
0.398
0.436
ETTh2
11-192
0.101
00.150
00,059
0.333
-.165
0.197
0.451
0,430
0.330
H=336
0.269
-0.154
0.185
0.219
H=720
0.053
-0.014
-0.069
0.106
0. 188
0.246
0,345
0.474
0.351
H=36
0.005
0.691
-0,407
-0,243
0.501
ETTml
H=192
0.005
0.079
0.079
0.552
-0.406
-0,243
0.567
-0.040
0.501
H-336
-0.529
-0.048
-0.048
0.099
191
0.075
0.590
-0.276
0.652
H=720
0.479
00027
0.027
0.173
1.166
0.169
0.266
-0.041
0.269
H-96
0.140
0,080
0.334
0.913
0.613
-0,164
0.067
0,283
0.847
ETTm2
H=192
0.128
0.020
0.164
0.568
0.520
00243
0.696
0.319
1.000
H=336
0..188
-0.21
0.159
0.700
0.473
-0,304
0.698
0.727
0.663
H=720
-0.088
0.050
0.163
0.485
0.165
-0.155
0.356
0.078
0.534
1136
-0037
0.317
0.317
0.559
0.002
0,060
0,311
0,162
0.361
Electrictty
H=192
0.043
0.306
0.306
0.685
-0.585
-0.161
0,549
0.093
0.240
H=336
-0330
-0.419
-0.419
-0,009
0.091
-0,098
0.358
-0.279
0,520
H=720
-0.403
-0.344
-0,344
0.027
0.148
0.009
0.356
0.029
0.394
1136
00.138
0.039
40124
40.0%
0.148
0.114
0.049
-0.312
0.247
Traffic
H=192
-0.444
-0.432
-0,432
-0.338
0.225
0.324
+0,005
+0.198
0.351
H=336
-0,569
-0.568
-0.568
-0.692
0.643
0.092
0,030
-0.026
0.066
H-720
-0.748
-0.565
-0.394
0.223
0.092
0.420
0.702
H=96
-0.214
0,120
0,222
0.359
-0.569
+0.050
0,452
0,308
0.222
Solar
H-192
00017
0,400
0.246
-0.022
0.070
[1=336
0.003
0.553
0.553
0,359
00299
-0,145
0,250
+0.395
0.277
H=720
0.527
0.055
-0.703
1156
0.015
0.381
01034
0.499
0.273
0,274
0.543
0.128
0.285
Weather
H=192
-.1188
0.466
0.024
-0.130
0.129
[1=366
0.171
0.102
0.0066
0.539
0.404
.0193
0,340
0,321
0.108
H=720
0,241
0.745
-0.155
0.316
1156
0.032
0.492
0.343
0.193
0.112
0.598
0.059
0.284
0.251
Exchange
H=192
-0.99
-0.414
0.152
-0,404
0.252
H=336
-0.112
-0.336
-03306
0.148
0,250
-0,552
0.230
-0.143
0.233
H-720
-0.210
-0617
-0,44
-0.024
0.536
-0.733
0.322
0,126
-0.386
H=96
-0.117
0.058
-0.148
0.113
-0.133
0.454
0,511
-0.384
0.656
ZafNoo
192
-0,285
-0.235
-0,274
-0.044
-0.035
0.454
0.436
-0.017
0.786
H=336
0.285
0.040
0.113
.0073
0.200
0.454
0.580
0.023
0.732
H=720
-0,224
-0.16
40225
0.129
-0,235
0.478
0,552
0,164
0.668
1196
0.103
0.071
00012
0.632
0.343
0.574
0.121
0.171
0.575
CzeLan
H=192
-0.37
-0.376
-0.258
0.337
0.362
0.499
0.217
0,171
0.527
H=336
0.069
0.090
0.155
...009
.0.154
0.573
.0.009
0.301
0.847
H=720
-0.125
-0214
40.74
40.125
-0.136
0.519
0.349
0,282
0.839
1196
0.371
0.283
0.270
4.117
0.107
0.390
0.414
0.349
0.9.9
AQShunyi
H=192
-0.407
0,328
0.328
-0.045
-0,224
0.438
0.126
0.309
0.734
H=336
-0.377
-0.184
-0.255
-0.277
0.276
0.411
0.084
0.420
0.723
H=720
-0.332
-0.140
-0.209
-0,253
119
0.370
0.355
0.675
0.701
H=96
0.211
0.142
0.062
0,417
-0.196
0.251
0.244
40.106
0.395
Wind
H=
0.211
0,258
0.231
0.136
0.482
0.251
0.355
-0.155
0.395
0.119
0.338
-0,532
0.097
0.262
I1=220
0,040
0.474
D.443
0.126
.0.377
0,015
0,202
0,153
0.162
H=9b
0.118
40253
0.1TO
0.036
4..00S
0.401
PEMSO8
[1=192
0.038
-0.003
-0,003
40321
-0068
0.044
003188
0.420
0.505
H=336
-0,296
.0.791
-0.029
-0.18
00.055
0.016
[1=720
0.637
-0.244
-0,244
-0.178
0.070
.0003
-0.345
0.452
0.442
H=96
0.056
0.318
0.003
0.069
0.319
0.470
[1=192
0.046
-0.027
0.006
0.212
0.023
0.079
0,301
0,104
0.453
H=336
-0.066
-0.004
0.066
0.045
0.411
H=720
-0,238
-0,090
-0.054
0.073
0.040
0.059
0.271
0,251
0.432
Nup-opp-1
28
202T), and economics (Exchange (Lai et al. 2018)). Dataset statistics are detailed in Appendix A. To ensure reproducibility, we follow standard dataset splits: training and validation sets are used for model selection, while the test set is reserved for evaluating ground-truth fine-tuning performance.
