TimeRecipe: A Time-Series Forecasting Recipe via Benchmarking Module Level Effectiveness
Authors: Zhiyuan Zhao
Juntong Ni
Shangqing Xu
Haoxin Liu
Wei Jin
B. Aditya Prakash
Venue: ICLR 2026 Poster (2026)
Keywords: Time-Series Forecasting
Module Effectiveness
Benchmark
Primary area: learning on time series and dynamical systems

Abstract: Time-series forecasting is an essential task with wide real-world applications across domains. While recent advances in deep learning have enabled time-series forecasting models with accurate predictions, there remains considerable debate over which architectures and design components, such as series decomposition or normalization, are most effective under varying conditions. Existing benchmarks primarily evaluate models at a high level, offering limited insight into why certain designs work better. To mitigate this gap, we propose TIMERECIPE, a unified benchmarking framework that systematically evaluates time-series forecasting methods at the module level. TIMERECIPE conducts over 10,000 experiments to assess the effectiveness of individual components across a diverse range of datasets, forecasting horizons, and task settings. Our results reveal that exhaustive exploration of the design space can yield models that outperform existing state-of-the-art methods and uncover meaningful intuitions linking specific design choices to forecasting scenarios. Furthermore, we release a practical toolkit within TIMERECIPE that recommends suitable model architectures based on these empirical insights.

Published as a conference paper at ICLR 2026
TIMERECIPE: A TIME-SERIES FORECASTING RECIPE VIA BENCHMARKING MODULE LEVEL EFFECTIVENESS
Zhiyuan Zhao
Juntong Ni
Georgia Institute of Technology leozhaol 997 9978gattch. edu
Emory University juntong. n @emory edu
Shangqing Xu
Haoxin Liu
Wei Jin
Georgia Institute of Technology sxu452@gatech. edu
Georgia Institute of Technology hliz763@gatech. edu
Emory University wei jineemory..n..mm edu edu
B. Aditya Prakash
Georgia Institute of Technology badityap&cc. hatpaappc...cccc.....oo.o..meee. wwtech.
ABSTRACT
Time-series forecasting is essential task with wide real-world applications across domains. While recent advances in deep learning have enabled time-series forecast- ing models with accurate predictions, there remains considerable debate which architectures and design components, such as series decomposition or normaliza- tion, most effective under varying conditions. Existing benchmarks primarily evaluate models at a high level, offering limited insight into why certain designs work better. To mitigate this gap, we propose TIMERECIPE, unified benchmark- ing framework that systematically evaluates time-series forecasting methods at the module level. TIMERECIPE conducts over 10,000 experiments assess the effec- tiveness of individual components across a diverse range of datasets, forecasting horizons, and task settings. Our results reveal that exhaustive exploration of the design space can yield models that outperform existing state-of-the-an methods and uncover meaningful intuitions linking specific design choices to forecasting scenarios. Furthermore, release practical toolkit within TIMERECIPE that recommends suitable model architectures based on these empirical insights.
INTRODUCTION
Time-series forecasting plays critical role in wide range of real-world domains, including eco- nomics, urban computing, and epidemiology (Zhu Shashal 2002) Zheng et al., 2014; Deb et al.] et al. 2024 These applications focus predicting future trends events based patterns observed in historical time-series data. Recently, the emergence of deep learning has signif-
icantly advanced the field, leading the development of numerous forecasting models (Lai al.
2018 Torres et al. [201 1021:500 (Salinas et al. 2020 Nie et al. 22023] Zhou et al. 2021: Liu & Kamarthi
2024 Liu et al. 2024b| Ni et al. 2025b Zhao al. (025c). These models have demonstrated strong
predictive accuracy and generalization capability across diverse datasets and domains, particularly
within the supervised time-series forecasting paradigm.
Despite recent successes, particularly at the model level (i.e., end-to-end forecasting architectures and pipelines), ongoing debates persist regarding the most effective deep learning strategies the module level, referring to the internal design components within forecasting models. For example, while Transeormer-based architectures are known for their ability to capture long-range temporal dependencies, they tend to struggle to generalize well on highly irregular time-series patterns, such as ETT time series. This has led to the reflection in reconsidering the effectiveness of MLP-bbsed designs (Zeng et al.] 2023 Xu al.) 2023 Wang et al.) 2024a Ni et al.) (222a)). Beyond architectural debates, further divergence arises in the design of specific modules and components. For instance, (Wang al. 2024a) highlights the importance of separately modeling trend and seasonal components

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via series decomposition. which is overlooked in other contemporary works (Shi et al. 2024). Additionally, (Zhao et al. (2025b) raises concerns for the effectiveness of instance normalization in short-term forecasting tasks when capturing rapid trend changes, despite it being commonly effective practice primarily associated with long-term forecasting scenarios.
However, despite ongoing debates surrounding divergent design choices module level, existing benchmarks only emphasize evaluation at the model level (Qiu et al., [024] Aksu et al. 2024 Li et al.
2024; Du et al. 2024), overlooking the importance of benchmarking the effectiveness of specific module-level components. These studies typically conclude with case-specific best-performing models, which can be less practical when applying benchmarked results to real-world forecasting scenarios that fall outside the benchmarked settings (Brigato et al., (025). Morcover, while these benchmarks are comprehensive and empirically informative, they offer limited intuitive insights into why certain models outperform others in specific forecasting scenarios, leaving important questions about model behavior and design choices underexplored.
To bridge this gap and gain a deeper understanding of the underlying factors driving model per- formance, we propose TIMERECIPE. While existing benchmarks focus primarily on model-level evaluation and offer limited interpretability, TIMERECIPE takes step further by benchmarking time-series forecasting methods at a finer-graine finer-grained, module level. Specifically. TIMERECIPE aims to assess the effectiveness of individual components commonly used in state-of-the-art forecasting models. This enables us to answer a key research question: Which modules and model designs most effective under specific time-series forecasting scenarios? Guided by this question, summarize the main contributions of this work as follows:
Unlike existing time-series forecasting benchmarks that focus primarily on holistic evaluation of entire state-of-the-art (SOTA) models, TIMERECIPE focuses on assessing the effectiveness of individual modules commonly used in model construction. To the best of our knowledge, TIMERECIPE the first benchmark systematically explore the design space of forecasting models for supervised time-series forecasting tasks at the modular level.
Novel Benchmarking Scope:
Comprehensive Evaluations: TIMERECIPE evaluates hundreds of module combinations across diverse forecasting scenarios, spanning univariate and multivariate settings, as well as short- and long-term horizons. The benchmark encompasses dozens of datasets and involves over 10,000 distinct experiments, offering robust and exhaustive evaluation framework.
The TIMERECIPE benchmark reveals that exhaustive exploration of the modular design space can yield forecasting models that outperform existing SOTA approaches. Moreover, uncovers meaningful correlations between module effectiveness and specific charac- teristics of time-series data and forecasting tasks, offering insights beyond raw accuracy.
Insightful Findings:
Building on the above insights, we develop training-free toolkit that makes model architecture selections within TIMERECIPE. We demonstrate its effectiveness by comparing the selected architectures against those discovered via exhaustive search.
Actionable Toolkit:
Problem Formulation. We define the time-series forecasting problem following popular existing formulations (Zhou et al., 2021 Liu et al. 2023a 2024a): Given historical observations X, (æt-L..... ) E 2xxxxxx consisting of past time steps and dx variables at time step I, the goal to predict the future H steps Y, { ..+H² E R xdx, For convenience, we denote X as the collection of all X, over the full time series of length T, and similarly, Y as the collection of all corresponding Y,, The time-series forecasting task aims learn model parameterized by 0 through empirical risk minimization (ERM) to obtain fo X for all time steps t E T.
Additional Related Work. Due to page limitations, provide extended discussion of related works in Appendix A including reviews of model designs for supervised learning and foundation models in time-series forecasting, as well as existing time-series forecasting benchmarks.
2 TIMERECIPE FRAMEWORK
Since the introduction of Transformer-bant based architectures to time-series forecasting, particularly following the release of Informer (Zhou et al., (202T). most modern approaches have converged toward common design paradigm, referred to here the Canonical Architecture, illustrated in Figure] [
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Intarca fameiaadin Devepartion
Endedding
Srepena husar hosk
Sencrediation d-Sene Sun
Input Series
Output Prediction
Latul Fusaany
Figure 1: The proposed canonical architecture in TIMERECIPE for constructing general time-series forecasting models. The canonical architecture comprises five key components: pre-processing, embedding, feed-forward modeling, projection, and post-processing.
This canonical architecture consists of five major components: pre-processing, embedding, feed- forward modeling, projection, and wost-processing (which is paired with pre-processing operations). The canonical architecture serves as the foundation of TIMERECIPE and captures the typical structure adopted by many state-of-the-art (SOTA) forecasting methods.
Following this structure, TIMERECIPE is designed to offer a systematic evaluation with in-depth intu- itions of alternative module choices across key components of the canonical architecture. Specifically, TIMERECIPE benchmarks common module designs for pre- processsin, embedding, and feed-forwart modeling, with the aim of understanding their relative effectiveness across diverse forecasting scenar- ios and in conjunction with other design choices. For example, one example question to answer by our benchmark could be: how do different embedding strategies perform under varying task settings, and how do they interact with other designs from other components of the canonical architecture?
We omit the benchmarking of the projection component. as it typically consists of a simple linear layer and has attracted less interest regarding its design effectiveness. Similarly, the post-processing component inherently paired with pre-processing operations; thus, evaluating the effectiveness of reepprocessing modules simultaneously assesses the corresponding post-processing steps. We detail all benchmarked module designs included by TIMERECIPE in the subsequent sections.
2.1
PRE- PRO-PSSCGSIINNG
In TIMERECIPE, we consider two types of popular time series pre-processing approaches that are widely used in time-series forecasting tasks: Instance Normalization (Kim et al. [221 Liu et al.
2022c
Fan et al. 2023 Liu et al. 2023b Han et al. 2024b) and Series Decomposition (Wu et al.
2021
Wang et
2024a 2025).
Instance Normalization. Instance normalization normalizes each input sample independently to standard 0-1 distribution, regardless of its original distribution. This process enables the model to Iearn translations from historical lookback to horizon predictions more stably, as all samples are mapped into consistent distributional space. Instance normalization is paired with denormalization step applied after the model output, projecting the predictions from the normalized space back to the original feature space. The full process as follows:
X, (X,
((X,)
Norm
X Norn
Denorm Y, = N-Nom o2((X) + (X())
(I)
Series Decomposition. Series decomposition in time-series forecasting aims to disentangle the seasonal and trend components within input instances using simple moving average operations. The trend component, obtained via moving average, captures the overall directional changes of the time series and primarily consists of fow-frequency variations. The seasonal component is defined as the residual between the original time series and the extracted trend, typically reflecting higher- feeeue-fe periodic patterns. We formulate this process as follows.
X TTrend AvPPool(Padding(X) X SSason X
X
Trend
For post-processing, the predictions of the trend and seasonal components from the feed-forward model are typically summed to reconstruct the final predictions (i.e., Y Tread Scason))
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2.2 EMBEDDING
In TIMERECIPE, we consider four popular embedding approaches widely adopted in time-series forecasting tasks: Token Zhou et al., 2021), Patch (Nie al.) (023). Invert (Liu al. (023a), and Frequency (Xu et al., 2023) Embedding. Additionally, we include no-embedding variant as controlled baseline for completeness, although typically yields inferior performance, e-g., applying feed-forwal modeling directly on the raw feature space. In short, the mathematical formulations of these embeddings are summarized in Equation
X E LJ,
X Taken = Conv (X (²
B,L, H]
PatchLen
x Patch
Ponv (Padding( (X!))
[ D.
Stride
X Linear(X{))
H.
X Preq rFFT(X.)
[B.
+1,
Here, the superscript T denotes the transpose operation between the second and third dimensions. D is the number of raw features (i.e., dx), and H represents the hidden dimension. We detail the specifics of each embedding strategy in the following subsections.
Token Embedding. Token embedding applies convolutional operations along the temporal axis of the input time series to project each timestamp into a higher-dimensional embedding space, analogous to word embeddings in natural language processing (Devlin al., 2019). Specifically, each timestamp. comprising all features and neighboring time steps (depending on the kernel size), is treated as an individual token. This approach preserves temporal order while enabling the model learn contextualized representations from sequences of embedded tokens.
Patch Embedding. Patch embedding segments the input time series into patches every several timestamps along the temporal dimension using convolution, similar to the patching mechanism in vision tasks (Dosovitskiy al. 2020). In the time-series context, patch embedding operates on each feature (channel) independently. The feed-forward model then treats the collection of patches as batch, resulting in a channel-inde -iduunee-ddeeeeeent processing scheme, which is a design introduced alongside the patch embedding paradigm for time-series forecasting.
Invert Embedding. Invert embedding performs linear projection across the temporal dimension for each feature independently, treating the entire lookback window of single variable token. This representation is typically followed by a feed-forward model that focuses on learning inter-feature booken-wisel dependencies. It enables the model to capture relationships across different variables while maintaining the temporal integrity of each.
Frequency Embedding. Frequency embedding applies the RealFFT (IFFT) (Brigham & Morrow 2009) to transform time-series sequences from the time domain into the frequency domain, enabling models operate on spectral components rather than raw temporal signals. The resulting representa- tion typically requires subsequent feed-forward models capable of handling complex-values inputs, currently limited MLPs in PyTorch implementations. To reconstruct the original temporal features, an inverse rFFT (irFFT) is employed in place of standard linear projections. Notably, frequency embedding a non-parametric operation, distinguishing it from other learnable embedding methods.
2.3 FEED-FORWARD MODELING
In TIMERECIPE, we consider various forwafo modeling approaches from both a model archi- tecture perspective (FF-type) and a model fusion perspective. Specifically, for model architectures, we include MI.ss, Transformers, and RNNs. For model fusion strategies, we distinguish between temporal fusion, which aims to capture temporal dependencies, and feature fusion, which focuses on modeling correlations among features. We provide detailed descriptions these feed-forward modeling approaches below.
While Transformer-Be based models have achieved notable success in time-series forecasting, largely due to their ability capture long-range dependencies across time steps or features, recent studies have also highlighted the effectiveness MLP-based models for this task (Xul
Model Architectures.
et al. 2023 Zeng et al. 2023 Ni et al. 2025a). Motívated by these findings, TIMERFCIPE aims
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to provide deeper understanding of the relative effectiveness of different model architectures. For completeness, we also include RNNs as a baseline, representing a classical class autoregressive models. RNN-based methods preceded the widespread adoption of Transformers, showing competi- tive performance earlier work (Salinas et al. 2020) Lai et al. 2018) and continue to demonstrate potential in more recent studies (Kong et 2005).
Modeling Fusion. Existing time-series forecasting approaches predict future values by either modeling temporal dependencies capturing feature correlations. When considering fusion types across different model architectures, we highlight that the processing differs even under the same fusion type, depending on the underlying architecture, as shown below:
Temporal:
MLP(X. (x.
LD),
Feature:
MLP(X Emb
[J)
R Limb
R Eimb [J)
(4)
Transformerrx E [B.L
Transformer(X; Eimb E [B, DJ
Here, we slightly abuse the notations: is the batchsize, is the temporal dimension, and the feature dimension, which are the 1st, 2nd, and 3rd dimension after the embedding, respectively, as to generalize the different shapes produced by various embedding strategies.
2.4 TIMERECIPE BENCHMARK
With the component designs introduced above, we now present TIMERECIPE, unified time-series forecasting framework that (i) implements the discussed module designs from each component of the canonical architecture, and (ii) automatically adjusts inter-module connections. TIMERECIPE controls the use of different designs through hyperparameters, including whether to apply instance normalization and series decomposition, the choice of embedding type, model architecture, and fusion type. Accordingly, TIMERECIPE constructs the full model pipeline by automatically adjusting hidden dimensions, initializing appropriate module connections, and applying proper tensor operations during the forward pass. Beyond providing a comprehensive benchmarking and intuition-driven study as in this work, TCIPE also offers practical benefits: enables time-series researchers to conveniently build and evaluate models their own data, and provides flexibility for exploring novel designs across different components within the canonical architecture framework.
Benchmark Scope and Coverage. Through exhaustive design space exploration enabled by TIMERECIPE, the framework covers over 100 types model architectures via module-level combina- tions. By adjusting the component configurations, TIMeRECIPE is able to encompass many popular time-series forecasting models, as partially illustrated in Table Consequently, comprehensive benchmarking of TIMERECIPE not only evaluates existing forecasting models, but also uncovers the potential of alternative combinations of model designs.
TiMERecipE Component
Published Work Model
IN
Fusion Embedding
FF-Type
Feature
Invert
Trans.
iTransformer (Liu et [202aa
V
Temporal
Freq-
MI.P
FITS (Xu al. 2023
Temporal
Patch
Trans.
PatehTST Nie
2025 PAtin
Tan ct 2024
X
Temporal
None
MLP
DLunear Zeng et al. 20233
X
Feature
Taken
Trans.
Autoformer (wu et al.
2021
X
Temporal
Token
Trans.
Informer (Zhou al.
2021
Table 1: Examples of existing methods that are covered by TIMERECIPE benchmark.
Remark 1. fhaamel-indeeendence (Nie al. 2023 Han et al. 2024a) is important property in time-series forecasting models, referring to the ability to forecast multiple time series independently while sharing model parameters. TIMERECIPE implicitly incorporates channel-inded iaauuell-ideeeeeence in its evaluations by combining specific embedding types and model architectures with temporal modeling fusion. For example, using invert embedding with MLP model architecture alongside temporal fusion serves as an instance of channel -ineeelliddeeeddem modeling.
Remark New modules can be readily incorporated into TIMERECIPE, We focus on representative modules that are widely adopted and inffuential design choices, while omitting others avoid the combinatorial explosion of possible configurations. The uncovered designs generally fall into two categories. First, highly specialized designs, such as tangled temporal and feature fusion with
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delicate design used specifically in Crossformer (Zhang & Yan 2023 Second, designs that are of less concern on module effectiveness, such as data augmentation based on down-sampling (Wang et al.) IN+SD+Tempore Fusion+ + Non-Emmbedding- +MLP (thus falling within ECIPERECIPE) with an additional augmentation applied at the pre-processing stage. Augmentation approaches exhibit general benefis for predictive models with fewer concerns; therefore, they are currently omitted from our benchmark studies.
2024at 2025) For instance. TimeMixer (Wang et al. 2024a) can be viewed
Remark 3. While many current SOTA forecasting methods focus on foundation and prompt- -hased methods, TIMERECIPE targets supervised learning and already includes the leading supervised approaches with existing module-level combinations. Foundation and prompt-baxen methods are typically built as end-to-end pre-trained frumeworks, where altering single module can disrupt the effectiveness of other pre-trained components. Furthermore, time-series foundation models remain at early and fragmented stage, with directions ranging from scaling Transformers (e.g.. Time-MOE (Shi et al. 2024). TimesFM (Das et al.)) to adapting LLMs (e.g., Chronos (Ansari et al. 2024g) repurposing tabular foundation models (e.g., TabPFN (Hollmann et al. 2022(). Rather than benchmarking these diverse paradigms, which have already been explored in works such as GifiEval (Aksu al. 20044), our focus is on delivering actionable insights into supervised models, which we believe can also inform the principled development of future time-series foundation models.
EVALUATION PROTOCOL
3.1 EVALUATION TASKS
We distinguish time-series forecasting tasks from two perspectives. First, from feature perspective, we categorize tasks into multivariate forecasting, where dx 1 and the goal is to predict the future values of all feature dimensions simultancously, and univariate forecasting, where dx = 1 and the task focuses on forecasting future values of single dimension based solely on its own historical observations without exogenous features. Second, from horizon length perspective, we classify tasks into short-term and long-term forecasting. We define short-term forecasting as cases where the lookback window is longer than the forecasting horizon (i.e., L > H), and long-term forecasting as cases where the lookback window is shorter than the forecasting horizon (i.e., L S H).
Following this distinction, TIMERECIPE aims comprehensively benchmark the effectivvness of the modules described Section 2 across all time-serics forecasting tasks, including short-term univariate, short-term multivariate, long-term univariate, and long-term multivariate forecasting tasks. These tasks cover a wide range of time-series forecasting scenarios, where the driven intuition on module effectivness can offer practical insights for real-world forecasting applications.
3.2 EVALUATION DATASET
LTSF. The Long-Term Time-Series Forecasting (LTSF) datasets Zhou al. 2021
widely adopted benchmarks for evaluating both short-term and long-term forecasting tasks. They test model's s ability generalize across diverse domains, including Electricity Transformer Temperature (ETT; ETTh1/2, ETTm1/2) (Zhou et al. (021). Influenza-like Illness statistics (ILI), Electricity Consumption Load (ECL) (Asuncion et al. 2007). meteorological data from the National Renewable Energy Laboratory (Weather), and foreign exchange rates across various countries (Exchange).
PEMS. The Performance Measurement System (PEMS, extended Traffic dataset in LTSF) datasets (Li et al,] 2017) are standard benchmarks for time-series forecasting, commonly used in traffic prediction research. These datasets contain road occupancy or flow measurements collected by loop detectors on highways across different districts in California. We include PEMS03, PEMS04, PEMS07, and PEMS08, each varying in geographic scope, number of sensors, and data volume.
M4. The M4 dataset (Makridakis al.) 2018) is large-scale benchmark for evaluating forecasting models across diverse real-world time series. It includes 100,000 series from domains such as macroeconomics, microeconomics, finance, industry, and demography. Each time series varies in length and frequency, spanning yearly, quarterly, monthly, weekly, daily, and hourly settings.
We include additional details and the rationale behind the selection of these datasets in Appendix B.1

