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Zero-Shot Time Series Forecasting with Covariates via In-Context Learning

T0 review · 3 major / 3 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read COSMIC is a pretrained transformer that performs zero-shot forecasting with covariates by inferring covariate-target relationships from context, trained on synthetically augmented covariate-free data.

desk verdict COSMIC is a genuine step forward in covariate-aware zero-shot forecasting, but the SOTA-with-covariates headline overstates what the evidence, including the paper's own linear in-context baseline, supports. read the letter →

arxiv 2506.03128 v1 pith:EKZBWSEH submitted 2025-06-03 cs.LG

Andreas Auer , Raghul Parthipan , Pedro Mercado , Abdul Fatir Ansari , Lorenzo Stella , Bernie Wang , Michael Bohlke-Schneider , Syama Sundar Rangapuram This is my paper · ORCID
classification cs.LG MSC 68T0762M10
keywords zero-shotforecastingcovariatesin-contextlearningtimeseriestransformersinformativecovariateaugmentationprobabilisticpretrainedmodels
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Zero-shot time series models typically ignore covariates or use them poorly. This paper introduces COSMIC, a pretrained transformer that forecasts a target from its history plus any number of covariate series, inferring the covariate-target relationship from the context alone at inference time. Because real covariate-labeled training data is scarce, the authors train COSMIC on covariate-free series to which they add synthetic, informative covariate effects, an approach they call Informative Covariate Augmentation, so the model learns to read these relationships without ever seeing a real covariate dataset. They report state-of-the-art zero-shot results with covariates, best probabilistic score on 9 of 11 dataset groups, and no loss of accuracy on no-covariate benchmarks, suggesting covariates can be a free improvement for pretrained forecasters.

What carries the argument

The load-bearing object is Informative Covariate Augmentation, which manufactures training samples by sampling covariates from a corpus or a synthetic generator and adding an impact function, a sparse piecewise-linear function of recent covariate lags active on quantile-selected time steps, to an otherwise covariate-free target series. Around it, COSMIC is an encoder-decoder transformer that z-score normalizes each series, patches them with shared weights, and inserts distinct separator tokens and rotary embeddings so the attention stack can tell the target from each covariate and align them in time. The output layer emits nine quantiles per horizon step, trained by quantile loss. The augmentation is what gives the model a training signal that covariates predict the future target; without it, covariates do not reduce the loss and the model has no reason to learn the in-context behavior.

What would settle it

A controlled benchmark where the target depends on a covariate through a stable but nonlinear map, such as threshold-switching or multiplicative interaction, with ample evidence of the relationship in the context: if COSMIC's covariate-input forecasts do not beat its no-covariate forecasts, the claim that it learns covariate-target relations in context would be falsified.

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Extended reading notes

Core claim

COSMIC is a pretrained encoder-decoder transformer that accepts a target series plus any number of past-only or past-and-future covariate series, normalizes each individually, patches them into tokens, and interleaves them with separator tokens so the attention stack can relate covariates to the target. At inference it reads the covariate-target relationship from the provided context and applies it to the forecast horizon, outputting nine quantiles per time step. The paper claims this yields state-of-the-art zero-shot probabilistic forecasts on covariate-included benchmarks, first place on 9 of 11 dataset groups in weighted quantile loss, and matches or exceeds prior zero-shot models on no-covariate benchmarks, while remaining competitive with task-specific models that are trained per dataset.

Load-bearing premise

The covariate-target relationship must be simple, roughly linear or piecewise-linear with small lags, and stable across the context and forecast horizon, and the synthetic covariate relationships used in pretraining must transfer to real-world covariates.

