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REVIEW 5 major objections 6 minor 46 references

Maximizing the Impact of Deep Learning on Subseasonal-to-Seasonal Climate Forecasting: The Essential Role of Optimization

T0 review · 5 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper's central claim is that optimization, not network architecture, is why deep learning fails at the 2-6 week scale, and a multi-stage teacher forcing schedule lifts a fixed backbone past ECMWF-S2S by 19-91%.

desk verdict Worth refereeing, but the 19-91% ECMWF beat is not established while the anomaly baselines differ and the paper itself warns that this can inflate skill. read the letter →

arxiv 2411.16728 v1 pith:L4IIFK3K submitted 2024-11-23 cs.LG cs.AIphysics.ao-ph

Yizhen Guo , Tian Zhou , Wanyi Jiang , Bo Wu , Liang Sun , Rong Jin This is my paper · ORCID
classification cs.LGcs.AIphysics.ao-ph MSC 68T0786A10
keywords subseasonal-to-seasonalforecastingdeeplearningweatherpredictionmulti-stageoptimizationteacherforcingrollingdirectECMWF-S2Sanomalycorrelationskill
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

This paper argues that the reason deep learning weather models collapse to climatology-level skill at the subseasonal-to-seasonal scale, roughly 2 to 6 weeks ahead, is not their architecture but how they are optimized. The authors build a multi-stage training recipe that lengthens the rolling forecast horizon step by step, from a one-day model to a seven-day roller to a full 42-day roller, while injecting observed values during training to interrupt error accumulation, a form of teacher forcing. With the same backbone model throughout, this recipe raises anomaly-correlation skill on six key variables so that the model surpasses the ECMWF-S2S operational system by 19-91%. The paper also claims the opposite of a recent benchmark result: properly trained rolling forecasting beats direct forecasting for S2S prediction. If correct, the result implies that existing deep learning weather models could gain subseasonal skill without any architectural redesign.

What carries the argument

The load-bearing mechanism is the multi-stage teacher forcing training schedule, understood through error accumulation in rolling prediction. When a model rolls forward, the parameter gradient contains products of Jacobians, $\prod_{k=j+1}^{T} J_k$, so any local parameter update is amplified or damped by the spectral growth of these products along the orbit, quantified by the maximum Lyapunov exponent $\lambda_{\max}$; in chaotic systems a positive $\lambda_{\max}$ produces diverging loss gradients. The recipe attacks this in three moves: it grows the rolling horizon in stages, $T = 1$, then $T = 7$, then $T = 42$, so each stage starts from a state with smaller Jacobians; it substitutes observed values for model predictions at controlled frequencies so the multiplicative path of the Jacobians is interrupted; and it freezes most parameters in the final stage, keeping only six adapter modules, one per seven-day block, trainable. The loss functions are computed on anomalies relative to an 11-day centered rolling climatology and combine latitude-weighted MSE with latitude-weighted Pearson correlation.

What would settle it

Recompute both systems' skill on a single shared anomaly baseline by applying the same 11-day centered rolling climatology from the same reference period to the model's forecasts, ERA5, and the ECMWF-S2S reforecasts, and check whether the 19-91% advantage in PCC and TCC survives; also recompute the headline averages over all ten modeled variables, including total precipitation, rather than the six reported ones.

Watch

Extended reading notes

Core claim

The paper's central claim is that optimization, not network structure, is the deciding factor in whether deep learning succeeds at subseasonal-to-seasonal forecasting. Using a fixed backbone, a Siamese-MAE-pretrained vision transformer, the authors show that training a 42-day rolling predictor end to end is unstable because the backpropagation path contains products of Jacobian matrices along the forecast orbit, whose growth is controlled by the orbit's maximum Lyapunov exponent. Their remedy is a three-stage curriculum: fine-tune the model as a one-day forecaster, then as a seven-day roller, then as a 42-day roller with parameter-efficient adapters, while teacher forcing substitutes observed values for predictions at intermediate steps to break the multiplicative path of the Jacobians. On latitude-weighted anomaly correlations for six variables, t2m, z500, t850, olr, u200, and u850, the resulting model outperforms the ECMWF-S2S system by 19-91% over the 2-to-6-week window and extends skillful MJO prediction from 23 to 30 days. The paper further claims that rolling forecasting trained this way beats direct forecasting by over 30%, directly contesting the ChaosBench finding that direct forecasting is superior for S2S.