A.
Pre-trained Models. To ensure robust evaluation, we select eight ofte-oofttheant time series pre- trained models from diverse architectures and training paradigms: (1) Encoder-only: MOIRAI (Woo)
et al. 2024). UniTS (Gao et al.] 2024), and Moment (Goswami et al. 2024); (2) Decoder-only:
TimesFM (Das et al. 2024) and Timer (Liu et al. 2024); (3) Encoder-decoder. TTM (Ekambaram
al.) 2024), ROSE (Wang al. 2024), and Chronos (Ansari et al.) 2024). We collect ground-
truth fine-tuning results from the TSFM-
benchmark (Li et al. (025) for common forecasting
horizons of (96, 192, 720). with the full results provided in the Appendix A.9
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Table 2: Methods comparison of Pr(top-k) and average across horizons on 14 datasets.
Table 3: Ablation studies for model embedding: Tw and average across horizons are listed below.
Pr(topl)
Pr(top2)
Pr(top3)
Tw
Va
Ve
96
192
336
720
avg
RankME
0.000
0.000
0.196
-0.119
0.341
0.283
0.331
0.401
0.339
LogME
0.071
0.196
0.268
-0.041
0.225
0.270
0.318
0.227
0.267
Regression
0.036
0.125
0.286
-0.019
v
0.365
0.401
0.317
0.397
0.370
Etran
0.304
0.393
0.536
0.150
0.361
0.383 0.315
0.417
0.369
DISCO 0.232
0.375
0.536
0.033
Model Spider
0.304
0.482
0,571
0.296
V
0.427
0.430
0.328
0.391
0.394
zero shot
0.286
0.464
0.589
0.125
V
0.380
0.422
0.437
0.403
0.411
SwiftTS 0.339
0.500
0.607
0.442
V v 0.470 0.453
0.411 0.432 0.442
Baselines and Metries. We compare various model selection methods under three paradigms:
(1) Feature-analytic methods: RankME (Garrido et al. 2023), LogME (You et al. 2021), Re-
gression (Gholami et al., [023), Etran (Gholami et al. 2023). DISCO (Zhang et al.,
2025).
(2)
Learning-based method: Model Spider (Zhang et al. 2023), AutoForecast (Abdallah et al. 2022
(3) Brute-force method: Zero-shot performance. Further details are provided Appendix A.2
For evaluation, we use weighted Kendall's Tw to measure the correlation between estimated scores
[ and fine-tuned results {rx 1/
following previous work (Shao et al. 2022 Gholami et al,
2023 Li et al. 2023 Zhang al.) 2025 A larger Tw indicates stronger alignment between estimated
and true rankings. Details are in Appendix A.3
Implementation. To assess generalization unseen tasks and prevent data leakage we adopt strict splitting protocol: in each training run, we randomly select out of the 14 benchmark datasets held out for testing, while the remaining 11 are split into training and validation sets using an 8:2 ratio. During training, a multiple-subset sampling strategy is applied to each dataset to construct the meta-dataset D meta- Once sampling is completed, the data encoder receives fixed set of subsets across runs to ensure reproducibility. During evaluation, the same multiple-subeet sampling strategy used. In the rare case where different subsets of the same dataset yield inconsistent rankings, we adopt voting-based ensemble to obtain the final model ranking. All experiments are conducted on an NVIDIA GeForce RTX 3090 GPU with batch size 16 for 80 epochs, using Optimization is performed with Adam (3) 0.9, 322 0.999). In the meta-learning process, the inner-loop and outer-loop learning rates are a = 0.001 and 7 = 0.005. The loss trade-off coefficient is A 0.7, with sensitivity analysis in Section A.8
experts.
5.2 EXPERIMENTAL RESULTS
Main Results. Table compares SwiftTS with various baselines across 14 datasets and four hori- zons of (96, 192, 336, 7203. The results demonstrate that SwiftTS outperforms the baselines in av- erage Tu across all horizons, highlighting its effectiveness in selecting high nigh-performing pre-traines models. Feature-analytic methods often suffer from inconsistent features derived from pre-trained models with diverse architectures and paradigms. Model Spider alleviates this issue by learning a similarity function between datasets and models, but it overlooks sequential dependencies in time series and prior knowledge of the models. In contrast, SwiftTS employs a dual architecture con- sisting of a temporal-aware data encoder and knowledge-infused encoder, which together enhance selection performance. Additionally, SwiftTS features a dorizon-adaptin expert composition mod- ule, allowing to handle multiple horizons simultaneously within a unified framework. By com- parison, all baselines require recomputation or retraining for different horizons. This efficiency makes SwiftTS well-suited for real-world applications demanding flexible multi-horizon forecast- ing. Morcover, while other methods exhibit varying degrees of negative correlation in different datasets and horizons, SwiftTS adopts transferable cross-task learning to maintain predominantly positive correlations across 14 datasets and different horizons, showing its OOD robustness.
Top-k Performance. We report the top-k selection probability Pr(top-k) as used in (Zhang et al. 2025 Gholami et al. 2023). This metric evaluates the likelihood that the best-performing model appears within the top-k of the estimated ranking. Results in Table 2 demonstrate that SwiftTS achieves the best top-k performance, validating the model selection effectiveness of our method.
