Feature to Dynamics: Feature-space to Autoregression strategy for Zero-shot Time Series Forecasting

Jian Lou; Junjie Wu; Kai Wu; Xiaoyu Zhang; Yifan Wu

arxiv: 2606.01289 · v1 · pith:ITGPB6DSnew · submitted 2026-05-31 · 💻 cs.LG

Feature to Dynamics: Feature-space to Autoregression strategy for Zero-shot Time Series Forecasting

Yifan Wu , Junjie Wu , Kai Wu , Xiaoyu Zhang , Jian Lou This is my paper

Pith reviewed 2026-06-28 17:18 UTC · model grok-4.3

classification 💻 cs.LG

keywords zero-shot forecastingtime seriesfeature spaceautoregressive strategyinductive biasesgeneralizationTransformer comparison

0 comments

The pith

Mapping from interpretable features to autoregressive strategies enables better zero-shot time series forecasting than direct sequence modeling.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes FSA as a framework that learns a structured mapping from an interpretable feature space to an autoregressive strategy space rather than modeling raw sequences directly. This introduces explicit inductive biases that separate global trends, periodic components, and local dynamics to capture transferable structure with fewer assumptions about the data. The goal is stronger generalization in zero-shot settings where training and test distributions may be disjoint. A sympathetic reader would care because the design reduces dependence on massive data coverage and implicit memorization that current foundation models often require.

Core claim

FSA learns a structured mapping from an interpretable feature space to an autoregressive strategy space. This design introduces explicit inductive biases that disentangle global trends, periodic components, and local temporal dynamics, enabling the model to capture transferable time-series structure with fewer data assumptions. Empirical results show that, under identical pretraining data, training protocol, and comparable parameter budgets, FSA outperforms Transformer-based architectures in the controlled zero-shot setting.

What carries the argument

The feature-to-autoregression strategy mapping that explicitly disentangles trends, periodic components, and local dynamics to produce transferable forecasting strategies.

If this is right

FSA achieves better zero-shot univariate forecasting performance than Transformers under matched pretraining conditions.
Explicit disentanglement supports generalization when source and target domains are disjoint.
The model captures transferable structure while relying on fewer implicit assumptions about data patterns.
Performance gains hold when data coverage is limited compared to broad pretraining approaches.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same feature-to-strategy mapping could be tested on multivariate series by extending the feature extraction step.
Autoregressive strategies produced by the mapping might be recombined for multi-horizon or hierarchical forecasting tasks.
The approach suggests that making the intermediate representation more interpretable could improve robustness to distribution shifts beyond what scale alone provides.

Load-bearing premise

An interpretable feature space can be constructed whose explicit disentanglement of trends, periodic components, and local dynamics produces transferable autoregressive strategies that generalize beyond the training distribution with fewer data assumptions than direct sequence modeling.

What would settle it

A controlled experiment with identical pretraining data and parameter budgets in which a Transformer-based model matches or exceeds FSA zero-shot performance on unseen series would falsify the superiority claim.

Figures

Figures reproduced from arXiv: 2606.01289 by Jian Lou, Junjie Wu, Kai Wu, Xiaoyu Zhang, Yifan Wu.

**Figure 1.** Figure 1: Paradigm shift: From the Seq2Seq pattern of timeseries models to our proposed mapping from feature space to strategy space. (a) The traditional sequence-to-sequence (Seq2Seq) paradigm for time-series forecasting; (b) Our proposed feature space to strategy space paradigm. patterns from massive, heterogeneous datasets. However, the prevailing architecture of many TSFMs remains tethered to the sequence-to-s… view at source ↗

**Figure 2.** Figure 2: The overall framework of the proposed method. The architecture consists of two main stages. First, the Feature Extraction Module normalizes the input series x1:T into x˜, and extracts global structural features Φ(x) (trend β, periodicity α, residual statistics γ) and local dynamic features ψ(x), concatenating them into a task feature vector z. Second, in the Strategy Space, the Strategy Generator (fEnc) ma… view at source ↗