Load-bearing premise

The headline claim that the model beats ECMWF-S2S by 19-91% assumes the two systems are scored on comparable anomaly baselines: the paper's own forecasts use an 11-day centered rolling climatology while ECMWF's published skill uses ECMWF's own climatology, and the paper itself warns that a different or longer climatology window can make apparent skill look inflated.

Editorial extensions

If this is right

  • Existing deep learning weather models that score at climatology level for 2-6 week leads could be upgraded to subseasonal skill by retraining with the multi-stage teacher forcing schedule, with no change to their architecture.
  • The benchmark conclusion that direct forecasting beats rolling forecasting for S2S would need revision, since rolling predictors trained this way win by over 30% on correlation skills and the comparison in that benchmark is confounded by how the rolling models were optimized.
  • Operational S2S forecasting could shift from running costly physics-based ensemble systems to much cheaper learned models, at least for the six large-scale variables studied.
  • The curriculum idea of gradually lengthening the prediction horizon while injecting ground truth transfers to any iterative spatiotemporal predictor, including other weather backbones and climate emulators.

Reading between the lines

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

  • The reported 19-91% margin may owe part of its size to a scoring asymmetry: the paper's own anomaly skill is computed against a sharp 11-day rolling climatology while ECMWF's skill figures use a fixed climatology, and the paper's own evaluation section warns that fixed or longer climatologies weaken the anomaly signal and can inflate apparent gains; a fair head-to-head needs a shared anomaly basel
  • The headline averages exclude four of the ten modeled variables, including total precipitation, which is typically among the hardest subseasonal targets, so the claim that deep learning surpasses ECMWF-S2S should be read as applying to the six selected variables.
  • The Jacobian-product analysis justifies the training schedule through a linearized model, but the paper does not directly measure the spectral norm of the actual network Jacobians; a natural test is to record $\| \prod J_k \|_2$ at each training stage and check that it decreases as the schedule progresses.
  • If the optimization-centered explanation is right, the current S2S skill ceiling is set by training difficulty rather than by expressivity or data, which predicts that applying this recipe to stronger backbones listed in the paper, such as GraphCast or Pangu-Weather, would yield further gains, a direct extension the paper leaves to future work.
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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

5 major / 6 minor

Summary. The paper argues that the poor performance of deep learning models at subseasonal-to-seasonal (S2S) forecasting is caused by the optimization procedure rather than by the model architecture. The authors propose a multi-stage teacher-forcing training scheme that first fine-tunes a pretrained 'Baguan' backbone to a 1-day forecast, then to a 7-day rolling horizon, and finally to a 42-day rolling horizon with adapter-based PEFT, using anomaly-based losses. They report that this scheme, with the same backbone, surpasses ECMWF-S2S by 19-91% in PCC and TCC, extends the skillful MJO forecast lead time from 23 to 30 days, and reverses the ChaosBench conclusion that direct forecasting outperforms rolling forecasting. A theoretical analysis based on deep linear models and Jacobian accumulation is included to explain why the curriculum-style training helps.

Significance. If the claims are substantiated, the paper would make an important contribution: it would show that a training recipe alone can push existing deep-learning architectures to S2S skill beyond a leading NWP system, and it would challenge a recent benchmark finding. The manuscript has concrete strengths: it ships an implementation, provides ablations over two backbones and two resolutions, and formulates a falsifiable claim about rolling versus direct forecasting. However, the headline results currently rest on a non-apples-to-apples evaluation (different climatology conventions), a selected variable subset, and unquantified run-to-run variability, so the significance cannot be fully assessed at this stage.