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3.3 EVALUATION METRIC
We adopt common evaluation metrics on each dataset. Specifically, we use mean squared error (MSE) and mean absolute error (MAE) for evaluations on LTSF and PEMS datasets, and symmetric mean absolute percentage eπror (SMAPE), mean absolute scaled error (MASE), and overall weighted average (OWA) for M4 dataset. The formula of these metrics is detailed in Appendix [.2
Since error scales vary significantly across datasets, we use averaged rank scores to enable fair comparisons of module effectiveness. For example, if module combination ranks 1s in MSE and 2nd in MAE, its average rank score is calculated as 1.5. This unified ranking metric facilitates consistent evaluation across datasets and forms the basis of our analysis in Section
Implementation. The implementation of TIMER follows the widely-used Time-Series Library (Wang et al. 2024b). For usability, we introduce hyperparameters that control the inclusion of each module, allowing users specify their usage of each module while TIMERECIPE automatically adjusts the internal architecture and dimensions accordingly. Detailed hyperparameter settings and tuning strategies provided in Appendix B.4
Reproducibility, For reproducibility, we provide all data, code, and scripts, publicly available at https://qithur www. yaattyaab///aa / TimeRecipel All experiments conducted 32GB V100 GPUs. For statistical robustness, all results are based on the average over four random seeds.
4 RESULTS AND DISCUSSION
In this section, present the benchmark results along with key insights and discussions derived from them. Due to space constraints, we include partial results in Appendix and full results (both raw and processed) are available at: ftttps://gitee
4.1 INSIGHTS DERIVED FROM BENCHMARK RESULTS
4.1.1 TIMERECIPE YIELDS MODEL ARCHITECTURES OUTPERFORMING SOTA
key observation from our evaluations is that exhaustive exploration of the design space across diverse datasets can identify model configurations that outperform existing SOTA approaches that are themselves included within the search space. For example, in the short-term multivariate forecasting on the PEMS03 dataset with horizon of 12, the top-ranked configuration achieves an MSE of 0.714, outperforming ITransformer, one of the best existing forecasting models also covered by TIMERECIPE, which attains MSE of 0.739 and ranks only 7th among all evaluated design combinations.
More importantly, this phenomenon is not a rare case: it holds in 92 out of 102 evaluated scenarios, detailed in Appendix C suggesting that in over 90% of cases, RIMER can identify model architecture that surpasses the SOTA. On average, the best existing approaches lag behind the top- performing configurations identified by TIMERECIPE by 13.66 ranking positions. By exhaustively exploring the design space, TIMERECIPE further achieves an average forecasting error reduction of 5.4% compared the best existing approaches (std.- 2.88%, t-test p-value= 0.0069).
This observation underscores the importance of exhaustive design space search, as by TIMERECIPE, for achieving superior forecasting performance across differrntt scenarios. Moreover, TIMERECIPE offers practical utility in the convenience of the construction of end-to-end forecasting pipelines. For instance, when introducing novel embedding technique for time-series forecasting, researchers can leverage the canonical architecture of TIMERECIPE to identify the optimal configuration that best complements the proposed component. This facilitates fair and effective evaluations across a wide range of scenarios and supports the development of new tfate-ofthhe-s solutions.
4.1.2 TIMERECIPE UNCOVERS MODULES EFFECTIVENESS LINKING TO DATA PROPERTIES
The major motivation of TIMERECIPE is to systematically investigate the effectiveness of various architectural modules across diverse time-series forecasting scenarios, especially in relation to the intrinsic characteristies of different datasets. This motivation stems from the variation observed in
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optimal architectural configurations across datasets. For instance, the pe-performing models on multivariate forecasting tasks using the ETT datasets often combine patch embeddings with MLP or RNN-based
networks. In contrast. the Electricity dataset, models that with invert embeddings with Transformer architectures yield the best results. Another noteworthy finding is that while instance normalization generally improves performance across many LTSF benchmarks, its performance on the PEMS datasets is degraded. These trends highlight the potential for uncovering meaningful interactions between model architecture choices and dataset properties.
To address this gap and answer our central research question: Which modules and model designs are most effective under specific time-series forecasting scenarios? As a first step, we establish a taxonomy of time-series data characteristics. This taxonomy includes key properties such as seasonality, trend, stationarity, transition, shifting, and correlation (Qiu et al. 2024), as detailed in Appendix [B.3] In addition to these intrinsic data properties, we further categorize forecasting tasks based on input structure, namely, whether the data is univariate or multivariate, as well as the number of input features (N-Feature) and the the effectiveness of specific module configurations.
ratio (HL-Ratio), which may also influence
Building on these data characteristics, conduct a correlation analysis to explore the relationship between dataset properties and the effectiveness of various module designs. Through the analysis, we observe patterns among the statistically significant module-Ievel effectiveness, as shown in Table 2 Specifically, we employ statistical hypothesis testing via t-tests to assess whether particular module configurations yield significantly improved performance under specific data conditions. This analysis directly supports our primary research goal of identifying the most appropriate design choices for diverse forecasting scenarios. A complete list of all statistically significant correlations (i.e., p-value < 0.05) is provided in Table 4 Appendix C.I
Setting
Choice
Condition
when n-feature is low hl-ratio is high shifting is low featur is low transition is high
correlation is high scasonality is low
Instance Norm.
shifting is high
trend is high
Series Decomp.
when
when
hl-ratio is high shifting high
correlation low trend is high
Multivariate
Temporal Fusion
scasonality is low
when
n- n-feature is high
correlation is high
transition is low
Invert Emhed.
shifting is low
when
hl-ratio is low
trend is low scasonality high
Taken Embed.
stationarity low
Patch Embed.
when
trend is high
when
n-feature is high
hi-ratio is low
shifting is low
RNN Arch.
trend is low
stationarity is low transition low scasonality high
Transformer Arch.
when
correlation high
Series Decomp. when
transition is high shifting high trend is high
stationarity is high hl-ratio is high
Univariate
Temporal Fusion when Non-Emhed. when
trend is high shifting is high seasonality is low
trend high
Transformer Arch. when
scasonality is high
Table 2: Module choices under specific data property conditions.
These findings provide a more granular view of module-level effectiveness, some of which align with well-established knowledge. For example, instance normalization, which is specifically designed to handle distribution shifts, is most beneficial when shifts are large or seasonality is low. Similarly, RNN architectures are more flexible when the HL-ratio is low, as errors tend to accumulate over longer horizons. Furthermore, our results highlight directions for future in-depth studies. For instance, while this work provides empirical insights, further investigation is warranted to understand how time series decomposition interacts with shifting patterns: being more effective under less shifting in multivariate setups and under more shifting in univariate setups. Overall, these results suggest that architectural choices should be carefully aligned with the characteristics the underlying data, with certain configurations consistently outperforming others under specific conditions.
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4.2 PRACTICAL IMPLICATIONS FROM THE INSIGHTS
Given the insights discussed above, a natural question arises: how can these findings be leveraged to inform better model architecture design for a given time-series dataset? To address this, TIMERECIPE integrates a training-free model selection mechanism based on a LightGBM (Ke et al. 2017) regres- sion model. Specifically, we train a regression model that maps both dataset characteristies and model configurations to their associated rank scores benchmarked by TIMERECIPE, For new forecasting task, we first compute the relevant data characteristics and then estimate the rank scores for range of candidate configurations. The configuration with the lowest predicted rank score will be selected.
We evaluate the model selection toolkit on two forecasting scenarios: (i) an in- in-distribution case involving short-term multivariate forecasting on the ETThl dataset (which is used in the TIMERECIPE, though this specific setting is not benchmarked), and (ii) three -iito---iittibttiin cases using a new univariate unemployment forecasting dataset introduced in Time-MMD (Liu et al. 2024a). where the dataset details are provided in Appendix B.I which is not part of the original TIMERECIPE benchmark. The results, presented in Table 3 and Table in Appendix C.2) demonstrate that even with simple tree-based approach, TIMERECIPE is capable of selecting models that are closer to the globally optimal architecture than the existing best-performing model. These findings underscore the potential of deploying TIMERECIPI in real-world model selection scenarios, where it is able to make model selections that can surpass the SOTA performance without the need for training.
Social
_1__
IN
SD
Fusion
Embed
FF-Type
Rank
MSE
MAE
TIMERECIPE Best
/
Feature
Patch
MLP
1.0
0.0854
0,2072
Existing Best (PatchTST)
X
Temporal
Patch
Trans.
25.5
0.0994
-16.4%
0.2256
-8.9%
/
V
Feature
Patch
RNN
14.0
0.0950
-11.2%
0.2202
-6.3%
V
V
Temporal
Invert
RNN
5.5
0.0897
-5.0%
0.2123
-2.4%
Top-3 Selection
X
X
Temporal
Token
MLP
70.0
0,1310
-53.4%
0.2689
-29.7%
Selection better than existing best: Yes (Selection 1&:2)
Table 3: Comparison of model configurations selected by our method against the best-performing existing model and the global best results found through exhaustive design space search. At least one of our top-3 selections consistently outperforms the existing best and closely approaches the optimal configuration on Social_12 (see Table Appendix C.2 for more and similar observations). This demonstrates the value of TIMERECIPE, even when using simple tree-based approach.
4.3 IMPLICATIONS FOR FUTURE RESEARCH
We identify key benefits of TIMERECIPE that can support future research in time-series forecasting.
Convenient Framework for Time-Series Module Design and Evaluation. The TIMERECIPE's canonical architecture provides a practical and extensible framework for testing new component de- signs in time-series forecasting. A key benefit is the ease with which novel modules can be integrated and evaluated in a standardized pipeline. For example, researchers can introduce new embedding strategies beyond those currently benchmarked and seamlessly insert them into the FCIPE framework. The system can then be used to automatically explore optimal configurations of the remaining components, such as pre-processing or ferw-forward types, and thereby facilitate efficient and systematic evaluation of new design choices within a comprehensive forecasting pipeline.
Implications for Designing Advanced Time-Series Forecasting Models. TIMERECIPE indicates that no single existing architecture consistently outperforms others across all time-series forecasting scenarios, even with taking recent SOTA into consideration (Shi al., 2024 Waag et al. 2025 Zhong et al. (2255] Kong et al.] (025). However, rather than interpreting this as a limitation that precludes the development of broadly effective models, we argue that this insight points to the potential of hybrid architectures. Future SOTA models may benefit from integrating multiple architectural components tailored to different data properties. For example, (Ni et al., 2025a) has shown that some temporal patterns are better captured by Transformer-basee models, while others are more effectively modeled by MLPs. Extending this intuition, TIMERECIPE aims to reveal that similar complementarities exist across wide range of design dimensions, such as normalization strategies, embedding schemes (e.g., patch vs. token), or architectural combinations. These findings suggest that next- next-generation forecasting systems, including foundation models, which are often derived from supervised learning