Editorial extensions

If this is right

  • Pretrained forecasters can now be deployed on covariate-rich domains such as energy, retail, and healthcare without any dataset-specific training or manual feature engineering.
  • Covariate-aware zero-shot models can be built from covariate-free corpora, so the scarcity of public covariate-labeled time series need not block this capability.
  • Providing locally informative covariates, including past-only ones, can improve forecasts, and on datasets where covariates carry no local signal, performance stays roughly flat.
  • COSMIC's probabilistic forecasts are competitive with task-specific models trained per dataset, at least on the aggregate weighted quantile loss benchmark, despite seeing none of the task data.
  • The ability to consume covariates does not degrade no-covariate zero-shot performance, since the same model matches or beats prior zero-shot models on the covariate-free benchmark.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural extension is to teach other auxiliary reasoning tasks, such as known interventions, calendar effects, or target-target correlations, by synthesizing them into the training corpus in the same way, without needing labeled examples.
  • Because the paper's analysis shows COSMIC uses covariates more strongly when more evidence of the relationship appears in context, larger models and longer contexts may close more of the remaining gap to task-specific covariate models.
  • The exclusion of static covariates suggests a hybrid design: a task-specific global encoder for static features combined with COSMIC's in-context machinery could handle datasets where the covariate signal lives outside the horizon.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The paper introduces COSMIC, an encoder-decoder transformer for zero-shot time series forecasting that accepts covariates through in-context learning. To avoid relying on scarce real-world covariate datasets, the authors propose Informative Covariate Augmentation, which generates synthetic covariates and adds piecewise-linear, quantile-threshold impact functions to standard no-covariate pretraining series. COSMIC is evaluated on 11 covariate-included dataset groups (split into Benchmark I and Benchmark II) and on the Chronos no-covariate benchmark. The paper reports first-place rankings on 9 of 11 WQL and 7 of 11 MASE dataset groups among pretrained zero-shot models, and competitive performance relative to task-specific models. The central claims are that COSMIC achieves state-of-the-art zero-shot forecasting both with and without covariates, and that the augmentation enables effective covariate usage.

Significance. If confirmed, COSMIC would be a useful contribution because it provides a way to train covariate-aware zero-shot forecasters without any covariate-included pretraining data, and its evaluation design is broad: multiple model sizes, both covariate and no-covariate benchmarks, an augmentation ablation (Table 1), analysis of Moirai's training overlap, past-only covariate experiments, inference-time measurements, and a comparison against an external linear in-context model (Appendix D.5). The synthetic-only pretraining recipe is appealing for practical deployment. The main weakness is that the headline state-of-the-art claim is not supported against the paper's own simple linear baseline on Benchmark I, and the question of how far the learned covariate mechanism generalizes beyond the synthetic impact-function family is left unmeasured.

major comments (3)
  1. [Appendix D.5, Figure 21] The paper's own comparison against a ridge-regression in-context covariate model combined with a no-covariate pretrained forecaster shows that this simple baseline outperforms COSMIC on Benchmark I for both MASE and WQL, while COSMIC wins only on Benchmark II (which excludes datasets where other targets are used as covariates). This directly qualifies the abstract's and Section 5.1's claim that COSMIC achieves state-of-the-art zero-shot forecasting with covariates. Because Benchmark I is the headline covariate-included evaluation, the authors should either include this baseline in the main results and revise the contribution claim, or justify carefully why Benchmark II is the appropriate basis for the claim and make that framing explicit throughout the paper.
  2. [Section 4, Impact Function] The impact function family F is restricted to piecewise-linear, threshold-triggered functions with coefficients that are constant over the whole series, and Section 4 explicitly assumes the covariate-target relationship is stable throughout the context and forecast horizon. Section 6 concedes that highly complex relationships cannot be captured. However, the paper does not provide a stress test or an analysis of where COSMIC's covariate mechanism breaks down as the relationship moves outside F, such as nonlinear, lag-varying, regime-dependent, or nonstationary effects. Given that the real-world datasets in Table 3 include electricity, traffic, and air-quality series where such effects are plausible, the evaluation does not establish how far the learned in-context covariate mechanism generalizes beyond the augmentation distribution. I would ask for a synthetic transfer experiment with out-of-family impact functions, or for a tempering of the generalization claims in the abstract and conclusion.
  3. [Section 5.1, Figures 3 and 6, Table 1] The quantitative support for the phrase 'effectively leverages covariates' is weaker than the rank-based claims suggest. Providing covariates improves aggregate MASE by only about 1% (Figure 6), and Table 1 shows that both the augmentation and the covariate-access benefit are concentrated in a few datasets, such as PEMS08 and ETTh. Moreover, no error bars or multiple seeds are reported anywhere in the experimental section, so small aggregate differences — for example COSMIC Base WQL 0.546 versus Chronos Bolt Base 0.552 in Figure 3 — cannot be separated from noise. Reporting confidence intervals, standard deviations across evaluation rolls, or repeated-seed results for the key comparisons would be necessary to support the 'state-of-the-art' wording.
minor comments (3)
  1. [Throughout] There are several typos, including 'Copmarision' in Section 5.1, 'zeros-hot' in Appendix C, 'pice-wise' in Appendix A, 'Aggreagted' in multiple figure captions, and 'covaraites' in Section 4; these should be corrected before publication.
  2. [Appendix A, Algorithm 2] Algorithm 2 returns the condition symbol inconsistently: line 12 writes '(, ⊕, z, q)' while line 13 writes '(>, y, 0)'. The notation should be harmonized, and the text around the algorithm should define what 'first order' and 'piece-wise' mean since these names appear in Table 2 but not in the main text.
  3. [Appendix D.5] The failure-case analysis introduces Rideshare and KDD2022 as datasets that are not part of the covariate-included benchmark in Table 3. The paper does state this, but it would help readers if Figure 21 and the surrounding text made explicit that these are auxiliary datasets chosen to probe the linear in-context model's limitations rather than part of the main evaluation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the covariate claim is evaluated on external real-world benchmarks, while the synthetic augmentation is an explicitly stated training-time transfer assumption.