major comments (5)
  1. [§4.1.2 and §4.2] The headline comparison with ECMWF-S2S is computed under two different anomaly baselines: the model and ERA5 use an 11-day centered rolling climatology, while ECMWF uses its own climatology, and the paper itself warns that 'using a longer average or fixed time period can weaken the climatology signal, making the results appear inflated.' Because PCC and TCC are correlations of anomalies, this difference directly changes the scores; without a sensitivity experiment in which ECMWF skill is recomputed with the same ERA5 climatology (or the model with ECMWF's), the reported 19–91% improvement cannot be attributed to forecast quality rather than scoring convention. This is load-bearing because the abstract, introduction, and conclusion all present the ECMWF comparison as the primary evidence for the 'optimization, not architecture' thesis.
  2. [§4.1.2 and §4.2] The stated 'over 19–91%' improvement is averaged over only 6 of the 10 modeled variables: t2m, z500, t850, olr, u200, and u850. The paper says these are 'primarily reported' because of 'importance of the signals,' but total precipitation (tp) and the other humidity and wind variables are excluded from the headline skill numbers; this is a selection on the outcome and can inflate the perceived improvement. The authors should report skill for all variables they claim to forecast or provide a principled reason for the subset and show that the conclusion is not sensitive to the choice.
  3. [§3 (Figure 3) and §5] The claim that the multi-stage rolling method outperforms direct forecasting by 'over 30%' is stated in the abstract and introduction, but the experimental section does not quantify this comparison: Figure 3 is illustrative, and the ablations in §5 compare only rolling variants (our method versus the naive method), not against direct forecasting models. Without a table or figure showing actual PCC and TCC values for direct forecasting under the same conditions, the challenge to the ChaosBench conclusion is not supported by the presented evidence.
  4. [Appendix B, Eqs. (8)–(14)] The theoretical explanation rests on inequality (8), |∇ℓ(Θ)|² ≥ 4L² ℓ(Θ)(1 − σ_min(Θ)), which is asserted as 'easy to verify' with no proof and no explicit statement of which lemma from the original paper is being modified. This inequality drives the convergence bound (14); if it is not established, the theoretical rationale for why curriculum-style training reduces optimization difficulty is unsupported. The authors need to provide a complete proof or a precise citation that contains this exact inequality.
  5. [§4.2 and §5] The paper reports no error bars, confidence intervals, or significance tests for any of the skill metrics, and the claims of 'significantly improves' and 'surpassing' are based on single training runs for each configuration. The differences in Table 1 (e.g., ViT 0.1168 versus 0.0807) are small in absolute PCC units, so a statement of run-to-run variability is necessary to judge whether the reported gains are reproducible and not due to training noise.
minor comments (6)
  1. [§3.2 and Reference [1]] The 'Baguan' backbone is described only through a non-archival blog link; the paper should include a full architectural description or cite a peer-reviewed/preprint source so that the base model is reproducible.
  2. [§4.1.1] For stage 1, the peak and minimum learning rates are both given as 1e−4, so the schedule is constant; please state this explicitly to avoid confusion.
  3. [Table 1] The 'Depth' column (51*42 and 15*42) is undefined; clarify how depth is computed and why it is reported as the product of network depth and rollout length.
  4. [§4.3] The MJO evaluation uses only the year 2015; state whether this is the standard verification period and whether the result is stable across other years.
  5. [Figures 5 and 6] The captions contain a spelling error ('comparsion'); also, the figures would benefit from axis labels defining the lead time range and the metric unit.
  6. [§3.2] The text in the loss-function paragraph says 'we use use A to denote anomaly values' — the duplicated 'use' should be removed.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the multi-stage optimization claim is tested against external baselines and controlled ablations; the only same-group citation (Baguan backbone) is not load-bearing.