**Figure 3.** Figure 3: Visualization of ablation study results. (a) By integrating local and global features, the model effectively captures both local dynamics and global periodicity. (b) With global features only, the model captures coarse-grained periodic patterns but misses local variations. (c) Relying solely on local features, the model fails to capture trends and tends to produce mean-value predictions. full model, which … view at source ↗

**Figure 4.** Figure 4: Visualization of AR and const parameter: Autoregressive dynamics at different sequences 5.5. Strategy Visualization One key advantage of FSA lies in its explicit and interpretable forecasting strategy. Unlike sequence-to-sequence models that implicitly encode forecasting behavior within high-dimensional hidden states, FSA predicts a lowdimensional autoregressive strategy whose parameters directly govern… view at source ↗

**Figure 5.** Figure 5: Visualization of pretrain datasets 13 [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗

read the original abstract

Zero-shot time series forecasting aims to predict future values for previously unseen series, requiring models to generalize temporal dynamics beyond the training distribution. While recent foundation models achieve strong in-domain performance through large-scale pretraining, their effectiveness often relies on broad data coverage and implicit pattern memorization, which can limit generalization when data are scarce or source and target domains are disjoint. In this work, we propose FSA, a feature-to-strategy framework for controlled zero-shot univariate forecasting. Instead of directly modeling raw sequences in the observation space, FSA learns a structured mapping from an interpretable feature space to an autoregressive strategy space. This design introduces explicit inductive biases that disentangle global trends, periodic components, and local temporal dynamics, enabling the model to capture transferable time-series structure with fewer data assumptions. Empirical results show that, under identical pretraining data, training protocol, and comparable parameter budgets, FSA outperforms Transformer-based architectures in our controlled zero-shot setting.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper's main move is an explicit feature-to-autoregressive-strategy mapping that disentangles trends, periodicity, and local dynamics for zero-shot TS forecasting, with a controlled claim of beating Transformers under matched pretraining.

read the letter

The headline result is that FSA, by learning a structured mapping from an interpretable feature space to autoregressive strategies, beats Transformer baselines in zero-shot univariate forecasting when pretraining data, protocol, and parameter budgets are held the same. The approach tries to make the handling of trends, periodic components, and local dynamics explicit rather than leaving it to implicit pattern capture in sequence models.

This framing is a reasonable attempt to inject targeted inductive biases. If the feature extraction and strategy mapping are lightweight and the outperformance survives proper controls, it could be useful for settings where data are scarce or domains shift. The paper at least states the comparison conditions clearly in the abstract, which is better than many claims that hide differences in data or compute.

The soft spot is exactly the one the stress-test flags: whether the feature-space construction adds unaccounted capacity, preprocessing steps, or auxiliary losses that the Transformer baselines do not receive. The abstract asserts identical conditions but gives no equations, module sizes, or ablation on the feature extractor itself. Without those details it is impossible to tell whether the gain comes from the strategy space or from extra machinery. The soundness score in the reader's report is low for the same reason—no derivations or dataset specifics are visible here.

This is for researchers already working on time-series foundation models who are looking for alternatives to raw sequence modeling. A reader who cares about explicit temporal structure would find the setup worth examining. It is coherent enough on its own terms to deserve a serious referee, even if the central claim needs tighter verification on the capacity-matching question.

Referee Report

1 major / 1 minor

Summary. The paper proposes FSA, a feature-to-strategy framework for zero-shot univariate time series forecasting. Instead of direct sequence modeling, it constructs an interpretable feature space that explicitly disentangles global trends, periodic components, and local dynamics, then learns a mapping from this space to autoregressive strategies. The central empirical claim is that, under identical pretraining data, training protocol, and comparable parameter budgets, FSA outperforms Transformer-based architectures in controlled zero-shot settings.