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Published as a conference paper at ICLR 2026
approaches, could possibly achieve broader robustness and improved generalization by dynamically leveraging hybrid designs tailored to specific forecasting scenarios and pattern types.
Advancing AutoML for Time-Series Forecasting, Another important contribution of TIMERECIPE lies in its potential to advance AutoML studies time-series forecasting, Earlier studies have mainly focused model-level searches combined with hyperparameter and learning scheme optimiza- tion (Alsharef et al.] 2022b at Shehur et al.] 2023 Westergaard et al.) 2024). With the canonical architecture introduced by TIMERECIPE, future AutoML for time-series forecasting may enable finer-grained module-level search across different components of the forecasting pipeline. This approach allows AutoML systems explore significantly broader and more flexible design space, in conjunction with traditional hyperparameter and learning scheme tuning. As a result, TIMERECIPE potentially benefits more granular and effective AutoMI, time- mer-ss applications.
5 CONCLUSION
In this work, we introduced TIMERECIPE, benchmarking framework that systematically evaluates the effectiveness individual modules for time-series forecasting. By decomposing forecast architec- tures into modular components, TIMERECIPE allows fine-grained analysis of design choices across a wide range of datasets and task settings. Our study presents comprehensive benchmark evaluations through more than 10,000 experiments to date, as well as the novel evaluation scope of module-level effectiveness to our best knowledge. We further include the limitation discussion in Appendix [D]
Our results highlight two core insights: first, that exhaustive design space search results in model designs that can outperform SOTA; and second, that module effectiveness is highly data-dependent, with single design universally superior across all scenarios. These findings not only challenge the notion of one-size-fits filze-fits-al solutions but also motivate future research into adaptive and hybrid model architectures. By releasing our benchmark and toolkit, we aim support the community in both evaluating existing designs and exploring new ones under a unified, interpretable framework.
ACKNOWLEDGMENT
The work from Georgia Institute of Technology was partly supported by the NSF (Expeditions CCF-1918770 CAREER IIS 102-202886. Medium IIS- 195588,, Medium IIS-2403240. Medium IIS- 2106961), NIH (IROIHL 184139), CDC MInD program, Meta. and Dolby faculty gifts. The work from Emory University was partly supported by NSF CNS-2437345 and by the National Institute of Allergy and Infectious Diseases of the NIH under Award No. 1R01A119711 The content is the sole responsibility of the authors and does necessarily represent the views of the NIH.
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A RELATED WORKS
Supervised Time-Series Forecasting, Time-series forecasting, predicting future values based on historical observations, is long-standing challenge across numerous domains. Early approaches have been dominated by statistical methods. Autoregressive Integrated Moving Average (ARIMA) models (Box) 2013) and Exponential Smoothing (ETS) techniques (Hyndman et al.] 2008) have become foundational, modeling temporal dependencies and trends through established statistical principles. These methods often assume linearity or specific data structures and can struggle with complex, non-linear patterns present in many real-world datasets.
As transformative architecture from deep learning, the introduction of the Transformer architecture (Vaswani et al. 2017). with its powerful self-attention mechanism, has marked pivotal moment for time-series forecasting. Early efforts have focused on enhancing the efficiency and effectiveness of Transformers for long sequential data, common characteristic of time series. Models like Reformer (Kitaev et al. 2020) have introduced techniques to reduce computational complexity. while Informer
(Zhou al. 2021 Autoformer (Wu al. 202I), Pyraformer (Liu et 2022b), and FEDformer 2022 have explored specialized attention mechanisms (c.g., sparse attention, auto- correlation, pyramidal attention) and decomposition strategies (e.g., trend-seasonal decomposition, frequency domain processing) to better capture temporal dependencies in long sequences. Further refinements have addressed specific challenges inherent time-series data (Liu al., 2024a Zhao et al. 2025a). For instance, Non-stationary Transformers (Liu et al.] 2022ch have incorporated mechanisms to handle distribution shifts over time, ETSformer (Woo et al. | 2022) has integrated principles from classical exponential smoothing, and Crossformer (Zhang & Yan (023) has focused on modeling dependencies across different variates in multivariate settings. PatchTST (Nie et al.) has proposed segmenting time series into patches, treating them tokens, which proves highly effective for long-term forecasting. More recently, iTransformer (Liu et al.) has inverted the roles of embedding and attention layers, achieving strong results.
(Zhou et al.
Despite the success of Transformer variants, recent research has spurred a debate regarding their ne- cessity, demonstrating that simpler architectures, particularly those based on Multi-Layer Perceptrons
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(MLPs) even linear layers, achieve competitive or superior performance many benchmarks. DLinear (Zeng et al. (202)) has proposed simple linear model with decomposition. challenging the complexity of contemporary Transformers. Subsequently, various MLP-based models have emerged, often emphasizing efficiency and specialized designs. LightTS (Zhang & Yan (022) has utilized sampling-ori corpeieg-oriented MIP structures, TSMixer (Chen al., 2023) has employed alI-MLP architec- ture with mixing across time steps and features. TimeMixer (Wang et al. 2024a) and TimeMixer++ (Wang et al. 2025) have further reflected on the competent duties of Transformer components and have repurposed the Transformer architecture.
Beyond Transformers and MLPs, other architectural paradigms continue to be explored. Convo- lutional approaches, such as MICN (Wang et al.] (023) using multi-scale local and global context modeling, SCINet (Liu et al. 2022a) employing sample convolution and interaction and TimesNet (Wu et ) modeling temporal 2D variations, offer alternative ways to capture temporal features. Recurrent architectures are also being revisited, exhibiting strong performance for forecasting (Kong al. 2025). Recent explorations also include leveraging pretrained language models for forecasting
tasks (Jin et al.] Tan et al. 2024; Liu et al., 2025a). This diverse landscape, i.e., various model architectures, highlights the necessity and urgency of this time-series forecasting recipe at the model level, which is developed in this paper.
Time-Series Foundation Models. Time-series foundation models, pre-trained vast amounts of diverse time-series data, aim to zero-shot adapt to unseen time-series datasets. Existing methods largely follow the architectural design of foundation language models. For instance, Chronos (Ansari et al.) is based on the T5 (Raffel et al., (020) architecture, TimesFM (Das et al.) employs the decoder-only Transformer architecture, Lag-Llama (Rasul et al.) explicitly leverages the Llama architecture. Recent advancements (Liu et al. 2024cc Shi et al. (0224) address computational scaling while enhancing capacity by introducing mixture of experts (MoE) (Cai al., (025) techniques from foundation language models. We envision that the model-level time-series forecasting recipe proposed in this paper provides key insights for the architectural design of the next generation of foundation time-series models.
Time-Series Benchmarks. Robust and standardized benchmarks are essential for evaluating the performance of time-series forecasting models, enabling fair comparison and reproducible research. Historically, the M4 and M5 competitions (Makridakis et al., 2020; 2022) have served as crucial benchmarks, providing large collections of diverse time series primarily in business, demographic, and economic domains, along with rigorous evaluation protocols (Makridakis et al.) 2020; (022)) Recent efforts focus on providing unified benchmarking frameworks and toolkits. TFB (Qiu et al.) 2024), for instance, introduces a scalable suite covering multiple domains and methods, emphasizing reproducibility and systematic, aspect-based analysis. Furthermore, BasieTTS (Liang et al. 2022)
focuses on benchmarking multivariate time series forecasting, ProbTS (Zhang et al. (2024) bench- marks both point and distributional forecasting, and GIFT-Eval (Aksu et al.] 2024) is designed for benchmarking foundation time-serie models. Recently, ReC4TS (Lu et al.) 20255) benchmarks how different reasoning strategies enhance zero-shot time-series forecasting. In addition, Time-MMD (Liu et al. 2024a) and CiK (Ashok et al. (024) are designed for benchmarking multimodal time-series forecasting. Different from all existing time-series benchmarks, our work uniquely focuses on evaluating the effectiveness of individual module-level design choices for time-series forecasting. To the best of our knowledge, this is the first benchmark to systematically address this underexplored yet critical aspect of model design.
Auto-ML in Time-Series. Automated Machine Learning (AutoML) aims to automate the end-to-end process of applying machine learning. enhancing accessibility and efficiency. AutoML research in time series can be categorized as: (1) automated feature engineering, which generates relevant temporal features like lags and rolling statistics (Cerqueira al. 1 Costa 202T); (2) automated model selection, searching across diverse model families from statistical methods (e.g.. ARIMA) to machine learning (e.g.. boosted trees) and deep learning architectures (c.g.. LSTMs, Transformers) (Ying et al. |020 Abdallah et al. 2022; Shchur et al. (003);; (3) hyperparameter optimization, using evolutionary algorithms tune model configurations (Wu)
techniques like Bayesian optimization et al. 2022 Fristiana et al. 2024); (4) neural architecture search, which specifically automates the design of deep learning model structures suitable for capturing complex temporal patterns (Rakhshani et al. 2020 Wu et al. 2023).
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B DETAILED EVALUATION SETUP
B.1 ADDITIONAL DATASET EXPLANATION
In this section, we will show more details of the datasets and our selection.
ETT. The ETT datset, alias Eleetricity Transformer Temperature (Zhou et al. 2021 contains collected oil temperature and electricity load data per minute of two Chinese stations between 2016/07 2018/07. The original data is then aggregated every one hour (ETTh1/2) every 15 minutes (ETTm1/2).
ILL The ILI dataset, alias Influenza-like Illness statistics, contains weekly influenza surveillance collected and released by the CDC starting from 1997-98 influenza season.
CDCBstarting
ECL. The ECL dataset, alias Electricity Consumption Load (Asuncion al. 2007 contains the hourly electricity consumption history of 321 clients covering two years.
Weather. The Weather dataset contains hourly meteorological data from 1,600 locations across the U.S. between 2010 and 2013.
Exchange. The Exchange Rate dataset(Lai et al., 2018) contains daily exchange rates of U.S. dollars in eight foreign countries, including Australia, Britain, Canada, Switzerland, China, Japan, New Zealand, and Singapore, between 1990 and 2016.
PEMS. The PEMS dataset, alias Performance Measurement System, contains traffic data per minute from 325 sensors in the Bay Area collected by California Transportation Agencies (CalTrans) between January 2017 and May 2017. We adopted data from 4 sparsely located sensors in our evaluations.
M4. The M4 dataset contains 100,000 domain series from domains such macroeconomics, microeconomics, finance, industry, and demography. Each time series is aggregated in various granularities, from hourly to yearly.
Our collected data covers multiple domains, multiple granularities, and multiple time ranges, ensuring plenty of diversity like the corresponding series. By evaluating such datasets, we guarantee that the outputted recipe from our method maintains considerable coverage in real-world time-series tasks.
Time-MMD. The Time- MMD dataset (Liu et al., 2024a) is a multimodal time-series benchmark covering nine domains, such economics, agriculture, and security. It consists of temporally aligned numerical time-series data and corresponding textual information collected from news articles and reports.
In this work, we use only the numerical time-series component for evaluation. Since Time-MMD is not included in the original TIMERECIPE benchmark, it serves as -iistii-iiiiitoo testbed to assess whether the architectural insights derived from Table 2 and our model selection strategy generalize beyond the benchmark datasets.
B.2 EVALUATION METRIC FORMULATION
We follow the common evaluation metrics across diverse forecasting datasets (Oreshkin al. 2019 Liu et al. 2022a Wang et al., 2024a). We evaluate the LTSF dataset and PEMS dataset by two metrics: mean squared error (MSE) and mean absolute error (MAE), aiming evaluate the errors under the same scale. Given predicted sequence Y {#++1,... f and corresponding ground
truth Y (244 where Y, Y E l xdx, these two metrics are calculated by:
H (Ie+i d
MSE
(5)
H
1=1
Prts Re42l
MAE
(6)
H
hhttp:://iis.de http:/ts/t.....ooo/////////////r
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Meanwhile, we evaluate the M4 dataset by three metries: Symmetric Mean Absolute Percentage Error (SMAPE), Mean Absolute Scaled Error (MASE), and Overall Weighted Average (OWA), to normalize the errors across vast scales inside the dataset:
200
[ztzi Tr+il
SMAPE H im1
Feti + [
1 Σ
1 Be+t
MASE H H-S 2jj=s1 (o44 Icts-ol
(8)
OWA 1 SMMPEENNII MASENaive2
SMAPE
MASE
B.3 DATASET PROPERTIES MEASUREMENT
We define the data properties involved TIMERECIPE following TFB (Qiu et al. 2024).
Trend. refers the long-tern changes of time-series. As shown in Algorithm involve Seasonal and Trend decomposition using Loess (STL) (Cleveland et al. 1990) as decomposition function to calculate the trending values.
Seasonality. refers to the changes in time-series that repeat every certain period. Similar to the calculation of Trend, we involve STL to calculate the seasonality, which is shown in Algorithm P
Stationarity. refers to the indicator of whether a time-series approximately satisfies all of the following: 1) the mean of any observation inside the series is constant, 2) the variance of any observation is finite, 3) the covariance between any two observations depends only on their distance. The caleulation is shown in Algorithm where ADF refers to the Augmented Dickey-Fuller (ADF) test.
Shifting. refers time-series changes upon certain direction over time. Given threshold m. calculate the shifting indicators in Algorithm
Transition refers the covariance of the transition matrix across symbols from 3-value windows. We calculate the transition values as shown in Algorithm 5
Correlation. refers the possibility that different channels of multivariate sequence share similar
distribution. As shown in algorithm 6 we calculate the correlation referring to Catch22 (Lubba et al. 2019) library, which designed to extract 22 features from time series.
Algorithm 1: Calculating Trend Strength of Lime--eriee
Input TTme-SSriie X Txx
Output: : Trend strength 3 of X
S, T, R <- STL(();;
return 3 max(0,
var(R) var +B)
Algorithm 2: Calculating Seasonality Strength of Time-Series
Input :Time-Series X E Tx
:tttuoaaSeasoaaiit strength ( of S. T. R < STL(X);
return Ç < max(0, 1
var( (2)
var (Sr
B.4 HYPERPARAMETER TUNING
For the modules involved in our evaluation, several components (c.g., series decomposition) are inherently non-parametric and do not introduce additional hyperparameters. For modules that do
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Algorithm 3: Calculating Stationarity Value of Time-Series
Input Timme-Series X E [RTx1
Output: :Stationarity value 7 of X
t (X)(X);
2 return y + (s 1 0.05);
Algorithm 4: Calculating Shifting Values of Time-Series
Input -Time-Series X Rxxx number of thresholds m Output:Shifiin value 5 of X
7. normalize(X)).
Zmin f- min(Z), Zmax f- max
{si|s: < Zunin (i 1) Zmur Zmin i E [1,m]]; for i to m do
m
K; < [jl Zj > 8.. j E [1,T]]:
M; + median(K:)
end
M' + Min Max (ormalization(MM):
return 8 +- median(M/))
involve architectural hyperparameters, we tune key parameters such as hidden dimension, number of layers, and method-spe speccifcc configurations (e.g., patch length). This design ensures that each module combination is sufficiently expressive without being over parameterized. thereby avoiding excessive training cost while maintaining fair architectural comparisons across different module combinations.
For optimization-related hyperparameters, such as learning rate, we follow the standard training protocols provided by the Time-Series Library. In particular, we fix these training hyperparameters, such using unified learning rate across most experiments, which is common practice in neural architecture search studies Ying et al. (2019); Qin et al. (2022). This strategy isolates the impact of architectural variations and ensures that performance differences are primarily attributable to module design rather than training configurations.
C DETAILED RESULTS
C.1 COMPREHENSIVE CLAIMS (SECTION 4.1.2 CONTD.)
Here we present all the claims on the correlations between the effectiveness of the module and the data characteristics that are statistically sigmificant (e.g., 50.05. The comprehensive results, including the t-test p-value, are shown in Table
C.2 MODEL SELECTION TOOLKIT EVALUATION (SECTION 4.2 CONTD.)
Here, present additional evaluation results for training-free model selection approach Envi ronment_ 4 and weccuritty12 As shown in Table these results consistent with the conelusions drawn from Table
C.3 PERFORMANCE RANKING DETAILS (SECTION CONTD.)
To present clearer comparison of the performance across different module combinations for each dataset and forecasting horizon, we present the top-10 ranked results. The ranking is based on the average of the ranks obtained from two metrics: MSE and MAE. Specifically, if a module combination ranks 1st in MSE and 2nd in MAE, its final rank score is computed as the average, i.e., 1.5. The detailed rankings summarized in the following tables.
For clarity, we denote each experimental setup using the format "I h instance, multivariate forecasting task on the ETTh1 dataset with forecasting horizon of 96 is
horizon feature]"
For
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Algorithm 5: Calculating Transition Values of Time-Series
Input :imme-Series X E [RTx1
Output:Transitinn Transitionn value A (0. of
of
First zero crossing of X's autocorrelation;
Y f Downsampling X with stride r;
f aYgsort(Y);
T < length (Y) for j E [0: :0:77 T do
Zj T I;
31,
end
.M
[0] for E [0:T" do
Z 1] 2+1 - 1] t MiZj 1][2,+1 - 1|+1
end
10 M' 7
C covariance matrix between the columns of M'
12 return A + tr(C))
Algorithm Calculating Correlation Values of Time-Series
Input Multivariate Time-Series X E R
Output: :uut:Corree Correlation value E (0, 1) of X
F (PL FN) E R22XN <- (at:
P (TPearson (F", FJ) i N1, j + [it,NN
return 1) + mean P) + I+var(P)
represented as "[ETTh1 111111999666611 M)". In particular, we present the results on multivariate forecasting on LTSF datasets through Table ~ [3] univariate forecasting results LTSF datasets through Table 19 26 multivariate forecasting results on PEMS datasets through Table 277-2/733 30 univariate
forecasting results PEMS datasets through Table T9 26 and univariate forecasting results M4
datasets on Table
D LIMITATION DISCUSSION
In this work, we break down time-serics models into five key design modules and benchmark a wide range of their combinations. Our framework identifies model configurations that can perform significantly better than existing standalone models. More importantly, our findings offer practitioners clear, understandable, and direct guidance. This ensures that the field advances with deeper understanding and more structured methodological approach, rather than through unsystematic exploration. However, we acknowledge that this work has the following limitations:
Not all time-series designs are covered. We recognize that TIMERECIPE does not include every existing module design in time-series forecasting. The designs not covered generally fall into two categories. First, there are highly specialized designs, such as those in Crossformer (Zhang & Yan 2023). These are specifically created for the Transformer architecture capture dependencies across time and dimensions but are difficult to apply to other model architectures. Second, some model architectures are not yet widely adopted, such as models based on large language models (LLMs), for example, Time-LLM (Jin et al.). Such models often have high computational costs, and their effectiveness is still a subject of ongoing discussion (Tan et al. 2024).
Nevertheless, the first-of-is-kknnd benchmark, TIMERECIPE has covered significant and represen- tative portion of the design space for supervised time-series forecasting at the modular level.
The findings are primarily empirical. The insights from TIMERECIPE are based extensive empirical evaluations. While these experiments provide robust and thorough evaluations, and the toolkit recommends model architectures based these empirical insights, deeper theoretical analysis of why certain module designs are most effective under specific time-series forecasting scenarios is beyond the current scope of this benchmark study.
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Setting
Property
Direction
Choice
p-value
IN=True
0.000
Fusion=Temporal
0.000
N-Feature
Embed=Invert
0.000
FF=RNN
0.000
Embed=Token
0.002
FF=RNN
0.000
HL-Ratio
IN=True
0.000
Fusion=Temporal
0.014
IN=True
0.000
Fusion=Temporal
0.000
Correlation
Embed=Invert
0.000
FF=Transformer
0.000
Embed=Invert
0.012
FF-Transformer
0.000
Transition
IN=TTrue
0.000
Fusion=Temporal
0.000
Multivariate
SD=True
0.034
Embed=Invert
0.000
Shifting
FF=RNN
0.000
IN=True
0.000
Fusion=Temporal
0.000
IN=True
0.000
Fusion=Temporal
0.000
Scasonality
Embed=Token
0.000
FF=Transformer
0.000
Embed=Token
0.006
FF=RNN
0.000
Trend
IN=True
0.000
Fusion=Temporal
0.001
Embed=Patch
0.000
Embed=Token
0.021
Stationarity
FF=RNN
0.000
Fusion=Temporal
0.026
HatRatio
Fusion=Temporal
0.022
Transition
SD=True
0.000
SD=TTrue
0.000
Shifting
Fusion=Temporal
0.011
Tusion=/eemporal
0.008
Univariate
Scasonality
FF=Transformer
0.000
SD=True
0.000
Trend
7
Fusion=Temmpral
0.000
7
Embed=None
0.044
Stationarity
7
SD=Truc
0.002
Table Statistical correlation between data/task properties and the effectiveness of specific architec- tural module choices in improving ranking performance (lower is better). Each row indicates whether a particular module configuration (e-g., input normalization, fusion type, embedding, feedforward block) is associated with significantly lower higher rank under certain data characteristics. The direction arrows ( or /) denote whether the choice favored when the property is low or high, respectively, and the p-value quantifies the strength of the statistical association. Results are grouped by multivariate and univariate forecasting settings.
Nonetheless, our claims are supported by comprehensive benchmarking, over 10,000 experiments across diverse datasets, forecasting horizons, and task settings. The results are also statistically meaningful, with reported outcomes averaged over multiple random seeds for statistical robustness. Furthermore, statistical hypothesis testing validates the correlation findings.
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RTTh1 _4 M
IN
SD
Fusion
Embed
FF-Type
Rank
MSE
MAE
TIMERECIPE Best
X
Feature
Patch
MLP
1.5
0.2963
0.3467
Existing Best (PaichTST)
Temporal
Patch
0.2988
-0.9%
0.3520
-1.5%
Feature
Patch
1.5
0.2963
0.0%
0.3467
0.0%
X
Temporal
Patch
20.5
0.3096
-4.3%
0.3586
-3.4%
Top-3 Selection
x
Temporal
Patch
Trans.
4.0
0.2988
-0.9%
0,3520
-1.5%
Selection better than existing best: Yes (Selection 18:3)
Envi conment. _
IN
SD
Fusion
Embed
FF-Type
Rank
MSE
MAE
TIMERECIPE Best
V
V
Temporal
Patch
RNN
2.0
0.2912
0.3786
Existing Best (DLineur)
/
Temporal
None
MLP
16.0
0.2950
-1.3%
0.3825
-1.0%
Feature
Patch
RNN
21.5
0.2987
-2.5%
0.3824
-1.0%
Top-3 Selection
Feature
Patch
RNN
36.5
0.3068
-5.3%
0.3936
-4.0%
Feature
Token
2.5
0.2920
-0.2%
0.3781
+0.1%
Selection better than existing best: Yes (Selection 3)
Security_ 2 2_8
IN
SD
Fusion
Embed
FF-Type
Rank
MSE
MAE
TIMERECIPE Best
/
X
Feature
None
RNN
2.5
74.2170
4.0465
Existing Best (DLineur)
/
4
Temporal
None
MLP
26.0
75.2914
-1.4%
4.3136
-6.6%
/
x
Feature
Invert
Trans.
56.0
86.9113
-17.1%
5.1710
-27.8%
Top-3 Selection
/
Temporal
Patch
RNN
19.0
75.2749
-1.4%
4.2357
-4.7%
/
Temporal
Patch
MLP
14.5
74.9425
-0.9%
4.2124
-0.4%
Selection better than existing best: Yes (Selection 28:3)
Table 5: Comparison of model configurations selected by method against the best-performing existing model and the global best results found through exhaustive design space search. At least one of our top-3 selections consistently outperforms the existing best and closely approaches the opti- mal configuration on ETThl 2 4_M, Envi www.irrommet__iem demonstrate the value of TIMERECIPE, even when using a simple tree-based approach.
and Security_ie ty__t_y___________ The results
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Setup
IN
Fusion
Embed
FF-Type
MSE
MAE
Rank
Total
X
Feature
Patch
MI.P
0.3761
0.3920
3
2.0
V
Feature
Patch
MLP
0.3783
0.3916
2
2.5
Temporal
Patch
RNN
0.3799
0.3952
5.0
X
Feature
Patch
MI.P
0.3794
0.4011
8
6.0
X
Temporal
Patch
RNN
0.3803
0.3971
6
6.5
8TTh1_96_M
Temporal
Frequency
MLP
0.3776
0.4019
11
Temporal
Patch
RNN
0.3828
13
0.3915
1
7.0
V
Temporal
None
MI.P
0,3801
0,4019
10
8.0
Temporal
Patch
RNN
0.3837
0.3930
Feature
None
Trans.
0.3811
0.4018
9
9.0
Feature
Patch
MLP
0,4328
0.4238
2
4.0
Temporal
Patch
RNN
0,4314
0.4265
x
Temporal
Patch
RNN
0.4314
0.4285
6
4.5
Temporal
Patch
RNN
0,4339
0.4216
5.0
Temporal
Frequency
MLP
0.4306
0.4314
RTTh1_192_1
Temporal
None
MLP
0,4292
0.4318
10
5.5
Feature
Patch
MI.P
0.4325
0.4310
8
6.5
Feature
Patch
MLP
0,4347
0.4260
Feature
None
Trans.
0.4336
0.4322
12
10.0
Temporal
Patch
MI.P
0.4334
0,4343
17
12.0
Temporal
Invert
MLP
0.4626
0.4462
1.5
Temporal
Patch
RNN
0.4766
0.4433
1
4.0
Temporal
Patch
Trans.
0.4713
0.4510
6
4.5
Temporal
None
MLP
0.4703
0.4526
Feature
Patch
MLP
0.4799
12
0.4467
3
7.5
BTTh1_336.0
Temporal
Invert
MI.P
0.4774
0,4518
7
7.5
Temporal
Patch
RNN
0.4746
0.4541
14
Temporal
Patch
RNN
0.4835
0,4482
4
10.0
V
Temporal
Frequency
MI.P
0.4744
0,4554
17
10.5
Feature
None
Trans.
0.4790
0,4538
11.0
Temporal
Invert
MI.P
0.4716
0.4698
1.0
Temporal
Patch
Trans.
0,4741
0.4722
3
2.5
Temporal
Invert
MLP
0.4818
0.4730
Temporal
Patch
RNN
0.4855
0.4719
2
4.5
Feature
None
Trans.
0.4792
0.4792
7
5.0
BTTh1_720_N
Temporal
None
MI.P
0.4842
0.4787
5.5
/
Temporal
Patch
RNN
0.4853
0.4730
5
5.5
/
Feature
Invert
Trans.
0.4979
0.4825
9
8.5
Temporal
None
MI.P
0.4982
0.4819
8
Temporal
Frequency
MLP
0.5009
12
0.4840
11
11.5
Table 6: Top- configurations for the ETTh1 dataset multivariate forecasting. IN: Instance Norm, SD: Series Decomposition. / indicates module used, X indicates not used. Red/blue highlights indicate best and second-best performances.
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Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
Feature
Patch
MLP
0.2888
0.3392
1.5
Temporal
Patch
RNN
0.2895
0.3397
2
2.5
Temporal
Patch
RNN
0.2877
0.3422
5
3.0
Feature
Patch
MLP
0,2904
0.3406
3
3.5
X
Temporal
Patch
RNN
0.2917
0.3410
4
5.5
2TTh2
Temporal
Invert
MLP
0,2913
0.3432
9
7.0
Temporal
Frequency
MLP
0,2920
0.3426
Temporal
None
MLP
0.2915
0.3430
8
7.0
Feature
Patch
RNN
0.2944
0.3427
7
9.0
Temporal
Frequency
MLP
0.2927
0.3440
11
10.0
Temporal
Patch
RNN
0.3684
0.3891
1.5
Feature
Patch
MLP
0.3677
0.3923
4
2.5
Feature
Patch
MLP
0.3705
0.3904
Temporal
Patch
MLP
0.3722
0.3917
3
4.5
Temporal
Patch
RNN
0.3718
0.3934
5
5.0
ETTh2_192 _922_
Temporal
None
MLP
0.3714
0.3952
11
Temporal
Frequency
MLP
0.3734
10
0.3937
6
8.0
Temporal
None
MLP
0.3723
0.3947
10
8.5
Feature
Patch
RNN
0.3731
0.3953
10.0
Temporal
Invert
MLP
0.3745
13
0.3943
8
10.5
Temporal
Patch
RNN
0.4142
0.4269
2.0
Feature
Invert
Trans.
0.4131
0.4292
Temporal
Invert
MLP
0.4159
0.4286
3
4.0
Temporal
Patch
RNN
0.4164
0.4289
5
5.5
Feature
None
Trans.
0,4173
0.4286
BTTh2_336_M
Temporal
Patch
MLP
0.4158
0.4293
9
6.5
Feature
Patch
RNN
0.4166
0.4294
10
8.5
Temporal
Patch
MLP
0.4196
0.4292
X
Temporal
Frequency
MLP
0.4187
0.4306
11
10.0
Feature
Patch
MLP
0.4206
13
0.4292
8
10.5
Temporal
Invert
RNN
0.4269
0.4286
11.5
Feature
Invert
Trans.
0.4218
0.4426
2
1.5
Temporal
Invert
MLP
0.4262
0.4426
2.5
Feature
None
Trans.
0.4257
0.4443
3
3.0
Temporal
Patch
MLP
0.4244
0.4446
5
3.5
X
Temporal
Patch
RNN
0.4265
0.4445
4
4.5
BTTh2_720_M
Temporal
None
MLP
0,4312
0.4455
Temporal
None
MLP
0.4290
0.4456
7
6.5
/
X
Temporal
Patch
MLP
0.4314
0.4483
10
9.0
Temporal
Invert
MLP
0.4320
0.4458
8
Temporal
Invert
RNN
0.4326
0.4464
9
10.0
Table 7: Top-10 configurations for the ETTh2 dataset multivariate forecasting. IN: Instance Norm, SD: Series Decomposition. / indicates module used, X indicates not used. Red/blue highlights indicate best and recond-best performances.
25