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Weigital Kendallts r
Waightd Kemdell's
Waghtel Kemdall''s
Weighted Kendall's
0.2
0.6
0.4
0.3
Regissiion
0.3-
0.2
0.2
0.2
IID
0.1
Wio (ooe--inkkk leoming leaning
0.1
0.0
EtTma
ZafNoo
Czel.n sa
AQShunyi
0.0
336
720
0.0
Ix10
2x10
5-10
4-10
-0.6
10
10"
10
Running Time
(a) IID vs. OOD
(b) Cross-task learning
(c) Time cost (ETTh1)
(d) Time cost (Traffic)
Figure 4: (a) Comparison of (a) average Tu for IID vs. OOD settings across four datasets and horizons, and (b) ablation study of cross-task learning, and method comparison w.r.t running time (second) and average Tu across horizons (c) ETThl (small-scale) and (d) Traffic (large-scale).
5.3 FURTHER ANALYSIS
Embedding ablation. The model encoder integrates three embeddings to represent neural net- work: mneaainformation embedding (Va), topological embedding (Vz), and functional embeddings (v.). To assess their individual contributions, we perform ablation studies by removing one or two embedding type time and measuring the resulting performance. As shown in Table 3 meta- information embedding Va and the functional embedding t, contribute the most to performance. The best results are obtained when all three embeddings are utilized together, demonstrating the complementary nature and necessity of each type of embedding.
IID vs. OOD, In Figure 4a we compare the average Tw performance of four forecasting horizons under IID and OOD settings across four datasets. Compared to OOD, the IID setting refers to evaluation on test data drawn from the same distribution the training data. The results show that our method achieves further improvements under the IID setting, indicating that increasing the diversity of training data can enhance model performance.
Cross-task learning ablation. To validate the effectiveness of the proposed transferable cross-task learning, we conduct an ablation experiment as illustrated in Figure Specifically, we evaluate the model's 's average performance observed when comparing the results from the w/o cross-task learning setting to those with the cross-task learning enabled. This consistent improvement across horizons demonstrates that cross-task learning effectively enhances the model's predictive capability and robustness.
14 downstream datasets across four horizons. A clear advantage
Efficiency and Scalability. We evaluate efficiency by analyzing runtime small (ETTh1) and large (Traffic) datasets (Figure 4c Figure 4d). Results show that model selection methods significantly reduce computational overhead compared full fine-tuning. For example, ETTh1, model selec- tion methods typically require only 1,000 to 4,000 seconds, whereas fully fine-tuning each model takes approximately 4.97 10a seconds the same GPU. This stark contrast highlights the critical importance of efficient model selection methods in practical applications. Moreover, the comparison across different dataset scales reveals that the runtime cost of SwfitTS remains relatively stable and is less sensitive to dataset size. In contrast, the time overhead of other model selection basclines increases dramatically as the dataset grows. The cost of fine-tuning on the Traffic dataset reaches up to 3.46 x 10" seconds, making it prohibitively expensive for large-scale applications. Overall, SwiftTS achieves both superior performance and minimal time overhead.
CONCLUSION
This paper tackles the challenge of pre-trained model selection from a model hub for time series forecasting, We propose SwiftTS, learning-guided framework with lightweight dual-encoder architecture that independently embeds time series and candidate models, computing patchwise compatibility scores for efficient selection. To further enhance adaptability, SwiftTS incorporates a horizon- adaptive expert composition module for multi-task forecasting and leverages transfer- able cross-task learning to improve generalization across datasets. Extensive experiments show that SwiftTS achieves SOTA with high efficiency and scalability for real-world deployment.
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ACKNOWLEDGMENTS
This work supported by the National Natural Science Foundation of China (62406112, 62306085, 62372179) and Shenzhen College Stability Support Plan (CXWD20231
ETHICS STATEMENT
This work is conducted entirely on publicly available benchmark datasets, detailed in the paper, and does not involve the release of any personal or sensitive information. No human subjects are involved in this research, ensuring that our work complies with ethical standards in research integrity.
REPRODUCIBILITY STATEMENT
The performance of SwiftTS and the datasets used in our work are real, and all experimental results can reproduced, as detailed in the paper. Details of model architecture, training procedures, and evaluation protocols are provided in the main text and appendix. To further facilitate reproducibility, we release the code and datasets at
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A APPENDIX
A.1 DATASETS
We evaluate SwiftTS on 14 multivariate time-series datasets spanning six distinct domains, including electricity, energy, traffic, environment, nature, and economics. (1) The ETT datasets (Zhou al. 2021) contain 7 variables collected from two different power transformers between July 2016 and July 2018. The dataset consists of four subsets: ETThl and ETTh2, recorded hourly, and ETTml and ETTm2, recorded at 15-minute intervals. (2) Electricity (Trindade 2015) records hourly elec- tricity consumption from 321 customers over three years, from July 2016 to July 2019. (3) Solar (Lai et al. 2018) captures solar power generation from 137 photovoltaic plants in 2006, sampled every 10 minutes. (4) Wind (Li et al. 2022) consists of historical wind measurements (c.g., speed, di- rection). (5) PEMS08 (Song et al. 2020) contains three months of aggregated statistics on traffic flow, speed, and occupancy rate. (6) Traffic (Wu et al.) 2021) contains hourly road occupancy rates measured by 862 sensors across freeways in the San Francisco Bay Area from 2015 to 2016. (7) Weather (Wu et al.] 2021) includes 21 meteorological variables (e.g., temperature, humidity, and barometric pressure), recorded every 10 minutes across Germany in 2020. (8) AQShunyi (Zhang) et al., 2017) provides hourly temperature measurements exhibiting strong seasonal patterns. (9) ZafNoo (Poyatos al. 2021) collected from the Sapflux data project and includes sap flow mea- surements and environmental variables. (10) CzeLan (Poyatos et al. 202T) is from the Sapflux data project, including sap flow measurements and environmental variables. (11) Exchange (Lai et al. 2018) comprises daily exchange rates for eight countries over multi-year period. Table summarizes the key statistics of these multivariate time series datasets.