Significance. If the controlled comparison is valid, the explicit inductive biases could improve generalization in data-scarce or domain-disjoint scenarios compared to implicit memorization in large foundation models. The interpretable feature design is a potential strength for transferability, though its advantage depends on whether the feature extraction overhead is truly matched to baselines.

major comments (1)

[Abstract] Abstract: The headline claim of outperformance 'under identical pretraining data, training protocol, and comparable parameter budgets' is load-bearing for the contribution. The description of an 'interpretable feature space' that 'explicitly disentangles' trends/periodicity/local dynamics implies either hand-crafted extractors or learned modules whose parameter count, forward-pass cost, and any auxiliary losses must be shown to be matched to the Transformer baselines; without this accounting, the performance difference cannot be attributed solely to the autoregressive strategy space.

minor comments (1)

[Abstract] The abstract states an empirical result but provides no dataset details, number of series, forecast horizons, or exclusion criteria; these should be summarized early to allow assessment of the zero-shot setting.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback. The concern regarding explicit matching of parameter counts, forward-pass costs, and auxiliary losses is valid and directly impacts the strength of our controlled comparison claim. We address it point-by-point below.

read point-by-point responses

Referee: [Abstract] Abstract: The headline claim of outperformance 'under identical pretraining data, training protocol, and comparable parameter budgets' is load-bearing for the contribution. The description of an 'interpretable feature space' that 'explicitly disentangles' trends/periodicity/local dynamics implies either hand-crafted extractors or learned modules whose parameter count, forward-pass cost, and any auxiliary losses must be shown to be matched to the Transformer baselines; without this accounting, the performance difference cannot be attributed solely to the autoregressive strategy space.

Authors: We agree that a transparent accounting of all components is required to support the headline claim. The feature extractors (for global trends, periodic components, and local dynamics) are implemented as lightweight, fixed-structure modules whose parameters are included in the reported comparable budgets; the mapping network itself constitutes the primary learnable component. In the revised version we will add a dedicated subsection under Experimental Setup that tabulates (i) exact parameter counts for each extractor and the full FSA model versus the Transformer baselines, (ii) measured forward-pass FLOPs on identical hardware, and (iii) confirmation that training uses only the standard autoregressive forecasting loss with no auxiliary objectives. This documentation will make explicit that the observed gains are attributable to the learned feature-to-strategy mapping rather than unaccounted capacity or losses. revision: yes

Circularity Check

0 steps flagged

No circularity detected; abstract and claims contain no equations, self-citations, or derivations that reduce outputs to inputs by construction.

full rationale

The provided abstract proposes FSA as a feature-to-autoregression mapping with explicit disentanglement of trends/periodicity/dynamics and reports empirical outperformance under matched pretraining conditions. No equations, parameter-fitting procedures, uniqueness theorems, or citations appear in the text. The enumerated circularity patterns (self-definitional, fitted-input-called-prediction, self-citation load-bearing, etc.) require specific reductions via equations or citations that are absent here. The central claim is therefore an empirical comparison whose grounding cannot be inspected for circularity from the given material; the derivation chain is self-contained at the level of description.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities. The central claim rests on the unstated premise that the proposed feature space is both interpretable and sufficient to capture transferable dynamics.

pith-pipeline@v0.9.1-grok · 5700 in / 1085 out tokens · 18692 ms · 2026-06-28T17:18:31.141201+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

18 extracted references · 13 canonical work pages · 3 internal anchors

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Aksu, T., Woo, G., Liu, J., Liu, X., Liu, C., Savarese, S., Xiong, C., and Sahoo, D. Gift-eval: A benchmark for general time series forecasting model evaluation.arXiv preprint arXiv:2410.10393,

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Time-moe: Billion-scale time series founda- tion models with mixture of experts.arXiv preprint arXiv:2409.16040,

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ISSN 2405-9595. doi: https://doi.org/10.1016/j.icte.2022.02