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
Feature
Patch
MLP
0.3274
0.3647
X
Temporal
Patch
RNN
0.3281
0,3640
2
2.5
Feature
Patch
RNN
0.3280
0,3654
Temporal
Patch
RNN
0.3308
0.3628
4.5
X
Temporal
Patch
MLP
0.3290
0.3661
5.5
ETTml_ M
Temporal
None
MI.P
0.3294
0.3655
Temporal
Invert
RNN
0.3292
0.3669
7.0
Feature
None
0.3311
0.3659
x
Feature
Patch
MI.P
0.3308
0.3662
8
8.5
Temporal
Patch
MI.P
0.3299
0.3682
9.0
Temporal
Patch
RNN
0.3681
0,3830
2.0
Feature
Patch
MLP
0.3669
0.3851
2.5
Temporal
Patch
0.3706
0,3836
X
Temporal
Patch
MLP
0.3667
0.3881
8
4.5
Temporal
Patch
0,3688
0.3872
5.0
__2___
Feature
Patch
RNN
0.3694
0.3862
5
5.0
X
Feature
Patch
MLP
0.3710
0.3855
5,5
Temporal
None
MLP
0.3722
0,3890
8.5
X
Temporal
None
MLP
0.3729
12
0.3878
7
9.5
Temporal
Freq
MLP
0.3724
0.3893
10
Temporal
Patch
RNN
0,4001
0.4065
2.0
Feature
Patch
MLP
0.4003
0.4082
4.0
x
Temporal
Patch
MLP
0.4000
0.4100
4.5
X
Temporal
Patch
RNN
0.4025
0,4069
2
4.5
Temporal
Patch
MI.P
0.3979
0,4109
ETIml 336
Feature
Patch
RNN
0.4003
0.4093
5
5,0
Feature
Patch
MI.P
0.4032
0.4073
Temporal
Invert
MLP
0.4030
0.4097
6
7.0
Temporal
Freq
MLP
0.4022
0.4107
7.0
Temporal
None
MI.P
0.4058
12
0.4110
10
11.0
X
Temporal
Patch
MI.P
0.4577
0.4424
2
2.0
Temporal
Patch
0.4558
0.4441
Temporal
Patch
RNN
0.4628
0.4393
2,5
Temporal
Patch
MI.P
0.4579
0.4486
10
6.5
Temporal
Invert
MLP
0.4653
0.4467
6
6.5
ETTmI_720_M
X
Temporal
Patch
RNN
0.4682
11
0.4462
4
7.5
Feature
Patch
0.4679
0,4463
Feature
Patch
RNN
0,4650
0.4485
9
7.5
Temporal
Freq
MLP
0.4648
0.4487
11
8.0
Temporal
None
MLP
0.4678
0.4484
8
8.5
Table 8: Top-10 10 configurations for the ETTml dataset multivariate forecasting. IN: Instance Norm, SD: Series Decomposition. / indicates module used, X indicates not used. Red/blue highlights indicate best and second-bes performances.
26

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
Temporal
Invert
RNN
0.1766
0.2576
Feature
Patch
MLP
0.1763
0.2581
3
3.0
Feature
Patch
RNN
0.1761
0,2590
x
Feature
Patch
MI.P
0.1768
0.2577
2
3.5
X
Feature
Patch
RNN
0.1761
0.2600
5,0
ETTm2_996 96_M
Temporal
Patch
MI.P
0.1771
0.2598
7.0
Temporal
Freq
MI.P
0.1772
0,2596
6
7.0
Feature
Token
Trans.
0.1770
0,2599
x
Temporal
Freq
MI.P
0.1795
16
0.2595
5
10.5
x
Feature
Token
Trans.
0.1783
0.26077
13
12.0
X
Feature
Patch
MLP
0.2403
0.2996
1.0
Feature
Patch
MLP
0,2405
0.2997
2
2.5
Temporal
Patch
0.2405
0,3008
Temporal
Invert
RNN
0.2422
0.3008
5
5.5
Temporal
Freq
MLP
0,2406
0.3017
ETIm2_192_M
Temporal
Patch
RNN
0.2427
0.3008
6
7.0
Feature
Patch
RNN
0.2417
0.3024
7.0
Temporal
Patch
RNN
0.2432
0.3007
3
7.0
Temporal
None
MLP
0.2426
0.3023
8
7.5
Temporal
Invert
MLP
0.2428
0.3031
10
Feature
Patch
MLP
0.2980
0.3378
2
1.5
Temporal
Patch
RNN
0,3009
0.3369
X
Feature
Patch
MLP
0.3002
0.3389
3.0
Temporal
Freq
MLP
0.2982
0.3393
3.5
Temporal
Patch
RNN
0.3017
0.3390
ETTm2_
Temporal
None
MLP
0.3003
0.3405
8
6,0
Feature
Patch
RNN
0.3010
0.3398
Temporal
Patch
MLP
0.3013
0.3398
7.0
X
Temporal
Freq
MLP
0.3018
0.3405
9.0
X
Temporal
Patch
MI.P
0.3024
10
0.3409
10
10.0
Temporal
Patch
RNN
0.3942
0.3924
1.0
Feature
Patch
MLP
0.3981
0,3960
Temporal
Invert
MLP
0.3965
0.3961
5
3,5
Feature
Patch
ML.P
0.3983
0.3958
3.5
X
Temporal
Patch
RNN
0.3991
0,3951
2
5.0
ETTm2_720_M
Temporal
Patch
MLP
0.3984
0.3963
6
5.5
Temporal
0.3990
0,3966
Temporal
None
MLP
0.3991
0.3968
8
7.5
X Temporal
Freq
MLP
0.3992
0.3980
10
9.5
X Temporal
None
MLP
0.4006
10
0.3975
9
9.5
Table 9: Top-10 10 configurations for the ETTm2 dataset multivariate forecasting. IN: Instance Norm, SD: Series Decomposition. / indicates module used, X indicates not used. Red/blue highlights indicate best and second-bes performances.
27

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
Feature
Patch
MLP
0.0821
1
0.1974
1.0
Temporal
Patch
RNN
0.0823
3
0.1978
2.5
Temporal
Patch
MI.P
0.0823
2
0.1988
3.0
X
Temporal
Patch
RNN
0.0828
0.1987 5
3
4.0
Temporal
Invert
MLP
0.0829
0,1994 6
6.0
Exchange_996 9__M
Feature
MLP
0.0833
0.1988 4
Temporal
Patch
Trans
0.0827
0.2002
8
6.0
Temporal
Patch
MLP
0.0836
9
0,2000
7
8.0
Temporal
Invert
MLP
0.0839
0.2004 10
9.5
Temporal
None
MLP
0.0845
0.2017 11
10.5
Temporal
Patch
MLP
0.1724
0.2939 2
1.0
Temporal
None
MLP
0.1734
0.2954
3.0
Feature
Patch
MLP
0.1742
0.2945
3.0
Temporal
Patch
RNN
0.1744
0.2948 5
4.0
Temporal
Invert
MLP
0.1741
3
0.2954
5
4.0
Exchange_192_M
Temporal
Patch
RNN
0.1754
0.2958
6.5
Temporal
MLP
0.1751
0,2965
7.0
Feature
Patch
MLP
0.1757
9
0.2962
7
8.0
Feature
Patch
RNN
0.1757
0.2972 8
8.5
Temporal
None
MLP
0.1761
0.2979
11.0
Temporal
Patch
MLP
0,3192
0.4075 2
1.0
Temporal
Invert
MLP
0.3246
0.4121
2
2.0
Temporal
Patch
RNN
0.3278
0.4127
4.0
Feature
Patch
RNN
0.3278
3
0.4143
5.0
Feature
Patch
MLP
0.3279
6
0,4134
5.0
Exchange_338
Temporal
Patch
RNN
0.3284
7
0.4135
6.0
Temporal
None
MLP
0.3278
0,4148
Feature
Patch
MLP
0.3296
8
0.4139
7.0
Feature
Invert
Trans.
0.3312
10
0.4165
9.5
Feature
None
Trans.
0.3307
0.4172
10
9.5
Temporal
Freq
MLP
0.8183
0.6837
1.0
Temporal
None
MLP
0.8337
3
0.6871
2
2.5
Temporal
Patch
MLP
0.8378
0,6872 4
3.5
Temporal
Freq
MLP
0.8205
0.6950
Temporal
Patch
Trans.
0.8411
0.6895 5
4.5
Rxchange_7200
Temporal
None
MLP
0.8490
8
0,6955
8.5
Temporal
Patch
RNN
0.8544
11
0.6948
8.5
Feature
Patch
MI.P
0.8545
12
0.6947
5
8.5
X
Feature
Patch
MI.P
0.8542
10
0.6954
8
9.0
X Temporal
Invert
MI.P
0.8493
9
0.6958
10
9.5
Table 10: Top-10 10 configurations for the Exchange Rate dataset multivariate forecasting. IN: Instance Norm, SD: Series Decomposition. / indicates module used, X indicates not used. Red/blue highlights indicate best and second-best performances.
28