Table 4: Statistics of datasets.
Dataset
Domain
Frequency Lengths Dim Split
ETTh1
Zhou et al.
2021
Electricity
hour
14,400
7 6:2:2
ETTh2
Zhou et al.,
202T
Electricity
hour
14,400
7 6:2:2
ETTml
Zhou et al.
2021
Electricity
15 mins
57,600
7 6:2:2
ETTm2
(Zhou al.
2021
Electricity
15 mins
57,600
7 6:2:2
Electricity (Irindaee)
2015
2015
Electricity
hour 26,304
321 7:1:2
Solar (Lai et al. 2018
Energy
10 mins
52,560
137 6:2:2
Wind Li et 2022
Energy
15 mins
48,673
7 7:1:2
PEMSO8 (Song et al.
2020)
Traffic
5 mins
17,856
170 6:2:2
Traffic (Wu et at.
202T)
Traffic
hour
17,544
862 7:1:2
Weather Wu et al. [2021]
Environment
10 mins
52,696
7:1:2
AQShunyı Zhang et al.
2017
Environment
hour 35,064
11 6:2:2
ZafNoo PPoyatos et al.
2021
Nature
30 mins
19,225
11 7:1:2
CzeLan (Poyatos et
2021
Nature
30 mins
19,934
11 7:1:2
Exchange [Lai et al.
2018
Economic
1 day
7,588
8 7:1:2
A.2 BASELINES
In our study, we compare various model selection methods for pre-trained time series models, which can be broadly categorized into three paradigms: (1) Feature-analytic methods: These methods rely on intrinsic properties or statistical characteristics of features extracted by the pre-trained mod- els to estimate their transferability. RankME (Garrido et al. 2023) evaluates the rank of feature ma- trices extracted from the model's representations. LogME You et al. 202T) computes the logarithm of the maximum label marginalized likelihood under a probabilistic model. Regression (Gholami et al. 2023) employs linear regression using Singular Value Decomposition (SVD) to approximate
the mapping from model features to target labels. Etran (Gholami et al. 2023) combines both the energy score and the regression score into unified metric. DISCO (Zhang et al. 2025) evaluates pre-trained models by analyzing the spectral distribution of their feature representations, enabling the assessment in both classification and regression tasks. (2) Learning-based method: Model Spider (Zhang et al,, 2023) learns model representations and a similarity function through align- ment with downstream task representations, facilitating model selection via the learned similarity.
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AutoForecast (Abdallah al. 2022) leverages the performance tensor and the meta-feature tensor to predict model performance under different hyperparameters. (3) Brute-force method: Zero- shot measures model's ability generalize to unseen tasks without any task-specific fine-tuning, offering valuable insights into its overall generalization capacity.
A.3 METRICS
Kendall's r measures the ordinal association between two rankings by evaluating the number of concordant and discordant pairs, which is defined as:
2 K(K- - ISiSJKK
sgn(r" - P )sgm(f' - Pt)
(11)
where sgn(r) is the sign function. However, in practical model selection scenarios, accurately iden- tifying the top-performing models often more critical than precisely ranking lower-performing ones. To reflect this priority, we employ the weighted version of Kendall's т, denoted as Tw- This variant adjusts the contribution of each pairwise comparison by assigning larger weights to higher- ranked models. A higher value of indicates stronger consistency between estimated and actual rankings, reflecting the reliability of the evaluation metric in guiding model selection.
A.4 ALGORITHM
Algorithm 1: Pseudo-code of Swi ftTS
Training:
Input: Meta-dataset Dmeta = {Di, Z, H r() Ji=1: Total training epochs E; Inner-loop learning rate o; Outer-loop learning rate 7
Randomly initialize the weights 0 of the whole model;
for E f to E do
T < Sample tasks from D menta: for j e n do supporlj, query; <- Obtain support and query from Tj;
8
4- Mode Rankinnnnnn (Z, supportj, H)
Evaluate va (T,; (): using 6
Compute 0j - 8 a supp Ty;0);
Update + 0 - Ve Σr, Equary (T₁; 03;;
Inference:
13 Input:
An unseen downstream dateset X, model hub Z, forecasting horizon H;
k- Model Meaeeinn (Z, X, H
15 Return: The predicted ranking scores for K candidate pre-trained models in the model hub.
16
Function ModelRanking X2 X)H H):
Ed, Em t- (x) Em (Z);
18
Eca + Compute patchwise CA using Eq.
w +- Compute the weights that router assigns to each expert using Eq. with H;
20
Return: <- Rank pre-trained models using Eq.
A.5 DETAILS META-INFORMATION PRE-TRAINED MODELS
The five types of meta-information of pre-trained models include: model architecture (category), model capacity (scalar), model complexity (scalar), model dimension (scalar), and pre-trained do- main (category). Categorical features converted into one-hot vectors. For the pre-trained do- main, which may involve multiple labels, a multi-label one-hot vector employed to represent each domain. Scalar features normalized based their minimum and maximum values across all
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Table 5: Embedding computation runtime (in seconds) for each model.