full rationale

I walked the claimed derivation chain. The central empirical claim is not circular: the multi-stage teacher-forcing schedule (T = 1, 7, 42, Sec. 3.2) is a training strategy, and its gains are measured against the naive 42-day fine-tune (Sec. 5.1, Table 1), direct forecasting (Fig. 3), and external ECMWF-S2S (Sec. 4.2). No fitted parameter is renamed as a prediction; the ablations hold the backbone fixed and vary only the optimization, so 'optimization, not architecture' is a controlled comparison. The theoretical motivation (Sec. 3.1) is the exact BPTT chain-rule identity containing products of Jacobians, which is standard calculus; the instability statement is explicitly supported by external reference [24], and Appendix B says 'Our analysis follows closely the work' of Bartlett et al. [2], adding 'we can follow the identical analysis from the original work.' That is a derivative analogy, not a self-referential proof. The one same-group citation is the Baguan pretrained backbone [1], a non-archival DAMO Academy blog; it supplies model weights rather than an argument, and the controlled experiments use identical weights for the compared training methods, so no result reduces to the citation. Two non-circular weaknesses deserve explicit flagging: (i) Sec. 4.1.2 scores model anomalies with an 11-day centered ERA5 climatology while 'ECMWF employs its own climatology,' and then warns that 'using a longer average or fixed time period can weaken the climatology signal, making the results appear inflated'; the headline 19-91% margin is therefore a benchmark-comparability risk, not a circularity; (ii) the same section defines climatology as 'the average values for each day of the year across all years,' potentially including test years, which is a leakage risk. Both are correctness concerns, not cases where the prediction equals its input by construction. Score 2 reflects the minor non-load-bearing self-citation only.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The method is a training recipe built from standard building blocks (teacher forcing, curriculum learning, adapters). The main load-bearing inputs are the pretrained Baguan backbone (unpublished, from the authors' organization) and several hand-chosen hyperparameters. No new physical entities are introduced.

free parameters (4)
  • Stage-wise peak and minimum learning rates = 1e-4/1e-4, 2e-6/1e-6, 2e-6/1e-6
    Hand-chosen per training stage; the staged schedule is part of the proposed recipe and affects convergence and final skill.
  • Rolling horizon schedule (T = 1, 7, 42) = 1 day, 7 days, 42 days
    Design choice tied to the 42-day target and weekly adapter grouping; not derived from theory.
  • Number of adapter sets and adapter size = 6 sets, each 4% of parameters, hidden dim 1024
    Chosen so one adapter set covers 7 days of the 42-day roll; the 4% ratio is a design choice.
  • Climatology averaging window = 11-day centered rolling mean
    Chosen for computing anomalies; the paper states that different windows affect results and can inflate skill.
assumptions (5)
  • standard math BPTT gradient formula for the rolling RNN (page 3): gradient is a sum of products of Jacobians J_k along the trajectory.
    Standard backpropagation through time; used to motivate the accumulation effect.
  • domain assumption Positive maximum Lyapunov exponent lambda_max > 0 leads to diverging loss gradients when training RNNs on chaotic series with gradient descent.
    Invoked from Mikhaeil et al. [24] as a prior result; not proven in this paper.
  • ad hoc to paper Deep-linear-model analysis in Appendix B: inequality (8), |grad ell|^2 >= 4 L^2 ell(Theta) (1 - sigma_min(Theta)), is asserted as 'easy to verify' and then drives the convergence bound (14).
    The modified inequality is stated without proof and is load-bearing for the theoretical explanation of why curriculum training helps.
  • domain assumption ERA5 reanalysis is treated as ground truth for training and verification.
    Standard practice in the ML weather literature; not independently validated here.
  • domain assumption ECMWF-S2S reforecasts (C47r3) are a fair operational baseline, and computing ECMWF's climatology over 2002-2021 while testing on 2015-2018 is acceptable.
    The paper does not cross-check ECMWF skill with the same anomaly definition used for the model.