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
X
Feature
Patch
Trans.
2.0338
2
0.8776
1
1.5
Feature
Patch
Trans.
2.0034
0.9064
3
X
Temporal
Freq
MLP
2.1586
3
0.8874
2
2.5
X
Temporal
Invert
MLP
2.1982
4
0,9084
4.0
X
Temporal
None
MLP
2.2416
5
0.9231
5
5.0
ILI_24_M
X
Temporal
Token
MLP
2.3280
9
0.9492
7
8.0
Temporal
Token
MLP
2.3096
7
0.9640
11
9.0
Temporal
Freq
MLP
2.4091
13
0.9563
9
11.0
X
Feature
Invert
RNN
2.4471
17
0.9480
6
11.5
x
Temporal
Token
Trans.
2.3071
6
1.0035
20
13.0
Temporal
Token
MLP
1.9663
0.9067
X
Feature
Invert
RNN
1.9444
1
0.9104
2
1.5
Feature
Invert
Trans.
2.1458
3
0.9381
X
Temporal
Invert
MLP
2.1907
6
0.9234
5
5.5
Feature
Invert
Trans.
2.1581
4
0.9414
9
6.5
ILI_36. 36_M
Feature
Patch
Trans.
2.2107
8
0.9257
7.0
X
Temporal
Freq
MLP
2.2220
11
0.9190
4
7.5
Feature
Patch
Trans.
2.2456
13
0.9117
3
8.0
Temporal
Token
MLP
2.1651
5
0.9516
12
8.5
Temporal
Invert
MLP
2.2197
10
0.9459
10.0
X
Feature
Patch
Trans.
1.9918
2
0.8685
1,5
Temporal
Token
MI.P
1.8707
0.8860
3
X
Temporal
Freq
MLP
2.0316
3
0.8844
2
2.5
Feature
Invert
Trans.
2.0593
5
0.8933
4
4.5
Temporal
Freq
MLP
2.0393
4
0.9152
8
6.0
ILI_48 48_M
Feature
Invert
Trans.
2.1405
7
0.9102
6
6.5
Feature
Patch
Trans.
2.1567
8
0.9074
6.5
X
Temporal
Invert
MLP
2.1383
6
0.9173
9
7.5
Feature
Invert
RNN
2.1660
0.9137
7
V
Temporal
Token
MLP
2.2079
12
0.9318
10
11.0
Feature
Patch
Trans.
1.9860
0.8950
1.0
Feature
Invert
Trans.
2.0064
2
0.8998
2
2.0
X
Temporal
Freq
MLP
2.0119
3
0.9087
3
3.0
X
Feature
Invent
Trans.
2.0342
4
0.9130
4
4.0
X
Feature
Invert
RNN
2.0992
6
0.9336
5
5.5
ILI_60_M
Temporal
Freq
MLP
2.0898
0.9378
8
6.5
X
Temporal
Invert
MLP
2.1317
8
0.9346
6
7.0
Feature
Patch
Trans.
2.1360
0.9376
/
Feature
Invert
RNN
2.10
7
0.9380
9
8.0
Temporal
Patch
ML.
2.1548
0.9435
Table 11: Top- 10 configurations for the Illness (National Flu) dataset multivariate forecasting. IN: Instance Norm, SD: Series Decomposition. / indicates module used, indicates used. Red/blue highlights indicate best and second-best performances.
29

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
X
Feature
Invert
Trans.
0.1545
0.2455
X
X
Feature
Invert
Trans.
0.1554
2
0.2523
3
2.5
V
Feature
Invert
Trans.
0.1599
3
0.2508
2
2.5
V
Feature
Invert
RNN
0.1602
4
0.2550
4
4.0
V
X
Feature
Invert
RNN
0.1618
5
0.2562
6
5.5
BCL_96_M
Feature
None
RNN
0.1630
0,2562
X
Feature
Invert
Trans.
0.1624
6
0.2578
9
7.5
Feature
None
Trans.
0.1682
12
0.2560
5
V
X
Feature
None
RNN
0.1651
10
0.2581
10
10.0
x
X
Feature
Invert
RNN
0.1634
0,2628 8
16
12.0
X
Feature
Invert
Trans.
0.1670
0.2564
1.0
x
X
Feature
Invert
Trans.
0.1688
0.2640 2
3
2.5
Feature
Invert
Trans.
0.1707
0.2602
2.5
X
Feature
Invert
Trans.
0.1721
4
0.2663
5
4.5
Feature
RNN
0.1756
5
0,2682
ECL 192_M
X
Feature
Patch
Trans.
0.1802
12
0.2657
4
8.0
x
X
Feature
Patch
Trans.
0.1784
8
0.2676
9
8.5
Feature
None
RNN
0.1771
6
0.2683
11
8.5
Feature
None
Trans.
0.1797
11
0.2669
8
9.5
V
X
Feature
Invert
RNN
0.1772
0.2687
13
10.0
X
Feature
Invert
Trans.
0.1827
0.2732
1
1.0
Feature
Invert
Trans.
0.1864
3
0.2769
2
2.5
x
x
Feature
Invert
Trans.
0.1852
2
0.2830
6
4.0
x
x
Feature
Patch
Trans.
0.1924
4
0,2835
7
5.5
Feature
Patch
Trans.
0.1965
0.2823
3
BCL_336_M
x
x
Feature
Patch
RNN
0.1942
7
0.2850
8
7.5
Feature
Patch
RNN
0.1947
0,2850
Feature
Invert
RNN
0.1937
6
0.2856
11
8.5
x
Feature
Trans.
0.1928
5
0.2873
15
V
X
Feature
Patch
RNN
0.1978
15
0.2825
5
10.0
/
X
Feature
Invert
Trans.
0.2201
2
0.3061
1
1.5
/
Feature
Invert
Trans.
0.2221
0.3082
2.5
x
X
Feature
Invert
Trans.
0.2177
0.3153
5
3.0
X
X
Feature
Patch
Trans.
0.2275
0.3152
X
X
Feature
Patch
RNN
0.2299
6
0.3166
8
7.0
BCI_720_M
X
Feature
Invert
Trans.
0.2234
4
0.3176
11
7.5
X
Feature
Patch
RNN
0.2308
7
0.3167
9
8.0
/
X
Feature
Patch
Trans.
0.2364
14
0.3152
4
9.0
V
X
Feature
Patch
RNN
0.2385
17
0.3157
6
11.5
/
Feature
None
Trans.
0.2358
13
0.3168
10
11.5
Table 12: Top- configurations for the Electricity (ECL) dataset multivariate forecasting. IN: Instance Norm, SD: Series Decomposition. indicates module used, indicates not used. Red/blue highlights indicate best and second-best performances.
30

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
Feature
Token
RNN
0.1588
0.2062
1
1.0
Temporal
Invert
RNN
0.1589
0.2068
2
2.0
V
x
Feature
Token
RNN
0.1614
0.2092
3
3.0
V
Temporal
Invert
RNN
0.1617
0.2100
6
5.0
Feature
RNN
0.1634
0.2097
Weather
V
Feature
None
RNN
0.1634
0.2097
5
5.5
V
Temporal
Token
MLP
0.1624
0.2117
9
7.0
Feature
RNN
0.1642
0,2104
Feature
Invert
RNN
0.1649
13
0,2108
8
10.5
V
Temporal
Token
MLP
0.1648
0.2131
11
11.0
Feature
Token
RNN
0.2096
0.2528
/
x
Feature
Token
RNN
0.2102
0.2531
2
3.5
Temporal
Invert
RNN
0.2100
0.2542
5.0
Feature
None
RNN
0.2119
0,2540
X
Feature
Invert
RNN
0.2126
13
0,2539
3
8.0
Weather 192
Feature
Invert
RNN
0.2127
14
0.2541
5
9.5
Feature
None
RNN
0.2125
0.2545
v
Temporal
Invert
RNN
0.2127
15
0,2558
9
12.0
x
Feature
Patch
RNN
0.2082
0.2656
38
20.0
Temporal
Freg
MLP
0.2058
0.2660
/
Temporal
Invert
RNN
0.2671
14
0.2954
7.5
/
Feature
Invert
RNN
0.2700
0.2964 18
4
11.0
Feature
RNN
0.2704
0,2960
11.5
Feature
None
RNN
0.2705
22
0,2966
8
15.0
X
Temporal
Freg
MLP
0.2566
0.3054
34
17.5
Weather_33d
Feature
None
RNN
0.2706
0.2973
18.5
V
Feature
Token
RNN
0.2719
26
0,2970
11
18.5
X
Temporal
None
MLP
0.2628
0.3078
39
21.0
Feature
Patch
RNN
0.2761
0.2965
x
Temporal
Patch
RNN
0.2631
0,3079
40
22.5
Temporal
Invert
RNN
0.3429
19
0.3465
10.0
Feature
Patch
RNN
0.3536
0.3469
x
Temporal
Patch
MLP
0.3534
37
0,3471
7
22.0
x
Temporal
Freq
MLP
0.3548
41
0.3468
4
22.5
Temporal
Token
MLP
0.3481
0.3499
22
Weather_720
Temporal
None
MLP
0.3552
0.3466
2
23.0
V
Feature
Invert
RNN
0.3505
31
0.3485
15
23.0
V
Temporal
Freq
ML.
0.3549
0.3470
24.0
X
Feature
Patch
MLP
0.3355
0,3588
42
26.0
/ X Feature
Invert
RNN
0.3517
32
0.3492
20
26.0
Table 13: Top-10 configurations for the Weather dataset multivariate forecasting. IN: Instance Norm, SD: Series Decomposition. indicates module used, X indicates not used. Red/blue highlights indicate best and second-bos performances.
31

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
Feature
Invert
RNN
0.0725
0.1777
V
Feature
Invert
Trans.
0.0714
0.1781
3
2.0
Feature
Invert
RNN
0.0726
0.1780
X
Feature
None
RNN
0.0726
0.1782
4.0
V
Feature
None
RNN
0,0734
0.1793
5.0
PEMSOS 03_12_M
Feature
Invert
Trans.
0.0739
0.1812
Feature
None
Trans.
0.0739
0,1820
8
7.0
Feature
Invert
Trans.
0.0744
0.1814
Temporal
Freq
MI.P
0.0750
10
0.1830
10
10.0
Temporal
Invert
RNN
0.0751
0.1823
10.0
Feature
Invert
RNN
0.0985
0,2090
1.0
Temporal
Invert
RNN
0.0990
0.2091
2
2.0
Feature
Invert
RNN
0.1003
0,2108
X
Feature
None
RNN
0.1006
0.2125
5
4.5
Feature
None
RNN
0.1009
0,2117
PEMS03_244 2__
Feature
Token
RNN
0.1023
0.2136
6
6.0
Temporal
Invert
RNN
0.1045
0.2140
7.5
Feature
Invert
Trans.
0.1030
0.2156
7.5
Feature
Invert
Trans.
0.1051
10
0.2156
9
9.5
Temporal
Token
MLP
0.1055
0.2176
10.0
Feature
Invert
RNN
0.1220
0.2330
2
1.5
Temporal
Invert
RNN
0.1251
0.2315
X
Feature
Invert
RNN
0.1230
0.2348
3.0
Feature
Token
RNN
0.1254
0.2341
3,5
Temporal
Invert
RNN
0.1259
0.2371
PEMS03
X
Feature
None
RNN
0.1265
0.2386
6
6,0
Feature
None
RNN
0.1280
0.2393
Feature
Token
RNN
0.1294
0.2401
8.5
X
Feature
Token
RNN
0.1314
10
0.2395
9.0
Feature
Token
Trans.
0.1310
0.2410
10.0
Feature
Token
RNN
0.1398
0.2489
1.0
Temporal
Invert
RNN
0.1426
0,2499
X
Temporal
Token
Trans.
0.1438
0.2530
5
4.5
Temporal
Token
RNN
0.1412
0.2543
4.5
X
Temporal
Invert
RNN
0.1461
0.2498
PEMS03_48_M
X
Feature
Invert
RNN
0.1445
0.2539
6
5.5
Feature
Token
RNN
0.1455
0,2525
X
Feature
Invert
RNN
0,1449
0.2552
8
7.0
Temporal
Token
Trans.
0.1450
0.2580
8.0
Feature
Token
Trans.
0.1499
0.2591
10
10.5
Table 14: Top- 10 configurations for the PEMS03 dataset. IN: Instance Norm, SD: Series Decomposi-
tion. / indicates module used, indicates not used. Red/blue highlights indicate best and second-best performances.
32

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
Feature
Invert
Trans.
0.0814
0.1891
V
Feature
Invert
RNN
0.0815
0.1894
2
2.0
Feature
Invert
RNN
0.0816
0.1899
X
Feature
Invert
Trans.
0.0825
0.1910
4.0
X
Feature
None
RNN
0.0826
0.1911
5.0
PEMS 04 12_M
Feature
None
RNN
0.0829
0.1913
Temporal
Invert
RNN
0.0830
0.1912
6
6.5
Feature
Token
RNN
0.0856
0.1953
X
Temporal
Invert
RNN
0.0856
10
0.1955
9
9.5
Temporal
Token
MI.P
0.0848
0.1958
9.5
Temporal
Invert
RNN
0.0992
0.2119
1.0
X
Temporal
Invert
RNN
0.1013
0.2146
2
2.0
Temporal
Token
RNN
0.1013
0,2146
X
Temporal
Token
Trans.
0.1026
0,2151
6
5,0
Feature
Invert
RNN
0.
0,2168
10
PEMS04 1188042240 2
Temporal
Token
Trans.
0.1043
0.2163
8
8.0
X
Feature
Invert
RNN
0.1032
0,2172
11
8.5
Temporal
Invert
RNN
0.1057
12
0.2155
9.5
Feature
Token
RNN
0.1034
0.2185
13
10.0
Feature
Invert
Trans.
0.1088
0.2187
14
12.0
Temporal
Invert
RNN
0.1108
0.2203
1.0
Temporal
Token
RNN
0.1134
0.2208
x
Temporal
Token
Trans.
0.1149
0.2228
3.5
Temporal
Token
Trans.
0.1147
0.2230
3,5
Temporal
Invert
RNN
0.1155
0.2240
PEMS04 36_M
Temporal
Invert
RNN
0.1151
0.2294
8
6.5
Feature
Token
RNN
0.1157
0.2268
X
Temporal
Token
RNN
0.1184
10
0.2268
6
8.0
X
Temporal
Token
Trans.
0.1171
0.2318
12
10.5
Temporal
Token
RNN
0.1165
0.2323
11.0
Temporal
Invert
RNN
0.1149
0.2246
1.0
Temporal
Token
Trans.
0.1168
0.2258
V
Temporal
Token
Trans.
0.1164
0.2261
3
2,5
X
Temporal
Invert
RNN
0.1174
0.2267
4.0
X
Temporal
Token
RNN
0.1195
0.2284
5.5
PEMS04_48_M
Temporal
Token
RNN
0.1192
0.2286
6
5.5
Feature
Token
0.1202
0,2312
X
X
Feature
Invert
MLP
0.1213
0.2322
8
8.0
Temporal
None
RNN
0.1236
0.2355
10
9.5
X
Temporal
None
RNN
0. 1242
0.2334
9
10.0
Table 15: Top- 10 configurations for the PEMS04 dataset. IN: Instance Norm, SD: Series Decomposi-
tion. / indicates module used, indicates not used. Red/blue highlights indicate best and second-best performances.
33