Embedding TimesFM
UniTS
Moment
TTM
Moirai
Rose
Timer
Chronos
functional
0.714
0.335
0.578
0.247
0.606
0.438
0.396
0.683
topological
1.092
0.471
2.328
0.317
1.084
0.532
0.490
1.720
models. The resulting normalized scalar features and one-hot encoded categorical features are then concatenated to construct the meta-information embedding. Since the meta-information embedding may have semantic gap with the topological and functional embedding, we apply linear projec- tion to map it into shared latent space. The projected embedding is subsequently integrated with the topological and functional embeddings, as described Equation 3 to generate the final model representation used in our model selection framework.
A.6 EFFICIENCY ANALYSIS OF TOPOLOGICAL AND FUNCTIONAL. EMBEDDINGS.
The construction of both topologiaal and functional embeddings an offline, dataset-agnostic pro- cess. It only requires feeding each candidate model fixed input with the correct dimensionality (e.g., fixed set of Gaussian random noise vectors, rather than full downstream datasets). This in- curs a total preprocessing cost of O( -Teb)),, where N is the number of candidate models and Temb denotes the time required to compute the embeddings for a single model. We empirically evaluate the runtime (in seconds) required to obtain these embeddings for each model in Table
In contrast, existing approaches require substantial forward pasds computation over the entire down- stream dataset for every candidate model. This results in total cost of O(N (D))). Here, (D( = D] Cmodel). where [D is size dataset and Cmodel represents the per-sample com- putational cost. Thus, their runtime depends not only model complexity but also heavily the size of the downstream data. For example, on the same hardware, the forward-pass runtime of TimesFM (200M) 654.98 seconds on the relatively small AQShunyi dataset, but increases to 5,426.12 seconds on the larger Solar dataset. Overall, because Temb < T' (D) and the embedding computation is performed offline, the linear cost growth with respect N remains highly tractable. The per-model embedding overhead of SwiftTS is minimal and does not introduce resource bot- tleneck as the candidate models increases. Moreover, since embedding computation fully offline, it can be precomputed if still concerns about runtime.
A.7 SCALABILITY THE MODEL HUB
To investigate how the number candidate models affects the performance of SwiftTS, we augment the original model hub by adding six additional models: Chronos-mini and Chronos-small (the hub originally contained Chronos- base) (Ansari et al. 2024). Moirai-small and Moirai-large large (originally Moirai-base) (Woo al.) ) well as TomeMoE-base and TimeMoE- largee et al.) 2025). This expansion results in total of 14 candidate models in the model hub. We then compare SwiftTS
against existing baselines under these more challenging conditions. The performance, measured by the average weighted Kendall's Tμ across horizons on 14 target datasets, is presented in Table 6 The results show that increasing the size and heterogeneity of the model pool indeed makes the model selection task more challenging, leading to a certain degree of performance degradation for all methods. However, our framework exhibits notably lower sensitivity to this expansion and continues to outperform existing baselines.
A.8 MORE EXPERIMENTAL RESULTS
The perforamnce of Topl-selected model. We report the actual forecasting performance of the topl-selected model for each selection method, with the average MSE across horizons shown in Table 7 The "Best model" column denotes the performance of the ground-truth topl model, representing the upper bound achievable by any selection method. The results demonstrate that SwiftTS not only selects pre-trained models effectively but also delivers superior actual forecasting performance across wide range of datasets.
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Table 6: Scalability analysis the model hub with an expanded and more diverse of candidate
models. The average weighted Kendall's Tw across horizons on 14 datasets is listed below.
RankME
LogME
Regression
Etran
DISCO
Model spider
zero-shol
SwiftTS
ETThl
-0.207
0.103
0.074
0.207
0.106
0.236
0.274
0.402
ETTh2
-0066
-0.018
-0.056
0.175
0.109
0.347
0.248
0,423
ETTml
0.050
0.131
0.111
0.217
0.065
0.149
0.290
0.415
ETTm2
-0.099
0.022
0.075
0.303
0.208
0.151
0.304
0.453
Electricity
0.174
-0.019
0.132
0.100
0.043
0.089
0.188
0,383
Traffic
0.069
0.081
0.086
0.065
0.341
0.175
0.190
0.453
Solar
0.005
0.190
0.105
0.189
0.090
0.243
0.139
0.240
Weather
0.121
0.080
0.032
0.251
0.227
0.173
0.209
0.238
Exchange
0.032
0.019
0.151
0.129
0.272
0.095
0.024
0,286
ZafNoo
-0.150
-0.020
0.087
-0.016
0.092
0.440
0.186
0.649
Czel.am Ln
-0.257
-0.076
-0.110
0.150
0.047
0.333
0.219
0,515
AQShunyi
-0.077
0,004
-0.012
0.021
0.269
0,455
0.438
0,575
Wind
-0.242
0.176
0.189
0.228
0.039
0.181
0.056
0,310
PEMSOS
0.112
0.037
0.009
0.092
0.097
0.267
0.302
0,373
Table Performance of topl seeeeceee model. The average MSE across horizons listed below.