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Cite this review

Pith. "Pith review of Maximizing the Impact of Deep Learning on Subseasonal-to-Seasonal Climate Forecasting: The Essential Role of Optimization." pith.science (2026). https://pith.science/paper/L4IIFK3K

@misc{pith2026241116728,
  author       = {Pith},
  title        = {Pith review of: Maximizing the Impact of Deep Learning on Subseasonal-to-Seasonal Climate Forecasting: The Essential Role of Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/L4IIFK3K}},
  note         = {Machine review of arXiv:2411.16728}
}
read the original abstract

Weather and climate forecasting is vital for sectors such as agriculture and disaster management. Although numerical weather prediction (NWP) systems have advanced, forecasting at the subseasonal-to-seasonal (S2S) scale, spanning 2 to 6 weeks, remains challenging due to the chaotic and sparse atmospheric signals at this interval. Even state-of-the-art deep learning models struggle to outperform simple climatology models in this domain. This paper identifies that optimization, instead of network structure, could be the root cause of this performance gap, and then we develop a novel multi-stage optimization strategy to close the gap. Extensive empirical studies demonstrate that our multi-stage optimization approach significantly improves key skill metrics, PCC and TCC, while utilizing the same backbone structure, surpassing the state-of-the-art NWP systems (ECMWF-S2S) by over \textbf{19-91\%}. Our research contests the recent study that direct forecasting outperforms rolling forecasting for S2S tasks. Through theoretical analysis, we propose that the underperformance of rolling forecasting may arise from the accumulation of Jacobian matrix products during training. Our multi-stage framework can be viewed as a form of teacher forcing to address this issue. Code is available at \url{https://anonymous.4open.science/r/Baguan-S2S-23E7/}

Figures

Figures reproduced from arXiv: 2411.16728 by the authors.

Figure 1
Figure 1. Left: comparison of the training processes of the multi￾stage method with the naive method. The naive method, while increasing T, exhibits a significant discrepancy in the model state, leads to gradient divergence. Our method gradually increases T while simultaneously reducing the discrepancy in model states at each stage, thereby lowering the training difficulty. Right: training stability comparison between naive t… view at source ↗
Figure 2
Figure 2. Principle of multi-stage progressive learning. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Comparison between direct prediction and different [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (16 more)
Figure 4
Figure 4. Figure 4: Performance of multi-stage training compared with [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: PCC comparsion between ECMWF-S2S and Our model. Our model surpassed the state-of-the-art NWP systems (ECMWF-S2S) [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: TCC comparsion between ECMWF-S2S and Our model. [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Comparison of globally-averaged and latitude-weighted [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: PCC comparison between naive method and our method. [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 11
Figure 11. Figure 11: PCC comparison between 5.625-degree model and [PITH_FULL_IMAGE:figures/full_fig_p009_11.png]
Figure 12
Figure 12. Figure 12: Implementation of 6 sets of adapter. D. Ablation of Different Backbones We compared the performance of our method and the naive method using ViT and UNet backbones, as shown in [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]
Figure 14
Figure 14. Figure 14: PCC comparison between our method and naive [PITH_FULL_IMAGE:figures/full_fig_p012_14.png]
Figure 15
Figure 15. Figure 15: PCC comparsion between ECMWF-S2S and Ours (5.625 degree). [PITH_FULL_IMAGE:figures/full_fig_p013_15.png]
Figure 16
Figure 16. Figure 16: TCC comparsion between ECMWF-S2S and Ours (5.625 degree). [PITH_FULL_IMAGE:figures/full_fig_p013_16.png]
Figure 18
Figure 18. Figure 18: z500 visualized error comparison between our method [PITH_FULL_IMAGE:figures/full_fig_p014_18.png]
Figure 19
Figure 19. Figure 19: u200 visualized error comparison between our method [PITH_FULL_IMAGE:figures/full_fig_p015_19.png]
Figure 20
Figure 20. Figure 20: PCC comparsions between ECMWF-S2S and Ours in three stages. [PITH_FULL_IMAGE:figures/full_fig_p016_20.png]
Figure 21
Figure 21. Figure 21: PCC comparsions between Our model trained with 5.625-degree and 1.40625-degree. [PITH_FULL_IMAGE:figures/full_fig_p016_21.png]
Figure 22
Figure 22. Figure 22: PCC comparsions between Our method and Naive method. [PITH_FULL_IMAGE:figures/full_fig_p017_22.png]
Figure 23
Figure 23. Figure 23: PCC comparsions between last stage full fine-tuning and PEFT. [PITH_FULL_IMAGE:figures/full_fig_p017_23.png]

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