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
Feature
Invert
Trans.
0.0663
0.1650
V
Feature
Invert
RNN
0.0664
0.1682
3
2.5
Feature
Invert
Trans.
0.0669
0.1676
X
Feature
Invert
RNN
0.0673
0.1696
5
4.5
X
Feature
Invert
Trans.
0.0682
0.1691
5.5
PEMSO7 17_12_M
X
Feature
None
RNN
0.0676
0.1698
Feature
None
RNN
0.0677
0.1699
6.5
Feature
Invert
Trans.
0.0699
0.1712
Feature
None
Trans.
0.0697
0.1717
9
8.5
Feature
Invert
RNN
0.0703
10
0.1737
10
10.0
Feature
Invert
Trans.
0.0901
0.1946
1.0
X
Feature
Invert
Trans.
0,0912
0.1959
2
2.0
Feature
Invert
RNN
0.0938
0,2009
X
Feature
Invert
RNN
0.0954
0.2027
5
5,0
Feature
None
RNN
0.0953
0.2031
PEMS07_24.
Temporal
Invert
RNN
0.0999
0.2013
6.0
Feature
None
RNN
0.0962
0,2043
8
7.0
Temporal
Invert
RNN
0.1017
0.2037
8.0
Feature
Invert
Trans.
0.0992
0.2053
8.0
Feature
Token
RNN
0.
0.2057
10
10.0
Feature
Invert
Trans.
0.1086
0.2159
1.0
Feature
Invert
Trans.
0.1118
0.2197
2.5
Temporal
Invert
RNN
0.1182
0.2195
2
3.0
X
Temporal
Invert
RNN
0.1206
0.2218
5.0
Feature
Invert
RNN
0.1175
0.2258
PEMSO7_
Feature
Token
RNN
0.1206
0.2234
5
6,0
Temporal
Token
RNN
0.1208
0.2241
X
Feature
Invert
RNN
0.1200
0.2282
12
8.5
X
Temporal
Token
RNN
0.1218
0.2249
9.0
Feature
Invert
MI.P
0.1216
10
0.2259
9.5
Feature
Invert
Trans.
0.1237
0.2319
1.0
Feature
Invert
Trans.
0.1283
0.2367
Temporal
Invert
RNN
0.1358
0.2378
3
3.0
X
Temporal
Token
RNN
0.1368
0.2396
4.0
X
Temporal
Invert
RNN
0.1377
0.2397
6.5
PEMS07_48_M
Temporal
Token
RNN
0.1373
6
0.2416
6.5
Feature
Token
RNN
0.1377
0,2399
X
Feature
Invert
RNN
0.1368
0.2457
10
7.5
X
Feature
Invert
RNN
0.1393
0.2472
14
11.5
Feature
Invert
MLP
0. 1.1400
10
0.2472
13
11.5
Table 16: Top- 10 configurations for the PEMS07 dataset. IN: Instance Norm, SD: Series Decomposi-
tion. / indicates module used, indicates not used. Red/blue highlights indicate best and second-best performances.
34

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
Feature
Invert
Trans.
0.0795
0.1819
X
Feature
Invert
Trans.
0.0834
0.1868
2
2.5
Feature
None
Trans.
0.0833
0.1877
Feature
Invert
RNN
0.0844
0.1895
6
5.0
X
Feature
Invert
RNN
0.0856
0.1908
6.5
PEMS 08 M
X
Feature
None
Trans.
0.0866
0.1913
10
Feature
None
RNN
0.0864
0.1918
11
8.5
Feature
None
RNN
0.0867
0.1920
12
10.0
Temporal
Freq
MI.P
0.0870
0.1929
13
11.0
X
Temporal
Freq
MLPP
0.0891
10
0.1955
14
12.0
Feature
Invert
Trans.
0.1162
0.2191
1.0
X
Feature
Invert
Trans.
0.1226
0.2263
4.0
Feature
None
Trans.
0.1267
0,2327
Temporal
Invert
RNN
0.1318
0.2307
6.5
Feature
Invert
RNN
0.1296
0,2359
PEMS08_244 M__M
Feature
Invert
RNN
0.1302
0.2361
10
7.5
Temporal
Freq
MLP
0.1319
0,2382
12
9.5
Feature
None
RNN
0.1325
0.2384
13
11.0
Feature
None
RNN
0.1325
0.2386
14
11.0
Feature
Token
RNN
0.1378
0.2376
12.5
Feature
Invert
Trans.
0.1581
0.2555
5
3.0
Temporal
Invert
RNN
0.1685
0.2638
4.5
X
Feature
Invert
Trans.
0.1689
0.2679
9
6.0
Feature
Token
RNN
0.1722
0.2681
10
7.5
Feature
None
Trans.
0.1711
0.2720
12
8.0
PEMS08
X
Temporal
Invert
RNN
0.1736
0.2710
11
8.5
Feature
Token
RNN
0.1745
0.2733
14
10.5
x
Temporal
Token
Trans.
0.1801
12
0.2725
13
12.5
Temporal
Freq
MLP
0.1768
0.2778
19
13.5
X
Feature
Token
Trans.
0.1769
0.2774
18
13.5
Feature
Invert
RNN
0.2135
0.2645
3.0
Feature
Invert
Trans.
0.2013
0,2892
Temporal
Invert
RNN
0.2052
0.2947
10
6.0
X
Feature
Invert
RNN
0.2170
0.2673
X
Temporal
Token
Trans.
0.2112
0.2975
12
8.0
PEMS08_48_M
/
Feature
Token
RNN
0.2101
0.2986
13
8.0
Feature
None
RNN
0.2191
0.2714
X
Feature
None
RNN
0.2267
22
0.2788
5
13.5
X
Feature
Token
RNN
0.2161
0.3063
21
15.0
X
Feature
Invert
Trans.
0.2170
0.3049
19
15.0
Table 17: Top- 10 configurations for the PEMS08 dataset. IN: Instance Norm, SD: Series Decomposi-
tion. / indicates module used, indicates not used. Red/blue highlights indicate best and second-best performances.
35

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FB-1ype
SMAPE
Rank
MASE
Rank
OWA
Rank
Total
X
Feature
Invert
Trans.
18,0080
2.6195
3
LJ0367
4,00
Temporal
17.8405
1.0968
K
Feature
Patch
Trans.
18.2368
2,4683
1.0115
4.67
K
Temporal
Patch
MLP
17.6707
3.0920
8
1.1260
5.33
X
X
Temporal
Invert
MLP
17,9402
3.0478
7
1.1240
5.67
M4_ _y_
X
Temporal
Patch
MLP
17.8320
3.1867
1.1500
Temporal
Trans.
18.7640
2.5265
Feature
Patch
RNN
18,0900
3,2920
12
1.1793
10.00
x
Feature
Invert
Trans.
19,0040
22
2,8540
4
1.1128
10.33
x
Temporal
Patch
RNN
17.9512
3,3385
15
1.1850
10.67
Temporal
None
MLP
2.9520
3,1000
0,9575
Temporal
Freq
2.9578
X
Feature
Patch
RNN
3.0127
3.1990
0.9825
3.33
X
X
Feature
Patch
RNN
3.0122
3.2135
0.9848
3.67
X
Fealure
Token
RNN
3.0137
3.2145
0.9850
5,00
Mr_Dally_s
Temporal
Temporal
Invert
ML.P
3.0265
3.2172
0.9875
X
Temporal
Patch
MLP
3.0213
3,2287
10
0.9885
8.33
X
X
Temporal
Freq
MLP
3.0215
3.2322
12
0.9890
9.67
X
Feature
Invert
RNN
3,0270
3,2283
0.9892
10.67
Feature
Trans.
9.3830
K
Feature
Patch
Trans.
9,4917
2.84133
1,0295
2.00
K
X
Feature
Patch
Trans.
9.5275
2,8433
1.0317
3.00
X
Feature
Patch
MLP
9.5322
2,9158
5
1.0453
4.33
Temporal
Patch
MLP
9.6020
2.9263
1.0507
M4 Keek S
Feature
Trans.
2,9268
K
Temporal
Invert
MLP
9.9285
12
2,8515
4
1.0550
7.67
x
Feature
Patch
MLP
9.6543
2.9610
10
1.0600
8.67
x
Temporal
Patch
MLP
9.6170
2,9830
11
1.0617
9.00
Feature
RNN
Feature
Invert
Trans.
12.5925
0.8682
x
Temporal
Freq
MLP
12.5025
0.9273
0.8693
3.00
Temporal
Freq
MLP
12.5617
0.9253
0.8705
3.33
Feature
Invert
Trans.
12.6427
0.9195
2
0.8708
4.33
Temporal
12,5102
M4 Monthly_
Feature
Patch
RNN
12.6077
0.9258
5
0.8725
5.67
Feature
Token
RNN
12,6585
0.9223
3
0.8723
5.67
Feature
Token
RNN
6908
0.9277
7
0.8760
10.00
Temporal
Token
MLP
12.6453
0.9335
13
Feature
Trans.
2906
0,9280
0.8762
X
Temporal
None
MLP
9.9145
1.1500
0,8693
1.00
x
/
Temporal
Freg
MLP
9.9375
1.1542
2
0.8722
2
2.00
X
Temporal
Freq
MLP
10.0032
1.1687
0.8802
3.67
Feature
Temporal
Froq
MLP
10,0080
1.1700
0.8810
5.33
M4_ M4_Quarterly_5
X
Feature
Invert
Trans.
10.0510
1.1667
3
0. 0.8820
6.00
x
Temporal
Token
MLP
10.0237
1.1720
0.8825
7.33
Temporal
Invert
MLP
10.0347
Feature
Trans.
10.0590
0.8830
x
Temporal
Invert
MLP
10.0503
1.1727
0.8840 12
10.33
X
/
Temporal
Frog
MLP
13.29400
2.9985
2
0.7840
1.33
X
X
Temporal
Frog
MLP
13.3235
2.9930
0,7843 1
1.67
X
Temporal
Invert
MLP
13.3570
3.00772
3
0.7870
Temporal
Token
MLP
13.3673
3.0122
0.7880 5
X
V
Feature
Patch
MLP
13.3887
3,0077
0.7880 4
5.33
M4_Yearly_S
X
X
Temporal
Freg
MLP
13,3937
3.0200
0.7898 11
8.67
X
Temporal
Invert
RNN
13,4353
3,0130
6
0.7900
9.00
Temporal
Temporal
MI.P
13.3723
3,0380
21
0.7913
12.00
/
Temporal
None
MLP
13,3663
3,0393
23
0.7913
10
12.33
Table 18: Top-10 configurations for the M4 dataset. IN: Instance Norm, SD: Series Decomposition.
/ indicates module used, X indicates not used. Red/blue highlights indicate best and second-best performances.
36

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
X
Temporal
Patch
RNN
0.0550
0.1781
X
Temporal
None
MLP
0.0550
0.1784
5
3.5
Feature
Patch
0.0552
0.1782
x
Feature
None
RNN
0.0552
0.1783
3
3.5
Temporal
Patch
RNN
0,0552
0.1785
6
4.5
ETTh1_ 9
Feature
Invert
MI.P
0.0553
0.1785
Temporal
Invert
RNN
0.0554
10
0.1783
4
7.0
Temporal
None
MLP
0.0554
0.1785
Feature
Invert
RNN
0.0556
14
0.1787
9
11.5
X
Temporal
Invert
MI.P
0.0555
0.1792
14
12.5
X
Temporal
Freq
MLP
0.0716
0.2028
2.0
X
Temporal
None
MLP
0.0717
0.2027
2
2.0
Feature
None
RNN
0.0718
0.2026
X
Feature
Invert
RNN
0.0718
0,2030
4
3.5
Temporal
Token
MLP
0.0722
0,2035
@TTh1_192._0
x
Temporal
Invert
MLP
0.0720
0.2036
9
7.5
X
Feature
Token
RNN
0.0719
0,2038
12
8.5
Feature
Token
RNN
0.0722
0.2035
8.5
Feature
Patch
MLP
0.0725
14
0.2033
5
9.5
Temporal
Patch
RNN
0.0721
0.2039
10.0
Temporal
Freq
MLP
0.0830
0.2242
1.0
Temporal
None
RNN
0.0833
0.2261
3.5
Temporal
Invert
RNN
0.0840
0.2263
6
5.0
Feature
None
RNN
0.0844
0,2261
5,5
Temporal
Patch
RNN
0.0842
0,2265
7.0
ETTh1 S
Feature
Token
RNN
0.0845
0.2264
7
7,0
Temporal
None
MI.P
0.0850
0.2256
Temporal
Token
MLP
0.0849
12
0.2258
3
7.5
Temporal
Patch
MLP
0.0830
0.2270
13
7.5
X
Temporal
Invert
RNN
0.0845
0.2266
10
9.0
Temporal
Token
RNN
0.0834
0,2284
2
1.5
Temporal
Patch
RNN
0.0841
0.2280
Feature
Token
MLP
0.0849
0.2302
3
3,0
Temporal
Token
Trans.
0.0851
0.2306
4.0
X
Temporal
Patch
Trans.
0.0862
0.2314
5.0
ETThI_720_S
X
Temporal
Patch
RNN
0.0871
0.2317
7.5
Feature
Token
0.0867
0,2329
Feature
Patch
MLP
0.0871
0.2315
6
7.5
Feature
None
MLP
0.0871
0.2331
10
8.5
X Temporal
Invert
RNN
0.0873
10
0.2321
8
9.0
Table 19: Top- 10 configurations for the ETThl dataset univariate forecasting. IN: Instance Norm, SD:
Series Decomposition. / indicates module used, X indicates used. Red/blue highlights indicate best and second-bes beett performances.
37

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
Temporal
Patch
RNN
0.1275
0.2732
X
Temporal
Patch
RNN
0.1275
0.2734
2
2.0
Feature
Patch
0.1284
0.2747
x
Feature
Invert
MI.P
0.1285
0.2747
4.0
Temporal
Invert
RNN
0.1287
0.2750
5,0
ETTh2_96 _
Feature
None
MI.P
0.1290
0.2759
7.0
Temporal
None
MI.P
0.1292
0,2756
6
7.0
Temporal
Invert
RNN
0.1293
0.2758
Feature
Invert
MI.P
0.1292
0.2760
9
8.0
Feature
Patch
MI.P
0.1296
10
0.2762
10
10.0
Temporal
Freq
MLP
0.1680
0.3195
1.0
Feature
Patch
MLP
0.1780
0.3293
2
3.0
Temporal
Patch
0.1785
0.3315
X
Temporal
Invert
RNN
0.1797
11
0.3297
3
7.0
Temporal
None
MLP
0.1794
0.3315
ETTh2_192_s
X
Feature
None
MLP
0.1804
15
0.3309
9.5
Feature
Invert
MLP
0.1796
10
0.3325
11
10.5
Temporal
None
MLP
0.1787
0.3329
15
11.0
Temporal
Patch
RNN
0.1802
14
0.3316
8
11.0
Feature
Invert
MLP
0.1800
0.3319
11.0
X
X
Feature
Patch
MLP
0.1933
0.3464
1.5
Feature
Patch
MLP
0.1908
0.3472
1.5
X
Temporal
Freq
MLP
0.1947
0.3507
3.0
Temporal
Freq
MLP
0.1969
0.3514
4.5
Temporal
Patch
Trans.
0.2005
0.3531
ETTh2_330 S
Temporal
Token
MLP
0.1969
0.3575
9
6.5
Feature
Invert
MI.P
0.1984
0.3534
Feature
Invert
RNN
0.1988
0.3532
6
6.5
Feature
Invert
Trans.
0.2025
0.3564
8.5
X
Feature
Invert
Trans.
0.2051
0.3586
10
10.5
X
Temporal
Patch
Trans.
0.2214
0.3782
1.0
Feature
Patch
MLP
0.2217
0.3790
V
Temporal
Invert
MLP
0.2238
0,3806
3
3.0
X
Feature
Invert
Trans.
0.2257
0.3814
4.5
Feature
Invert
RNN
0.2256
0,3823
4.5
ETTh2_720_S
Feature
Patch
MLP
0.2260
0.3828
6.0
Temporal
Token
0.2267
0,3834
Temporal
None
MLP
0.2269
0,3833
7
7.5
X
Feature
Invert
RNN
0.2275
0.3840
9.0
X
Temporal
Patch
MLP
0.2297
0,3847
10
10.5
Table 20: Top- 10 configurations for the ETTh2 dataset univariate forecasting. IN: Instance Norm, SD: Series Decomposition. / indicates module used, X indicates used. Red/blue highlights indicate best and second-bes bbott performances.
38

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
Temporal
Patch
RNN
0.0286
0.1255
Feature
Patch
MLP
0.0287
0.1258
3
2.5
Feature
Invert
0.0287
0.1256
Feature
Patch
RNN
0.0287
0.1260
4.0
Temporal
Invert
RNN
0.0288
0.1260
5.5
ETTml_ 9
Feature
None
RNN
0.0288
0.1260
Feature
Invert
RNN
0.0288
0,1261
8
8.0
Temporal
Invert
RNN
0.0288
0.1263
Feature
None
MI.P
0.0289
10
0.1263
12
11.0
Temporal
Invert
MI.P
0.0289
13
0.1262
10
11.5
Temporal
None
RNN
0.0433
0.1583
2.0
Feature
None
MLP
0.0436
0.1582
2.0
Feature
None
0.0435
0.1585
Feature
Invert
MLP
0.0437
0.1582
2
3.5
Feature
Patch
RNN
0.0436
0.1586
5.0
ETImI_192_s
Temporal
Patch
MLP
0.0438
0.1586
5
6.0
Feature
Token
MLP
0.0437
0.1587
6.5
Temporal
Invert
RNN
0.0439
0.1588
8.5
X
Temporal
Patch
MLP
0.0439
10
0.1588
9
9.5
Temporal
Patch
RNN
0.0440
0.1588
10
10.5
X
Feature
None
MLP
0.0568
0.1837
2
1.5
Feature
None
MLP
0.0572
0.1831
1.5
Temporal
Patch
MLP
0.0574
0.1840
3.5
Feature
Patch
RNN
0.0576
0.1839
4,0
Feature
Token
MI.P
0.0575
0.1843
ETIml 3
Temporal
None
MLP
0.0S77
0.1840
5
6,0
Feature
Invert
MI.P
0.0578
0.1841
Temporal
Invert
RNN
0.0579
0.1845
9
9.0
Temporal
None
RNN
0.0576
0.1848
12
9.0
Temporal
Freq
MI.P
0.0581
0.1845
9.5
Temporal
Invert
RNN
0.0809
0.2172
1.5
Feature
None
MLP
0.0807
0.2175
X
Feature
Freq
MLP
0.08 10
0.2179
5
4.0
Temporal
None
MI.P
0.0811
0.2179
5.0
Feature
Token
MLP
0.0811
0.2180
9
7.0
ETImI_720_S
Feature
Invert
RNN
0.0815
11
0.2177
7.0
Temporal
Freq
0.0815
0,2177
Temporal
Token
MLP
0.0815
0.2182
10
9.5
Temporal
Patch
MLP
0.0816
13
0.2179
10.0
X
Temporal
Patch
MLP
0.0812
0.2185
17
11.5
Table 21: Top-10 10 configurations for the ETTml I dataset univariate forecasting, IN: Instance Norm, SD: Series Decomposition. / indicates module used, X indicates not used. Red/blue highlights indicate best and second-bes performances.
39