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Wetterstation. Weather. https://www.bgc-jena. mpg.de/wetter/. Woo, G., Liu, C., Kumar, A., and Sahoo, D. Pushing the limits of pre-training for time series forecasting in the cloudops domain.arXiv preprint arXiv:2310.05063,

work page arXiv
[14]

Experiments use a 90/10 train-validation split of the pretraining corpus; validation MSE is used for early stopping and model selection

with learning rate 10−4, weight decay 0.01, a cosine learning-rate schedule, 10% linear warmup, batch size 64, and gradient clipping at 1.0. Experiments use a 90/10 train-validation split of the pretraining corpus; validation MSE is used for early stopping and model selection. Model Configurations:FSA uses 22 input features, a 3-layer MLP strategy generat...

2023
[15]

To avoid redundancy and enhance training diversity, we sample only one instance from each series

hugging face repository. To avoid redundancy and enhance training diversity, we sample only one instance from each series. We conduct Zero-shot experiments on four benchmark time series datasets:ETT(Yu et al., 2018),Electricity(UCI), Exchange Rate(Lai et al., 2018), andWeather(Wetterstation). The ETT dataset contains data collected from electricity transf...

2018
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The Electricity dataset consists of the hourly electricity consumption of 321 customers between 2012 and

2012
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The Exchange rate dataset records the daily exchange rates of eight foreign countries spanning from 1990 to

1990
[18]

11 FSA B.2

The Weather dataset includes meteorological observations recorded every 10 minutes throughout the year 2020, containing 21 weather-related indicators such as air temperature, humidity, and wind speed. 11 FSA B.2. Baseline models We use baseline models from these repositories: https://github.com/google-research/timesfm https://github.com/amazon-science/chr...

2020

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Gift- EVAL : A benchmark for general time series forecasting model evaluation

Aksu, T., Woo, G., Liu, J., Liu, X., Liu, C., Savarese, S., Xiong, C., and Sahoo, D. Gift-eval: A benchmark for general time series forecasting model evaluation.arXiv preprint arXiv:2410.10393,

work page arXiv

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Chronos: Learning the Language of Time Series

Ansari, A. F., Stella, L., Turkmen, C., Zhang, X., Mercado, P., Shen, H., Shchur, O., Rangapuram, S. S., Arango, S. P., Kapoor, S., et al. Chronos: Learning the language of time series.arXiv preprint arXiv:2403.07815,

work page internal anchor Pith review Pith/arXiv arXiv

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Chronos-2: From Univariate to Universal Forecasting

Ansari, A. F., Shchur, O., K ¨uken, J., Auer, A., Han, B., Mercado, P., Rangapuram, S. S., Shen, H., Stella, L., Zhang, X., et al. Chronos-2: From univariate to universal forecasting.arXiv preprint arXiv:2510.15821,

work page internal anchor Pith review Pith/arXiv arXiv

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This time is different: An observability perspective on time series foundation models.arXiv preprint arXiv:2505.14766, 2025

Cohen, B., Khwaja, E., Doubli, Y ., Lemaachi, S., Lettieri, C., Masson, C., Miccinilli, H., Ram ´e, E., Ren, Q., Ros- tamizadeh, A., et al. This time is different: An observabil- ity perspective on time series foundation models.arXiv preprint arXiv:2505.14766,

work page arXiv

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Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al- Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Alex Vaughan, and 1 others

Godahewa, R., Bergmeir, C., Webb, G. I., Hyndman, R. J., and Montero-Manso, P. Monash time series forecasting archive.arXiv preprint arXiv:2105.06643,

work page arXiv

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From tables to time: Extending tabpfn-v2 to time series forecasting

Hoo, S. B., M ¨uller, S., Salinas, D., and Hutter, F. From tables to time: Extending tabpfn-v2 to time series fore- casting.arXiv preprint arXiv:2501.02945,

work page arXiv

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Panda: A pretrained forecast model for chaotic dynamics.arXiv preprint arXiv:2505.13755,