RankME
LogME
Regression
Eiran
DISCO
Model spider
zero-shot
SwilTTS
Best model
ETTHi
0,404
0.404
0.403
0.421
0.425
0,403
0.413
0,393
0.391
ETTh2
0,349
0.345
0.343
0.343
0.352
0.347
0.342
0.340
0.331
ETTml
0.735
0.345
0.345
0.346
0.436
0.383
0.345
0.341
0.340
ETTm2
0.304
0.258
0.258
0,251
0.276
0.269
0.253
0.251
0.246
Electricity
0.250
0,212
0.212
0.169
0.195
0.196
0.250
0.163
0. 0.155
Traflic
0.539
0.668
0.668
0.390
0.393
0.555
0.555
0.390
0.380
Solar
0.252
0.186
0.186
0.552
0.905
0.252
0.358
0.252
0.180
Weather
0.269
0.250
0.245
0.236
0,243
0.243
0.255
0.236
0.217
Exchange
0.407
0.477
0.484
0.490
0.388
0.407
0.419
0.406
0.362
ZafNoo
0.608
0.561
0.589
0.522
0.533
0.542
0.513
0.511
0.502
CzeLan
0.755
0.695
0.755
0.232
0.326
0.606
0.217
0.206
0.206
AQShunyi
0.692
Wind
1.194
1
1.163
1.101
1.372
1.194
1.243
1,138
1.101
PEMS08
0.687
0.255
0.319
0,538
0.496
0.505
0.479
0.495
0.490
0.436
0,402
0.381
Sensitivity Analysis. We examine the impact of X E [0.0, 0.5, 0.7, 1.0] and report average results across all datasets. As shown in Figure 5a the performance remains relatively stable due to the complementary roles of the two loss components: Lrank constrains the relative ranking among pre-trained models, while fpred enforces an absolute constraint on the gap between predicted per- formance and actual fine-tuning results, The experimental results highlight the indispensable role of the prediction loss and suggest that the best performance is achieved when À is set to 0.7.
Choices of Expert Numbers. We study the impact expert number G E [2,4, 6, 8, 10) (Figure 5b). A small G fails to adequately capture the differences across horizons, limiting its ability to perform effective multi-task forecasting. Conversely, a large G increases computational cost and model complexity, which may lead overfitting and degraded performance on downstream tasks. Overall, G = provides the best trade-off between accuracy and efficiency, making it ideal for practical use.
Visualization. We visualize the patchwise cross-attention weights in Figure 6 which reveal several key observations: (1) Figure 6a 6a]aand and Figure 66b compare the data embeddings E, obtained from dif- ferent ETTh2 subsets. We observe that the weight distributions across different patches for the same model (same row) are quite similar. Furthermore, TTM and ROSE, the two best-perforning mod- els on ETTh2, also exhibit similar patchwise weight distributions. This suggests that models with comparable performance tend to share similar patchwise attention patterns within the same dataset. (2) When comparing F. from two similar datasets, ETTh2 (Figure (b)) and ETTh1 (Figure (6c), we find that the patchwise weight distributions for the same model remain relatively consistent. This indicates that similar attention patterns are exhibited not only across different subsets of the same dataset, but also between similar datasets. (3) In contrast, when comparing two more dis- tinct datasets, ETThl (Figure (c) and PEMS08 (Figure 6d), significant differences emerge in the patchwise weight distributions of the same model. Moreover, among the top- pop-efoormnng models PEMS08, such as Moirai, TimesFM, Moment, similar patchwise distributions are evident. The best model, Moirai, places the highest attention the 8-th patch, whereas weaker models, TTM and
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0.8
0.8
Weightd Kenally
0.6
Weightd Kenbills
0.4
0.4
0.2
0.2
1140
H-100
Ascage
H Avcage
19036
10036
0.0
0.0
03
1.0
0.0
values
mimber Hapert
(a) Sensitivity of X
(b) Choice of G
Figure 5: (a) Sensitivity analysis of the loss coefficient X, (b) choice of the number of experts G.
Closss
Cheasss TimeeMM
Ctrmes
Cheome
TimesFM
TimesM
Mamen
Momers
Momeni
TTM
Roo
83
Linls
1TM
9.2
0.1
UniS
TIM
Rose
0.1
UsIS
TIM
Roac
0.50
0.5
Timer
Timer
Timer
Timor
4.5
7
Pda
Park
Panch
Path
(a) Th (subsetl)
(b) ETTh2 (subset2)
(c) ETTh1
(d) PEMS08
Figure 6: Visualization of patchwise cross-attention weights.
ROSE, show considerably lower weights for that patch. This indicates that models with different performance levels tend to focus on different patches.
A.9 GROUND-TRUTH FINE-TUNING RESULTS
We obtain the ground-truth forecasting results of the pretrained models after fine-tuning from the TSFM-Bench benchmark to ensure fairness and reproducibility. For completeness, we further report the results Table
20

---

Published as a conference paper at ICLR 2026
Table 8: The ground-truth fine-tuning results of the pre-trained models in the model hub. The results are MSE of each prediction length.