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
Feature
None
RNN
0.0655
0.1823
X
Feature
Patch
MLP
0.0658
0.1828
2
3.5
Feature
Invert
RNN
0.0657
0.1834
Temporal
Invert
RNN
0.0658
0.1831
3
4.5
X
Feature
Invert
Trans
0.0657
0.1838
6.0
ETTm2_966 _
X
Feature
None
RNN
0.0660
0.1836
X
Temporal
Patch
MI.P
0.06660
0,1836
7.5
Feature
Patch
0.0661
0.1836
x
Temporal
Freq
MI.P
0.0657
0.1848
14
8.0
x
Temporal
Invert
RNN
0.0665
0.1844
10
11.5
X
Feature
Patch
RNN
0.0989
0,2325
1.0
Temporal
Invert
RNN
0.0996
0,2332
2
2.5
Feature
Patch
0.0996
0,2335
Feature
Invert
MLP
0.0996
0.2338
5
4.5
Feature
None
RNN
0.0998
0.2337
ETIm2_192_s
X
Feature
None
RNN
0.0997
0.2341
7
6.5
Temporal
None
MLP
0,0995
0.2347
12
7.0
Temporal
Patch
MLP
0.1005
13
0.2340
6
9.5
Feature
Invert
RNN
0.1000
0.2345
10
9.5
Temporal
Patch
MLP
0.10
0.2344
11.0
Feature
None
MLP
0.1289
0.2723
1.0
Feature
None
MLP
0.1290
0.2728
Feature
Invert
MLP
0. 1.97
0.2732
3.0
Feature
Patch
MLP
031304
0.2736
5.0
Temporal
Token
MI.P
0.1303
0.2744
ETTm2_ _
Temporal
Patch
RNN
0.1308
0.2743
6
7.0
Temporal
Token
MI.P
0.1302
0.2746
12
x
Temporal
Patch
RNN
0.1311
13
0.2740
9.0
X
Temporal
Invert
RNN
0.1308
0.2745
11
9.0
Temporal
Invert
RNN
0.1309
0.2744
9.0
X
Feature
None
MI.P
0.1795
0.3290
2
1.5
Feature
None
0.1802
0.3287
Temporal
Patch
MLP
0.1824
0.3306
4,0
Temporal
None
RNN
0.1822
0.3315
4.0
Feature
Invert
MLP
0.1823
0,3312
4,0
ETTm2_720_S
Temporal
Token
MLP
0.1827
0.3318
6.5
Temporal
0.1829
0.3318
Temporal
Freq
MLP
0,1830
0.3320
9
9,0
X Temporal
Freq
MLP
0.1828
0.3322
13
10.0
X Temporal
Invert
RNN
0.1833
11
0.3322
11
11.0
Table 22: Top- 10 configurations for the ETTm2 dataset univariate forecasting, IN: Instance Norm, SD: Series Decomposition. / indicates module used, X indicates not used. Red/blue highlights indicate best and second-bes performances.
40

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
Temporal
Patch
RNN
0.0887
1
0.2202
1.0
Temporal
Patch
ML.
0.0923
2
0.2230
2.0
Temporal
Token
MI.P
0.0925
3
0.2246
3.5
X
Feature
Patch
MLP
0.0942
4
0.2237
3
3.5
Feature
Invert
MLP
0.0974
0.2283 7
6.5
Exchange_966 _6_s
Temporal
Freq
MLP
0.0971
0,2285
7.0
Temporal
Invert
RNN
0.0969
5
0.2298
10
7.5
Feature
Patch
MLP
0.0995
11
0.2281
5
8.0
Temporal
None
MLP
0.0978
0.2293 8
8.5
Feature
None
RNN
0.0986
0,2299 10
10.5
V
Temporal
Patch
MLP
0.1998
0.3336
1.0
Temporal
Patch
RNN
0.2047
0.3353
3.0
Temporal
RNN
0.2046
0.3356 7
4.0
Temporal
Invert
RNN
0,2056
0.3355
4
5.5
Temporal
Token
MLP
0.2038
2
0.3390
11
6.5
Exchange_192_s
Feature
None
RNN
0.2068
9
0.3369
7.5
Feature
Putch
MLP
0,2082
15
0,3354
9.0
Feature
Invert
MLP
0,2053
5
0.3393
13
9.0
Feature
Patch
MLP
0.2072
12
0.3370
7
9.5
Temporal
MLP
0.2055
0.3404
10.0
Feature
None
Trans
0.4017
0.4832 4
1.0
Feature
None
RNN
0.4168
0.4854
5
4.5
Feature
Patch
RNN
0.4204
0.4852 8
5.5
Feature
Patch
RNN
0.4189
0.4865 6
6.0
Temporal
Patch
RNN
0.4217
11
0.4841
2
6.5
Exchange_338 _33__
Feature
None
RNN
0.4205
0.4853 9
4
6.5
Temporal
None
MLP
0.4166
0.4898
7.5
Temporal
Token
MLP
0.4182
5
0.4901
17
11.0
Temporal
Patch
MLP
0.4247
15
0.4872
8
11.5
Feature
Invert
RNN
0.4247
16
0,4880
10
13.0
Temporal
Token
RNN
0.7083
1
0.7244
1.0
x
Temporal
Invert
MLP
0.8477
3
0.7296
2
2.5
Feature
Token
MLP
0.8456
0.7729 2
3.5
Temporal
RNN
0.8950
0.7391
Temporal
Freq
MLP
0.9377
0.7404 6
5.0
Rxchange_720.
X
Feature
Token
MLP
0.8575
0.7779 4
5.0
Feature
None
Trans
1.0907
0.7944 11
9.5
Temporal
None
MI.P
1.0925
14
0.7931
10.5
Feature
None
MI.P
1.0923
13
0.7972
9
11.0
Feature
Token
Trans
1.0908
12
0.8024
11
11.5
Table 23: Top-10 configurations for the Exchange Rate dataset univariate forecasting. IN: Instance Norm, SD: Series Decomposition. / indicates module used, X indicates not used. Red/blue highlights indicate best and second-best performances.
41

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
Temporal
Patch
RNN
0.6131
1
0.5881
3
2.0
Feature
Patch
Trans.
0.6292
0.5877
Temporal
Patch
MLP
0.6405
4
0.5831
1
2.5
Temporal
Invert
RNN
0.6338
3
0.5981
6
4.5
Feature
Patch
RNN
0.6613
7
0.5920
4
5.5
ILI_24_8
Feature
None
Trans.
0.6568
6
0.5949
5
5.5
X
Feature
None
Trans.
0.6564
5
0.6093
12
8.5
x
Temporal
Patch
RNN
0.6904
10
0.6036
8
9.0
Temporal
Token
MLP
0.6968
12
0.6036
7
9.5
Feature
Invert
MLP
0.6791
9
0.6081
10
9.5
Temporal
Patch
MLP
0.6331
0.6096
Feature
Patch
Trans
0.6416
2
0.6118
2
2,0
Temporal
Token
RNN
0.6491
3
0.6270
3
Feature
Invert
MLP
0.6713
6
0,6312
5
5.5
Temporal
Patch
RNN
0.6636
4
0.6345
8
6.0
36_S
Feature
Patch
RNN
0.6790
8
0.6302
4
6.0
Temporal
Patch
RNN
0.6649
5
0.6381
10
7.5
Feature
Patch
MLP
0.7038
12
0.6321
6
9.0
Temporal
Invert
RNN
0,6750
7
0,6462
12
9.5
V
Feature
Patch
Trans.
0.7069
14
0.6327
7
10.5
Feature
Patch
Trans.
0.6473
1
0.6268
1.0
Temporal
Patch
MI.P
0.6568
0.6412
Feature
Invert
Trans.
0.6850
4
0.6439
3
3.5
Feature
Patch
RNN
0.6836
3
0.6539
5
4.0
X
Feature
Patch
RNN
0.7004
0.6603
8
7.0
_LI_48_S
Feature
Patch
Trans.
0.7013
8
0.6584
7
7.5
Temporal
Token
RNN
0.6879
0.6635
7.5
Temporal
Invert
MLP
0.7047
12
0.6622
9
10.5
Temporal
Invert
MLP
0.7113
18
0.6645
11
V
X
Feature
Token
RNN
0.7095
15
0.6671
14
14.5
Feature
Patch
Trans.
0.6730
0.6682
1.0
/
X
Feature
Invert
Trans.
0.6822
2
0.6739
3
2.5
Temporal
Patch
MLP
0.6992
4
0.6830
7
5.5
Feature
Patch
Trans.
0.7022
0.6784
5
5.5
X
Temporal
Patch
MLP
0.6969
3
0.6849
9
6.0
60_S
Temporal
Patch
Trans.
0.7154
13
0.6744
8.5
X
Temporal
Invert
MLP
0.7008
5
0.6883
13
9,0
Temporal
Patch
Trans.
0.7215
16
0.6715
/
Feature
Invert
Trans.
0.7085
8
0.6872
11
9.5
Temporal
Invert
ML.
0.7113
0.6866
10.0
Table 24: Top-10 configurations for the Illness (National Flu) dataset univariate forecasting. IN: Instance Norm, SD: Series Decomposition. / indicates module used, indicates used. Red/blue highlights indicate best and second-best performances.
42

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
Fy-Type
MSE
Rank
MAE
Rank
Total
X
Feature
Invert
Trans.
0.2829
0.3794
2.0
Feature
None
Trans.
0.2825
0.3798
2.0
X
X
Feature
Invert
Trans.
0,2899
0.3768
3.0
Feature
Invert
MI.P
0.2879
0.3829
4.0
X
Feature
Invert
MI.P
0.2868
0,3833
4.0
BCI_96_S
Feature
Invert
Trans.
0.2946
0.3848
7.0
X
X
Feature
None
Trans.
0.2930
0,3852
7.5
Feature
None
RNN
0.2973
0.3838
8.5
x
Feature
Patch
RNN
0.2962
10
0.3852
8
9.0
Feature
Invert
MLP
0.2947
0.3899
11.0
X
Feature
Invert
MLP
0.3013
0.3917
2
1.5
Feature
None
Trans.
0.3019
0.3912
x
Feature
Invert
MLP
0.3107
0.3961
5
4.0
X
Feature
Invert
Trans.
0.3128
0.3931
X
Feature
None
Trans.
0.3112
0.3957
4
4.0
_CL_192_
X
Feature
Invert
Trans.
0.3145
0.4006
Feature
Invert
Trans.
0.3199
0.3962
7.5
Feature
Invert
MLP
0.3193
0.4007
x
Temporal
Patch
RNN
0.3223
11
0.4009
11
11.0
Temporal
Invert
RNN
0.3183
0.4043
13.5
X
Feature
Invert
MLP
0.3437
0.4245
3
2.0
Feature
Invert
Trans.
0.3452
0.4243
x
Feature
None
Trans.
0.3462
0.4250
4
3.5
Invert
Trans.
0.3575
0.4226
Temporal
Invert
RNN
0.3489
4
0.4277
5.0
ECL BCL_336_S
Feature
None
Trans.
0.3554
0.4270
x
Feature
Invert
MI.P
0.3546
0.4287
8
6.5
Feature
Invert
MLP
0.3665
0.4286
x
Feature
Patch
RNN
0.3578
0.4295
8.5
Feature
Patch
Trans.
0.3665
10
0.4327
X
Feature
Invert
MLP
0.3867
0.4638
1.0
Feature
Invert
ML.P
0.3997
0,4682
x
Feature
None
Trans.
0.3974
0.4691
4
3.0
Feature
Invert
Trans.
0.4095
0.4646
X
Feature
Invert
Trans.
0.4067
0.4745
7
5.5
ECI_720_8
Feature
None
Trans.
0.4167
10
0.4706
X
Temporal
Invert
RNN
0.4112
0.4756
9
8.0
Feature
Freq
ML.P
0.4076
0.4764
X
Feature
Patch
MLP
0.4165
0.4756
8
8.5
Temporal
Patch
RNN
0.4237
12
0.4724
9.0
Table 25: Top-10 configurations for the Electricity (ECL.) dataset univariate forecasting. IN: Instance
Norm, SD: Series Decomposition. / indicates module used, X indicates used. Red/blue highlights indicate best and second-bes best performances.
43

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
V
Temporal
Patch
RNN
0.0012
0.0254
1
1.0
Temporal
Patch
RNN
0.0012
0.0255
2
2.0
V
Temporal
Invert
RNN
0.0013
0.0258
4
3.5
Temporal
Invert
RNN
0.0013
0.0260
5
4.5
Feature
RNN
0.0013
0.0256
Weather _6__
Feature
None
MLP
0.0013
0.0261
7
6.0
V
Feature
Patch
MLP
0.0013
0.0261
6
7.0
Feature
MLP
0.0013
0.0263
v
Feature
Patch
RNN
0.0013
0.0264
10
9.5
Feature
Patch
MLP
0.0013
0.0264
9
10.0
Temporal
RNN
0.0015
0.0280
/
x
Temporal
Token
Trans.
0.0015
0.0286
3
2.5
/
Temporal
Token
RNN
0.0015
0.0287
6
4.5
Temporal
Freq
MLP
0.0015
0.0286
Temporal
Patch
RNN
0.0015
0.0287
5
5.0
Weather 192
Temporal
Invert
RNN
0.0015
0.0288
7
5.5
Feature
Patch
RNN
0.0015
0.0286
x
Feature
None
MLP
0.0015
0.0288
8
7.0
Feature
Token
MLP
0.0015
0.0291
11
9.5
/
Feature
Patch
RNN
0.0015
0.0291
11.5
/
Feature
Patch
RNN
0.0017
0.0300
1
2.5
/
Temporal
Token
RNN
0.0016
0.0302
6
3.5
Temporal
Trans.
0.0017
0.0301
Temporal
Patch
RNN
0.0016
0.0303
9
5.5
Feature
None
MLP
0.0017
0.0301
4
5,5
Weather_33e
Temporal
None
MLP
0.0017
0.0304
11
Temporal
Freq
MLP
0.0017
13
0.0301
3
8.0
x
Feature
Token
MLP
0.0017
11
0.0303
7
9.0
/
Feature
Invert
MLP
0.0017
0.0307
d
Temporal
Freq
MLP
0.0017
0.0302
5
10.0
Temporal
Token
Trans.
0.0021
0.0335
1.5
Temporal
Freq
MLP
0.0021
0.0337
1.5
Temporal
Freq
MLP
0.0021
0.0337
3
3.0
Feature
Patch
RNN
0.0021
0.0341
5
4.5
Feature
Token
MLP
0.0021
0.0340
Weather_720_6
Feature
None
MLP
0.0021
10
0.0341
6
8.0
/
Temporal
None
MLP
0.0021
0.0344
11
8.0
V
Temporal
Token
RNN
0.0021
0.0346
13
10.0
Feature
Token
MLP
0.0022
14
0.0341
7
10.5
/
X Temporal
None
MLP
0.0021
0.0347
14
11.5
Table 26: Top-10 10 configurations for the Weather dataset univariate forecasting. IN: Instance Norm, SD: Series Decomposition. indicates module used, X indicates not used. Red/blue highlights indicate best and second-bes performances.
44

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
Temporal
Freq
MLP
0.0325
0.1331
V
Temporal
Freq
MLP
0.0333
0.1340
2
2.0
Temporal
Token
MLP
0.0346
0.1357
V
Temporal
Token
MI.P
0.0346
0.1353
3
3.5
X
Feature
Token
RNN
0.0350
0.1368
5.0
PEMSO3 03_12_S
X
Temporal
Token
RNN
0.0350
0.1371
X
Feature
Patch
RNN
0.0354
0.1381
8
7.5
Temporal
None
MLP
0.0359
0.1378
x
Feature
Token
RNN
0.0358
0.1383
9
9.0
X
Feature
Patch
RNN
0.0358
10
0.1384
10
10.0
Temporal
Freq
MLP
0.0467
0.1548
1.0
X
Feature
Patch
RNN
0.0473
0.1564
2
2.5
X
Feature
Token
RNN
0.0471
0.1565
X
Temporal
Token
RNN
0.0480
0.1582
5.5
Temporal
None
MLP
0.0488
0.1580
PEMS03_244 _
X
Feature
Patch
RNN
0.0490
0.1577
5
6.0
X
Temporal
Token
MLP
0.0499
10
0.1575
4
7,0
x
Feature
Token
RNN
0.0483
0.1595
10
7.5
X
Temporal
Freq
MLP
0.0499
0,1582
9
9.0
Feature
Patch
Trans.
0.0493
0.1598
X
Feature
Patch
RNN
0.0575
0.1678
1.0
X
Feature
Patch
Trans.
0.0586
0.1728
X
Temporal
None
MLP
0.0593
0.1715
4.0
X
Feature
Patch
RNN
0.0607
0.1690
2
4,0
X
Feature
Token
RNN
0.0598
0.1713
PEMS03 36_
X
Temporal
Token
RNN
0.0587
0.1736
6
4.5
Temporal
None
MI.P
0.0614
0.1741
x
Temporal
Freq
MLP
0.0634
0.1760
9.0
X
Feature
Token
RNN
0.0643
10
0.1758
9.0
X
Feature
Patch
Trans.
0.0619
0.1797
9.5
X
Feature
Patch
RNN
0.0675
0.1771
1.5
Temporal
None
MLP
0.0702
0.1807
X
Feature
Patch
Trans.
0.0672
081858
7
4,0
X
Feature
Patch
RNN
0.0720
0.1778
4.5
X
Feature
Token
RNN
0.0714
18433
6
5.5
PEMS03_48_S
Temporal
None
MLP
0.0741
0.1827
4
6.5
X
Feature
Patch
Trans.
0.0701
0.1896
10
X
Feature
Token
RNN
0.0739
0.1840
5
6,5
X
Temporal
Token
RNN
0.0718
0.1875
7.0
Temporal
Token
RNN
0.0778
0.1894
9
10.0
Table 27: Top- 10 configurations for the PEMS03 dataset univariate forecasting. IN: Instance Norm, SD: Series Decomposition. / indicates module used, X indicates not used. Red/blue highlights indicate best and second-bes performances.
45