Lai, J., Bao, A., and Gilpin, W. Panda: A pretrained forecast model for universal representation of chaotic dynamics. arXiv preprint arXiv:2505.13755,

work page arXiv

[8] [8]

Moirai 2.0: When less is more for time series forecasting

Liu, C., Aksu, T., Liu, J., Liu, X., Yan, H., Pham, Q., Savarese, S., Sahoo, D., Xiong, C., and Li, J. Moirai 2.0: When less is more for time series forecasting.arXiv preprint arXiv:2511.11698, 2025a. Liu, Y ., Qin, G., Shi, Z., Chen, Z., Yang, C., Huang, X., Wang, J., and Long, M. Sundial: A family of highly capable time series foundation models.arXiv pr...

work page arXiv

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net/forum?id=Bkg6RiCqY7

URL https://openreview. net/forum?id=Bkg6RiCqY7. Moroshan, V ., Siems, J., Zela, A., Carstensen, T., and Hutter, F. Tempopfn: Synthetic pre-training of linear rnns for zero-shot time series forecasting.arXiv preprint arXiv:2510.25502,

work page arXiv

[10] [10]

A Time Series is Worth 64 Words: Long-term Forecasting with Transformers

Nie, Y . A time series is worth 64words: Long-term forecast- ing with transformers.arXiv preprint arXiv:2211.14730,

work page internal anchor Pith review Pith/arXiv arXiv

[11] [11]

Time-moe: Billion-scale time series founda- tion models with mixture of experts.arXiv preprint arXiv:2409.16040,

Shi, X., Wang, S., Nie, Y ., Li, D., Ye, Z., Wen, Q., and Jin, M. Time-moe: Billion-scale time series founda- tion models with mixture of experts.arXiv preprint arXiv:2409.16040,

work page arXiv

[12] [12]

doi: https://doi.org/10.1016/j.icte.2022.02

ISSN 2405-9595. doi: https://doi.org/10.1016/j.icte.2022.02

work page doi:10.1016/j.icte.2022.02 2022

[13] [13]

Wetterstation. Weather. https://www.bgc-jena. mpg.de/wetter/. Woo, G., Liu, C., Kumar, A., and Sahoo, D. Pushing the limits of pre-training for time series forecasting in the cloudops domain.arXiv preprint arXiv:2310.05063,

work page arXiv

[14] [14]

Experiments use a 90/10 train-validation split of the pretraining corpus; validation MSE is used for early stopping and model selection

with learning rate 10−4, weight decay 0.01, a cosine learning-rate schedule, 10% linear warmup, batch size 64, and gradient clipping at 1.0. Experiments use a 90/10 train-validation split of the pretraining corpus; validation MSE is used for early stopping and model selection. Model Configurations:FSA uses 22 input features, a 3-layer MLP strategy generat...

2023

[15] [15]

To avoid redundancy and enhance training diversity, we sample only one instance from each series

hugging face repository. To avoid redundancy and enhance training diversity, we sample only one instance from each series. We conduct Zero-shot experiments on four benchmark time series datasets:ETT(Yu et al., 2018),Electricity(UCI), Exchange Rate(Lai et al., 2018), andWeather(Wetterstation). The ETT dataset contains data collected from electricity transf...

2018

[16] [16]

The Electricity dataset consists of the hourly electricity consumption of 321 customers between 2012 and

2012

[17] [17]

The Exchange rate dataset records the daily exchange rates of eight foreign countries spanning from 1990 to

1990

[18] [18]

11 FSA B.2

The Weather dataset includes meteorological observations recorded every 10 minutes throughout the year 2020, containing 21 weather-related indicators such as air temperature, humidity, and wind speed. 11 FSA B.2. Baseline models We use baseline models from these repositories: https://github.com/google-research/timesfm https://github.com/amazon-science/chr...

2020