full rationale

COSMIC's central claim is supported by evaluations on held-out real-world covariate-included datasets (Electricity, ETTh, ETTm, ProEnfo, PEMS, ChinaAir, and others) that are not generated by Informative Covariate Augmentation. Algorithm 1 constructs training targets by adding sampled impact functions to Chronos-corpus series, but the reported WQL and MASE numbers in Figures 3-4 and Tables 6-9 are computed on real series, so the evaluation is not an alias of the training objective. The restricted linear/piecewise impact-function family is a stated inductive bias and transfer assumption, explicitly acknowledged in Section 6 as a limitation, rather than an input-output identity: the model is not defined in terms of the benchmark outcome, and no parameter is fitted to the evaluation data. Self-citations to the Chronos corpus and its benchmark protocol provide the training pool and normalization procedure, but they do not by themselves force the result, and the comparison includes external baselines (Moirai, TimesFM, TTM, task-specific and local models). No equation reduces the central prediction to its input by construction, and no load-bearing uniqueness theorem or fitted parameter is renamed as a prediction. The paper is therefore self-contained against external benchmarks, and the appropriate finding is no significant circularity.

Assumptions & free parameters 11 free parameters · 4 assumptions · 0 invented entities

The central claim leans on a set of hand-picked augmentation hyperparameters and on the domain assumption that real covariate-target relationships are simple, local, and stable. No new physical or conceptual entities are introduced beyond the training method itself. The free parameters are not fitted to the evaluation data, but they shape the synthetic distribution and therefore influence what the model can learn.

free parameters (11)
  • p = 0.25
    Geometric distribution parameter for the number of covariates sampled per training sample; hand-picked.
  • pFO = 0.2
    Probability of sampling a first-order (linear lag) impact; chosen by hand.
  • pPW = 0.15
    Probability of sampling a piecewise impact; chosen by hand.
  • kmax = 10
    Maximum number of covariates per sample.
  • plagcount = 0.85
    Geometric parameter for the number of active lags in the impact function.
  • plagpos = 0.15
    Geometric parameter for lag position, biasing toward recent lags.
  • l = 500
    Maximum lag between covariate observation and target impact.
  • s_eps = 0.02
    Scale of Gaussian noise added to the impact.
  • cmax_e = 20
    Maximum number of events in the synthetic covariate generator.
  • cmax_cp = 8
    Maximum number of change-points in the synthetic covariate generator.
  • sigma_cp = 2
    Variance of change-point amplitudes in the synthetic covariate generator.
assumptions (4)
  • domain assumption Covariate-target relationships are stable across the context and forecast horizon within a sample.
    Stated in Section 4: 'we assume that the relationship between the covariates and the target is stable throughout the context and the forecast horizon.'
  • domain assumption Simple linear and piecewise-linear impact functions can approximate real-world covariate-target relationships well enough for zero-shot transfer.
    The impact function space F is restricted to simple functions (Section 4); if real relationships are complex, COSMIC may fail, as acknowledged in Section 6.
  • ad hoc to paper The synthetic augmentation distribution over covariates and impacts is similar enough to real-world covariate-included data for the learned in-context capability to transfer.
    The entire training scheme relies on this transfer, and the paper does not independently verify it outside the evaluation sets.
  • domain assumption Transformers can learn to infer covariate-target relationships from local context after seeing synthetic examples.
    This is the empirical premise of the in-context learning approach; the ablation in Table 1 supports it, but it is not guaranteed.

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Cite this review

Pith. "Pith review of Zero-Shot Time Series Forecasting with Covariates via In-Context Learning." pith.science (2026). https://pith.science/paper/EKZBWSEH

@misc{pith2026250603128,
  author       = {Pith},
  title        = {Pith review of: Zero-Shot Time Series Forecasting with Covariates via In-Context Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EKZBWSEH}},
  note         = {Machine review of arXiv:2506.03128}
}
read the original abstract

Pretrained time series models, capable of zero-shot forecasting, have demonstrated significant potential in enhancing both the performance and accessibility of time series forecasting. However, existing pretrained models either do not support covariates or fail to incorporate them effectively. We introduce COSMIC, a zero-shot forecasting model that utilizes covariates via in-context learning. To address the challenge of data scarcity, we propose Informative Covariate Augmentation, which enables the training of COSMIC without requiring any datasets that include covariates. COSMIC achieves state-of-the-art performance in zero-shot forecasting, both with and without covariates. Our quantitative and qualitative analysis demonstrates that COSMIC effectively leverages covariates in zero-shot forecasting.