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
Temporal
Freq
MLP
0.0483
0.1638
X
Temporal
Freq
MLP
0.0488
0.1637
1
2.0
Feature
Invert
Trans.
0.0485
0.1646
X
X
Feature
Token
RNN
0.0495
0.1648
4.0
V
Temporal
Invert
MLP
0.0496
0.1656
5.0
PEMS 04 $
X
Feature
Patch
Trans.
0.0496
0.1658
X
Feature
Patch
RNN
0.0503
0.1660
7.0
Temporal
Invert
MLP
0.0508
0.1670
x
Feature
Invert
RNN
0.0507
10
0.1675
9
9.5
Temporal
None
ML.P
0.0506
0.1678
10.0
X
Feature
Patch
Trans.
0.0607
0.1838
1.0
X
Feature
Invert
Trans.
0.0655
0.1838
2
2.0
Feature
Token
0.0687
0.1866
X
Feature
Invert
Trans.
0.0700
0.1916
6.5
Feature
None
Trans.
0.0703
0.1918
PEMS04_244
x
Feature
Token
RNN
0.0713
12
0.1914
6
9.0
X
Feature
Invert
RNN
0.0711
10
0.1926
10
10.0
x
Temporal
Patch
Trans.
0.0669
0.1952
18
10.5
X
Feature
Patch
RNN
0.0720
17
0.1898
4
10.5
Feature
Patch
Trans.
0.0719
0.1906
10.5
X
Feature
Patch
RNN
0.0652
0.1867
1.5
X
Feature
Invert
Trans.
0.0645
0.1877
X
Feature
Patch
Trans.
0.0652
0.1874
2
2.5
X
Feature
Patch
RNN
0.0659
0.1885
4,0
X
Temporal
Freq
MI.P
0.0667
1.19
PEMS04 36_S
X
Feature
Invert
Trans.
0.0686
0.1936
6
6,0
Feature
Patch
Trans.
0.0687
0.1948
x
Temporal
Invert
MLP
0.0702
0.1957
9
8.5
x
Feature
Token
RNN
0.0711
10
0.1954
9.0
X
Temporal
None
MI.P
0.0708
0.1958
10
9.5
X
Feature
Patch
Trans.
0.0670
0.1900
1.0
Feature
Patch
RNN
0.0709
0.1939
X
Feature
Patch
RNN
0.0706
0.1949
3
2.5
X
Feature
Patch
Trans.
0.0721
0.1970
4.0
X
Feature
Invert
Trans.
0.0729
0.1978
5.0
PEMS04_48_S
/
X
Feature
Token
RNN
0.0750
0.2004
6
6,0
X
Feature
Token
0.0758
0.2007
X
Feature
Invert
Trans.
0.0763
0.2043
9
8.5
X
Temporal
None
MLP
0.0771
10
0.2027
9.0
X
Temporal
Freq
MLP
0.0766
0.2043
10
9.5
Table 28: Top- 10 configurations for the PEMS04 dataset univariate forecasting, IN: Instance Norm, SD: Series Decomposition. / indicates module used, X indicates not used. Red/blue highlights indicate best and second-bes performances.
46

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
X
Temporal
Token
RNN
0.0795
0.2047
X
Feature
Patch
Trans.
0.0823
0.2080
3
2.5
Feature
Token
RNN
0.0830
0.2079
X
Temporal
Freq
MI.P
0.0834
0.2095
5
4.5
X
Temporal
None
MLP
0.0834
0.2096
5.5
PEMS 07_12_S
X
Feature
Invert
RNN
0.0839
0.2093
X
Feature
Patch
Trans.
0.0835
0,2111
6.5
Feature
None
Trans.
0.0848
0.2114
x
Feature
Invert
Trans.
0.0857
10
0.2112
8
9.0
X
Feature
None
RNN
0.0856
0.2122
10
9.5
X
Feature
Patch
RNN
0.1015
0,2292
1.0
X
Feature
Patch
RNN
0.1059
0.2331
2
2.0
Temporal
0.1085
0,2333
X
Feature
Patch
Trans.
0.1065
0.2347
4
3.5
Temporal
Invert
MLP
0.1112
0.2368
PEMS07_24_
X
Temporal
Token
RNN
0.1087
0.2410
8
6.5
X
Temporal
None
MLP
0.1121
0.2395
7.5
X
Feature
Invert
RNN
0.1113
0.2418
8.0
X
Temporal
Freg
MLP
0.1136
10
0.2396
8.5
Temporal
Token
Trans.
0.1117
0.2420
10
X
Feature
Patch
RNN
0.1241
0.2491
1.5
Temporal
Token
RNN
0.1204
0.2560
X
Feature
Patch
Trans.
0.1284
0.2554
3
3.0
X
Temporal
Invert
MLP
0.1321
0,2530
4,0
X
Temporal
None
MI.P
0.1310
0.2575
PEMSO7_
X
Feature
Patch
RNN
0.1319
0.2570
5
5,0
Temporal
Invert
MI.P
0.1346
0.2587
X
Feature
Token
RNN
0.1362
0.2583
7
8.0
X
Feature
Token
Trans.
0.1358
0.2625
11
9.5
X
Feature
None
Trans.
0.1366
0.2619
10
10.5
X
Temporal
None
MI.P
0.1408
0.2677
2
2.0
Feature
Patch
RNN
0.1429
0.2661
X
X
Temporal
Token
RNN
0.1349
0.2744
6
3.5
X
Temporal
Invert
MLP
0.1449
0.2716
4.0
X
Feature
Patch
RNN
0.1501
0.2682
3
6.0
PEMS07_48_S
X
Feature
Patch
Trans.
0.1466
0.2775
10
8.0
X
Feature
0.1462
0,2800
X
X
Feature
None
Trans.
0,1502
10
0.2748
8
9,0
X
Temporal
Token
Trans.
0.1490
0.2803
12
10.0
X Feature
Invert
Trans.
0.1529
15
0.2741
5
10.0
Table 29: Top- 10 configurations for the PEMS07 dataset univariate forecasting, IN: Instance Norm, SD: Series Decomposition. / indicates module used, X indicates not used. Red/blue highlights indicate best and second-bes performances.
47

---

Published as a conference paper at ICLR 2026
Setup
IN
SD
Fusion
Embed
FF-Type
MSE
Rank
MAE
Rank
Total
X
Temporal
Freq
ML.
0.1575
0.2768
X
Temporal
Token
RNN
0.1597
0.2812
3
2.5
Feature
Patch
RNN
0.1608
0.2805
X
X
Feature
None
Trans.
0.1652
0.2847
6
5.5
X
Temporal
Token
Trans.
0.1659
0.2828
6.0
PEMS 08 _
X
Feature
Token
RNN
0.1668
0.2822
X
Feature
Patch
Trans.
0.1653
0,2869
8
7.0
Feature
Patch
RNN
0.1671
0.2863
x
Temporal
Patch
MI.P
0.1623
0.2902
15
9.5
X
Feature
Invert
Trans.
0.1696
0.2883
10
10.5
X
Feature
Patch
RNN
0.1796
0.2985
1.0
X
Temporal
Freq
MLP
0.1802
0.3012
2
2.0
Feature
Token
RNN
0.1859
0.3029
X
Feature
Patch
Trans.
0.1851
0.3059
7
5,0
Temporal
Token
MLP
0.1866
0,3030
PEMSO8_244 _
X
Temporal
Invert
MLP
0.1880
0.3028
6.0
X
Temporal
Token
Trans.
0,1880
0.3046
7.0
X
Feature
Invert
Trans.
0.1879
0.3070
11
9.0
X
Feature
Patch
RNN
0.1864
0.3078
13
9.0
Temporal
None
MLP
0.1911
0.3065
10.0
X
Temporal
Invert
MLP
0.1980
0.3148
1.5
X
Feature
Invert
Trans.
0.1979
0.3163
X
Feature
Token
RNN
0.1994
0.3160
2
2.5
X
Feature
Patch
RNN
0.1994
0.3191
5,5
X
Feature
Invert
RNN
0.2018
0.3167
PEMS08
X
Temporal
Token
MLP
0.2036
10
0.3163
4
7.0
Feature
Patch
Trans.
0.2006
0.3198
x
Temporal
None
MLP
0.2028
0.3182
7.5
X
Feature
Patch
RNN
0.2012
0.3204
10
8.0
X
Temporal
Freq
MI.P
0.2023
0.3206
9.5
X
Temporal
Token
MI.P
0.2059
0.3204
2.0
Temporal
Invert
0.2039
0.3236
X
Temporal
None
MLP
0.2055
0.3234
4
3,0
X
Feature
Invert
RNN
0.2073
0.3221
3.5
X
Feature
Patch
RNN
0.2078
0.3227
3
4.5
PEMS08_48_S
X
Feature
Invert
Trans.
0.2067
0.3241
6
5.0
X
Feature
Token
RNN
0.2099
0.3247
X
X
Feature
Patch
Trans.
0.2097
0.3283
8
7.5
X
Temporal
Invert
MLP
0.2129
10
0.3315
11
10.5
X Feature
None
RNN
0.2155
12
0.3318
12
12.0
Table 30: Top- 10 configurations for the PEMS08 dataset univariate forecasting. IN: Instance Norm, SD: Series Decomposition. / indicates module used, X indicates not used. Red/blue highlights indicate best and second-bes performances.
48


Reviews:
[{"review_id": "2NP5S1yUVw", "reviewer": "Reviewer_Vm6s", "summary": "This paper focuses on time series forecasting applications. Building TSFM requires many modules, and testing each module is an important task. The introduction section is written clearly - the 4 outcomes of the study.", "questions": "Please address all the weak points.", "limitations": "", "rating": 4, "confidence": 5, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "The paper has conducted an extensive survey of reusable components and then performed a systematic study. The Table 2 is an output of such extensive study.", "weaknesses": "- Given a paper submitted on learning time series and dynamical systems, I feel the paper is more suitable for the benchmark and dataset track. Thus, I have started looking at the paper from a benchmarking and experimental task perspective. Why are the foundation models not part of this work?  \n\n- Motivation. If I am a developer, how can I consume the outcome of your study? For example, can you provide a case study on how tord- get a leaderboatopping agent on GiftEval? GiftEval is a time series leaderboard, so it shows how much gain I have made using Table 2. \n\n- There is an alternate thought: I would go to Leaderboard, compile all the models listed there along with their performance, and then generate Table 2. How accurate can it be? In summary, can I generate the same table 2 but without going into the entire time recipe framework? Can you compare and contrast this alternate, more dynamic approach? \n\n- Hyperparameter tuning, I did not see how you capture the effect of parameter tuning? \n\n- What are the new datasets that studies bring and then demonstrate the value of learning?", "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": "kBXY71kMtD", "reviewer": "Reviewer_NBVJ", "summary": "The paper advances a module-centric framework for time-series forecasting. Specifically, the authors decompose canonical architectures into pre-processing, embedding, backbone, fusion strategies, and projection/post-processing. Building on this decomposition, the authors conduct a large-scale benchmarking study that enumerates and evaluates numerous module combinations across diverse tasks and datasets. The study yields statistically grounded mappings from data characteristics, such as trend strength, seasonality, and cross-channel correlation, to appropriate module choices.", "questions": "1. Do the authors plan to modularize regularization, optimizers, schedulers, and augmentation so that training choices can be benchmarked with the same rigor as architecture?\n2. How would this framework integrate with pretrained time-series backbones, for example, by swapping embeddings/fusion while freezing a large backbone, or by using the selector to choose adaptation routes?", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 1, "strengths": "1. The paper is well written and easy to understand.\n2. The mapping from measured properties to module choices is an interesting idea and worthy of investigation.\n3. The training-free selector is a pragmatic contribution that can reduce exploration cost.", "weaknesses": "1. Regularization, optimization, schedulers, and data augmentation are not systematically modularized, though they often rival architecture in impact. The historical-window length is also unclear, despite its significant effect on performance.\n2. The choice of datasets and prediction horizons (e.g., 720) has been criticized by researchers as impractical in real-world settings (https://cbergmeir.com/talks/bergmeir2024NeurIPSInvTalk.pdf), which weakens the reliability of the conclusions and suggests the findings may be primarily academic.\n3. Some intertwined cross-channel mixers and hybrid designs are only partially represented within the studied design space.", "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": "VknxdmP7WF", "reviewer": "Reviewer_qk8s", "summary": "This paper introduces TimeRecipe, a modular benchmarking framework for time-series forecasting that evaluates the effectiveness of common architectural components (e.g., normalization, decomposition, embedding, fusion, feed-forward modeling) across a wide range of forecasting tasks, horizons, and datasets. By systematically exploring over 10,000 combinations, TimeRecipe identifies component-level contributions to performance, offers statistical correlations between data properties and module choices, and supplies a training-free recommendation toolkit for model selection. Extensive results demonstrate that exhaustive module-level exploration can yield architectures that outperform existing state-of-the-art (SOTA) methods and provide practical guidance for real-world forecasting.", "questions": "1、How robust are the results to changes in hyperparameters, default training budgets, or random seeds? Are the observed improvements for best configurations consistent under different parameterizations?\n\n2、For the model selection toolkit: How does the training-free strategy compare to stronger meta-learning or AutoML approaches? Is LightGBM sufficient, or do more advanced selectors close the gap further to the global best configurations?\n\n3、Can the authors provide additional clarity or pseudocode for the inter-module dimension handling, especially for embeddings (patch vs. invert) and their compatibility with MLP/Transformer/RNN blocks?\n\n4、Is there a sense in which the best module combinations generalize beyond the datasets tested, or are they highly scenario-dependent? Are any “failure” cases (where TimeRecipe-selected models underperform SOTA) documented, and why do they arise?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1、The paper introduces a new paradigm for time-series forecasting benchmarking by breaking down models into five core modules and systematically benchmarking their combinations. \n\n2、There are quite a few nice illustrations.\n\n3、 This work focuses on an important problem that could have real-world applications.\n\n4、 The figures and tables used in this work are clear and easy to read.", "weaknesses": "1、While the coverage of LTSF, PEMS, and M4 datasets is excellent, novel datasets introduced (e.g., unemployment forecasting from Time-MMD) are only briefly mentioned and lack rigorous description (see Section 4.2 and Appendix B). For maximal transparency, the properties, preprocessing, and evaluation setup should be as detailed for these new datasets as for the standard ones.\n\n2、While Table 2 and Figure 1 are helpful, many of the empirical summaries require close reading to decipher key findings. It would be helpful if the text more directly guided the reader through takeaways from these visualizations; for example, highlighting trends or “rules” in Table 2, or explicit failure cases identified in the configuration tables.\n\n3、A large combinatorial space is searched, but more discussion of robustness to random seed, hyperparameters, or the presence of multiple optima would be valuable. Are the best configurations stable across resamplings—or is performance sensitive to chance initialization? Furthermore, are error magnitudes meaningful under operational constraints for real-world forecasting tasks?", "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": "GVi9LUNlX6", "reviewer": "Reviewer_W7W6", "summary": "TimeRecipe is a benchmarking framework designed to systematically evaluate time-series forecasting methods at the module level, rather than just assessing complete end-to-end models. This paper is well-written and easy to follow and reproduce, providing interesting view for designing/selecting TSF methods/modules.", "questions": "Please see the weaknesses.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "1. It pioneers a systematic evaluation focused on the effectiveness of individual forecasting model components (modules), addressing a gap left by existing benchmarks that primarily assess entire models.\n2. the study is built upon a large-scale experimental setup, encompassing over 10,000 experiments that cover numerous module combinations.\n3. this benchmark successfully identifies module combinations that outperform established SOTA models in over 90% of evaluated scenarios , achieving an average error reduction. Crucially, it provides practical insights by correlating module effectiveness with data properties and offers a toolkit for model selection.", "weaknesses": "1. The connections drawn between module effectiveness and data characteristics are based on extensive empirical results and statistical tests, the paper provides limited theoretical analysis or causal explanation.\n2. The benchmark focuses solely on predictive accuracy and completely omits analysis of computational efficiency. This oversight limits the benchmark's practical applicability, as users cannot assess the crucial accuracy-efficiency trade-offs needed for real-world deployments, especially in resource-constrained or latency-sensitive scenarios. Incorporating complexity analysis, like in LightCTS, would significantly enhance the framework's value.", "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)