Dataset
H
Chronos
TimesFM
Moment
UniTS
Moirai
TTM
Rose
Timer
0,388
0.373
0,383
0.399
0.394
0.361
0.354
0.416
0,418
0.415
0.441
0.430
0.393
0.389
0.557
ETTh1
336
0,477
0,457
0.425
0.503
0.450
0.411
0.406
0,502
720
0.475
0,458
0.447
0.468
0.457
0.426
0.413
0.525
96
0.292
0.288
0.287
0.311
0.285
0.270
0.265
0.305
192
0,362
0.371
0.350
0,470
0.352
0.338
0.328
0.394
ETTh2
336
0.404
0.418
0,367
0,429
0.384
0.367
0.353
0.414
720
0.412
0.441
0,404
0.424
0.419
0.384
0.376
0.521
96
0.339
0.313
0.287
0.321
0.464
0.285
0.275
0.344
192
0.392
0.353
0.326
0.373
0.488
0.325
0.324
0.447
ETTml
336
0,440
1.177
0.353
0.388
0.520
0.357
0.354
0.457
720
0,530
1.095
0.408
0.452
0.598
0.413
0.411
1.444
0.170
0.198
0.224
0.157
0.188
192
0,253
0,234
0,230
0,252
0.308
0.225
0.213
0.281
ETTm2
336
0,357
0,283
0,334
0,369
0.275
0.266
0.328
720
0,454
0.375
0.468
0.460
0.367
0.347
0.493
96
0,133
0,142
0.148
0.133
0.170
0.132
0.125
0.136
192
0.152
0.163
0.165
0.153
0.186
0.149
0.142
0.169
Electricity
336
0.171
0.332
0.182
0.175
0.205
0.270
0.162
0.196
720
0.201
0.364
0.223
0.204
0.247
0.297
0.191
0.364
96
0.385
0.419
0.383
0.377
0.358
0.379
0.354
0.362
192
0,411
0.450
0.397
0.387
0.372
0.396
0.377
0.396
Traffic
336
0.521
0.939
0.407
0.395
0.380
0.945
0.396
0.427
720
0.623
0.957
0.443
0.436
0.412
0.952
0.434
0.970
0,430
0.174
0.172
0.163
0.877
0.174
0.170
0.183
192
0.396
0.198
0.187
0.176
0.928
0.181
0.204
0.225
Solar
336
0.409
1,530
0.196
0.184
0.956
0.189
1.616
0.244
720
0,453
1.322
0.206
0.196
1.016
0,200
0.215
0.355
96
0.183
0.161
0.152
0.147
0.206
0.149
0.145
0.164
192
0.227
0.207
0.196
0.191
0.278
0.199
0.183
0.243
Weather
336
0.286
0,311
0.245
0.243
0.335
0.256
0.232
0.321
720
0.368
0.370
0,316
0.317
0.413
0.340
0.309
0.349
96
0.093
0.086
0.085
0.444
0.096
0.113
0.086
0.104
192
0.199
0.193
0.178
0.507
0.200
0.223
0.178
0.221
Exchange
336
0.370
0.354
0.333
0.489
0.381
0.439
0.341
0.382
720
0.856
0.988
0.851
0.997
1.133
1.185
0.947
0.965
96
0.463
0.457
0.430
0.444
0.439
0.426
0.431
0.470
192
0,524
0,576
0.486
0,507
0,501
0.479
0.487
0.548
ZafNon
336
0.575
0.650
0.530
0.563
0.551
0.523
0.538
0.588
720
0.684
0.748
0.585
0.602
0.616
0,583
0.578
0.637
96
0.505
0.198
0.171
0.196
0.611
0.162
0.164
0.224
192
0.565
0.244
0.201
0.226
0.623
0.192
0.198
1.198
CzeLan
336
0.669
1.232
0.225
0.250
0.654
0.217
0.221
0.750
720
0.838
1.214
0.264
0.323
0.702
0.253
0.253
0.848
96
0.728
0.662
0.660
0.739
0.621
0.640
0.632
0.814
192
0.802
0.746
0.707
0.784
0.665
0.683
0.677
0.882
AQShunyi
336
0.843
0.795
0.727
0.829
0.697
0.706
0.706
0.890
720
0.897
0.820
0.782
0.857
0.740
0.763
0.770
0.953
96
1.177
0.913
0.915
0.949
0.957
0.889
0.904
1.087
192
1,391
1.098
L.101
1.151
1.164
1.056
1.086
1.341
Wind
336
1,540
1.326
1.231
1.329
1.333
1.189
1.238
1,514
720
1,685
1.437
L.303
1.545
1.466
1.271
1.330
1.751
96
0.804
0.167
0.261
0.519
0.144
0.177
0.199
0.194
192
1.264
0.267
0.335
0.654
0.211
0.268
0.391
0.359
PEMS08
336
1.317
1.285
0.365
0.599
0.276
1.206
1.441
0.385
720
1.521
1.111
0.381
0.660
0.333
1.097
1.351
2.235
21


Reviews:
[{"review_id": "1bSK5dLtsP", "reviewer": "Reviewer_SQsf", "summary": "This paper proposes SwiftTS, a framework for fast and scalable selection of pre-trained time series models via multi-task meta-learning. Rather than fine-tuning each candidate model or relying on computationally expensive feature extraction for each selection, SwiftTS uses a lightweight dual-encoder to embed datasets and models, computes patchwise compatibility via cross-attention, and applies a horizon-adaptive mixture-of-experts approach. Further, the method leverages transferable cross-task meta-learning across datasets and forecasting horizons to enhance out-of-distribution robustness. The framework is evaluated on 14 real-world datasets and 8 pre-trained model families, showing state-of-the-art ranking accuracy and efficiency across a variety of horizons and domains.", "questions": "1. How is the meta information embedded and utilized? In particular, how are the five types of meta information combined within the model?\n\n2.SwiftTS performs selection among multiple pretrained models. Could it support the addition or removal of models without retraining SwiftTS? This consideration may have implications for the scalability of the approach.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The proposed dual-encoder architecture is well-conceived and technically sound. One encoder incorporates temporal awareness through the use of patching and attention mechanisms, while the other enables knowledge injection by integrating architectural metadata, graph-based topological structures, and functional embeddings derived from model behavior. This design is particularly well-justified for highly diverse model repositories.\n\n2. The manuscript presents extensive experimental results and visualizations, which provide strong and multifaceted evidence supporting the effectiveness of the proposed model.\n\n3. The application of meta-learning to address the heterogeneity of time-series domains and various pretrained models is highly appropriate and demonstrates solid methodological reasoning.", "weaknesses": "Although the paper shows runtime savings over fine-tuning, there's insufficient discussion of the the practical scaling beyond a fixed model zoo. For example, how does graph2vec embedding scale with hundreds or thousands of models with complex DAGs? Is there a resource bottleneck for functional embedding inference as the number of candidate models grows? The scalability arguments are more empirical than architectural; a more detailed analysis would be valuable.