Figures

Figures reproduced from arXiv: 2506.03128 by the authors.

Figure 1
Figure 1. Two synthetic examples demonstrating how COSMIC leverages covariate information. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Architecture of COSMIC. The illustration shows an example with 4 context tokens and one [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Comparison of pretrained model on all covariate-included evaluation data (Benchmark I). Left: Count of first-place rankings within dataset groups, considering only zero-shot models. Moirai and TTM never rank first for datasets where they zero-shot forecast. COSMIC’s results without covariates access presented in grey. Middle/Right: Average rank and aggregated score of the MASE and WQL metrics. Scores of the individu… view at source ↗
Figures from the paper (20 more)
Figure 4
Figure 4. Figure 4: Aggreagted MASE and WQL performances on the [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Two COSMIC forecasts with and without the access to covariates (Left: Electricity DE, [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Relative MASE difference for four dataset specific and the aggregate results when covariates are provided to COSMIC [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Aggregated WQL scores on the no-covariate zero-shot evaluation benchmark. Lower values are better. The individual scores of the dataset groups are normalized by naive seasonal scores before aggregation. “Pretrained Models (Others)” refers to models where datasets overl…
Figure 8
Figure 8. Figure 8: Aggreagted MASE and WQL performances of different zero-shot models on the [PITH_FULL_IMAGE:figures/full_fig_p020_8.png]
Figure 9
Figure 9. Figure 9: Average rank regarding MASE and WQL scores on the [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]
Figure 10
Figure 10. Figure 10: Average rank regarding MASE and WQL scores on the [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]
Figure 11
Figure 11. Figure 11: Relative MASE difference for all covariate-included dataset evaluations and the aggregate [PITH_FULL_IMAGE:figures/full_fig_p021_11.png]
Figure 12
Figure 12. Figure 12: Multiple forecasts of COSMIC with and without the access to covariates. Each example [PITH_FULL_IMAGE:figures/full_fig_p022_12.png]
Figure 13
Figure 13. Figure 13: Forecast of COSMIC including a visualization of the quantile predictions. Three plots [PITH_FULL_IMAGE:figures/full_fig_p023_13.png]
Figure 14
Figure 14. Figure 14: Aggreagted MASE and WQL scores on the no-covariate zeros-shot evaluation benchmark. Lower values are better. The individual scores of the dataset groups are normalized by naive seasonal scores before aggregation. The “Pretrained Models (Others)” category refers to mod…
Figure 15
Figure 15. Figure 15: Relative MASE difference for all covariate-included dataset evaluations and the aggregate [PITH_FULL_IMAGE:figures/full_fig_p024_15.png]
Figure 16
Figure 16. Figure 16: Four forecasts of COSMIC with and without the access to covariates [PITH_FULL_IMAGE:figures/full_fig_p025_16.png]
Figure 17
Figure 17. Figure 17: Aggregated MASE and WQL scores and the average ranks regarding all datasets that are [PITH_FULL_IMAGE:figures/full_fig_p026_17.png]
Figure 18
Figure 18. Figure 18: Relative MASE difference for all covariate-included dataset evaluations and the aggregate [PITH_FULL_IMAGE:figures/full_fig_p026_18.png]
Figure 19
Figure 19. Figure 19: Aggreagted MASE and WQL scores on the covariate-included evaluation data, comparing COSMIC and Chronos Bolt with 512 and 2048 context length. Benchmark I includes all datasets, Benchmark II which excludes datasets where other targets are used as covariates (Section 5.…
Figure 20
Figure 20. Figure 20: Inference runtime analysis: Runtime per sample depending on the number of covariates [PITH_FULL_IMAGE:figures/full_fig_p027_20.png]
Figure 21
Figure 21. Figure 21: WQL and MASE scores for different sized Chronos and COSMIC models compared to [PITH_FULL_IMAGE:figures/full_fig_p029_21.png]
Figure 22
Figure 22. Figure 22: Analysis of the effect of varying numbers of impact observations in the context, on [PITH_FULL_IMAGE:figures/full_fig_p030_22.png]
Figure 23
Figure 23. Figure 23: Multiple forecasts for which the application of an external linear in-context covariate [PITH_FULL_IMAGE:figures/full_fig_p031_23.png]

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Forward citations

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.