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "9ZmDxr7YJZ", "reviewer": "Reviewer_ERT9", "summary": "The paper presents SwiftTS, a learning-based framework for selecting pre-trained time series models efficiently. It uses a dual-encoder architecture (data encoder + model encoder) and multi-task meta-learning to predict model–dataset compatibility without exhaustive fine-tuning. Experiments on 14 datasets and 8 models show strong gains over existing methods.", "questions": "See weaknesses.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "- Addresses an important and under-explored problem in time series foundation model selection.\n- Well-designed method combining meta, topological, and functional model embeddings.\n- Extensive experiments with clear, consistent improvements.", "weaknesses": "- The design choices for the data and model encoders appear somewhat heuristic and lack sufficient justification. For example, why does the model encoder capture domain information while the data encoder does not? The paper could be strengthened by clarifying the design rationale of these encoders.  \n- The meta-learner is trained on a relatively small pool (14 datasets × 8 models); a data-efficiency analysis or a discussion explaining why this scale suffices to learn reliable dataset–model correlations would improve credibility.  \n- The functional embedding is obtained by probing models with Gaussian noise, which seems heuristic. Random noise may not reflect how models respond to real-world temporal structures; a justification for using Gaussian inputs would be helpful.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "YP50i3fSpI", "reviewer": "Reviewer_SnbV", "summary": "This paper introduces SwiftTS, a learning-guided framework for rapid selection of time series pre-trained models using a multi-task meta-learning strategy. The approach employs a dual-encoder (temporal-aware data encoder and knowledge-infused model encoder) to encapsulate both dataset and model features, leveraging patch-wise cross-attention to compute compatibility scores for model selection across various horizons. To improve generalization across datasets and forecasting horizons, the method incorporates horizon-adaptive expert composition as well as a cross-task meta-learning protocol. SwiftTS is evaluated on 14 real-world time series datasets and 8 pre-trained models, demonstrating strong results against a wide range of feature-analytic and learning-based baselines.", "questions": "See weaknesses.", "limitations": "", "rating": 2, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1.\tThe idea of selecting more suitable pretrained models for different downstream tasks and datasets is both interesting and valuable, addressing a practically important yet underexplored challenge in time-series foundation modeling.\n\n2.\tThe dual-encoder architecture is well-motivated for heterogeneous time series model pools and directly addresses the issue of costly, inconsistent feature extraction in prior work. The use of a patch-wise attention mechanism reflects a careful design choice that captures local temporal structures relevant for model-dataset compatibility.\n\n3.\tSwiftTS introduces a horizon-adaptive expert composition module that flexibly and effectively addresses horizon-specific variability, as showcased in both the framework diagram and associated experimental tables.", "weaknesses": "1.\tThe paper emphasizes that SwiftTS avoids costly forward passes through all candidate models. Yet, the functional embedding module still requires each candidate model to be evaluated (albeit offline) on synthetic inputs such as Gaussian noise. This operation remains linearly proportional to the number of candidate models and does not scale well to continuously evolving model pools. The efficiency claim is therefore only partially valid and should be quantified more carefully.\n2.\tDoes the sampling strategy used in the Temporal-Aware Data Encoder introduce randomness that leads to different results across runs? If so, how is this variance controlled or mitigated during training and evaluation?\n3.\tWhat exactly does the topological structure represent? Specifically, what are the semantic meanings of the nodes and edges in this context?\n4.\tThe results only report the alignment metric between the estimated and true rankings, but not the actual forecasting performance of different selection methods. Without these results, it is difficult to assess the real effectiveness of the proposed selection strategy.\n5.\tWhat are the forecasting results of the pretrained models on these datasets without applying the selection process? Reporting these would provide a clear baseline for evaluating the benefit of the proposed selection mechanism.\n6.\tThere exist many other meta-learning-based methods for time-series forecasting, such as AutoForecast [1], which should be included for comparison in the experimental section.\n7.\tCould the authors clarify the rationale and empirical justification for using Gaussian noise to generate the functional embeddings of candidate models? Would using real or synthetic time-series inputs affect the informativeness or stability of these embeddings?\n8.\tHow sensitive are the framework’s predictions to the number of candidate models in the hub? Does performance degrade with larger, more heterogeneous model pools, and what are the observed scaling behaviors?\n9.\tCould the authors provide more clarity about the construction of meta-training tasks, especially the sampling policy for forecasting horizons and dataset divisions?\n10.\tCould the authors clarify how they handle cases where meta-training tasks share overlapping datasets or closely related forecasting horizons, which may cause distribution leakage or task redundancy?\n\n[1] Abdallah M, Rossi R, Mahadik K, et al. Autoforecast: Automatic time-series forecasting model selection[C]//Proceedings of the 31st ACM International Conference on Information & Knowledge Management. 2022: 5-14.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)