Zero Shot Time Series Forecasting Using Kolmogorov Arnold Networks

Abhiroop Bhattacharya; Nandinee Haq

REVIEW 5 major objections 6 minor 1 cited by

Zero Shot Time Series Forecasting Using Kolmogorov Arnold Networks

T0 review · 5 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper proposes that a doubly residual N-BEATS network built on Kolmogorov-Arnold Networks and trained with adversarial domain adaptation can forecast day-ahead electricity prices for an unseen market, reporting 13% and 24% lower error…

desk verdict Plausible architecture, unconvincing evidence: the zero-shot gains aren't established because the evaluation has temporal leakage and missing statistics. read the letter →

arxiv 2412.17853 v2 pith:SDD5L24C submitted 2024-12-19 cs.LG

Abhiroop Bhattacharya , Nandinee Haq This is my paper · ORCID

classification cs.LG

keywords zero-shotforecastingelectricitypriceKolmogorov-ArnoldnetworksN-BEATSdomainadaptationadversarialtrainingsplineactivationsday-aheadmarket

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 tries to establish that a forecasting model can transfer across electricity markets without ever seeing the target market. The model stacks Kolmogorov-Arnold Networks, which use learnable univariate spline functions on their edges, inside a doubly residual N-BEATS structure, and trains the whole system adversarially on two source markets so that the learned features become market-invariant. Tested by forecasting Nord Pool day-ahead prices for all of 2018 with no Nord Pool data in training, the model reports lower mean absolute error and symmetric MAPE than standard KAN and N-BEATS baselines, by about 24% and 13%. If this holds, a trader entering a new market could generate usable day-ahead forecasts immediately, without years of local price history.

What carries the argument

The load-bearing object is a doubly residual KAN stack: a sequence of blocks, each a Kolmogorov-Arnold Network whose edge operations are learnable univariate B-spline functions, wired together with backcast residuals and hierarchical forecast aggregation in the style of N-BEATS. Around this backbone, a gradient reversal layer implements the adversarial game between the price forecaster and a domain classifier, forcing the early representation to hide which source market produced a sample while later layers keep market-specific detail. This combined structure is what the paper claims generates domain-invariant features, and it is the mechanism by which the zero-shot transfer is supposed to happen.

What would settle it

Inspect the Bayesian optimization logs and training configuration: if any Nord Pool 2018 prices were passed to hyperparameter search, or if the reported model was chosen after looking at Nord Pool test errors, the zero-shot claim collapses. A cleaner test is to truncate every training market before 2018, fix hyperparameters using only pre-2018 data, and rerun; if the 13% and 24% margins vanish, the central claim fails.

Watch

Extended reading notes

Core claim

The central claim is that replacing the MLP blocks of N-BEATS with Kolmogorov-Arnold Networks and adding a gradient-reversal domain classifier to the training objective yields representations that transfer to a market excluded from training. In the reported experiments, the proposed model reaches a mean absolute error around 2.51 and a symmetric MAPE around 0.086 on the Nord Pool 2018 test year, regardless of which of the three source markets is treated as primary; the best N-BEATS and KAN baselines are higher on both metrics. The authors state this is an improvement of roughly 13% over N-BEATS and 24% over KAN, and that the adversarial framework learns market-invariant representations.

Load-bearing premise

The result depends on the target market's data never entering training or model selection; the paper does not specify which data the Bayesian optimizer saw, and the PJM training set runs through the same calendar year as the Nord Pool test period.

Editorial extensions

If this is right

A market operator opening in a new region could issue day-ahead forecasts on day one, using only price histories from established markets.
The reported 13% and 24% error reductions imply that, among the architectures tested, the KAN-based adversarial backbone is the better default for cross-market zero-shot forecasting.
The zero-shot errors sit in the same order of magnitude as published supervised results with NBEATSx, so the approach could substitute for local training when target-market data are unavailable.
Because the KAN layers learn smooth B-spline curves, forecasts come with a visual account of the functional shapes the model uses, which is not available from opaque large models.

Reading between the lines

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

Ablating the gradient reversal layer while keeping the KAN backbone would show whether the domain-adversarial term, rather than the spline architecture alone, causes the zero-shot gain; the paper does not report that comparison.
The current model ingests only the price series, so a testable extension is to add exogenous drivers such as temperature or load forecasts to the KAN inputs, which the spline activations can accommodate without a change in the adversarial objective.
The paper trains with one primary and one secondary market per run; a natural extension is to feed several secondary markets through the same domain classifier, since the objective only requires a domain label per sample.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: the paper's central claim — that a KAN-based doubly residual N-BEATS with adversarial domain adaptation beats plain KAN and N-BEATS on zero-shot Nord Pool forecasting — is plausible but not supported by the experiments as reported. The architecture combination is genuinely new (I don't know of prior work mixing KAN layers, N-BEATS residual stacks, and a gradient reversal layer for energy price forecasting), and the problem is a real one: day-ahead markets with scarce data need off-the-shelf forecasters. The authors also deserve credit for testing on an unseen market with three different primary markets, and for keeping the model description reasonably clear.

Where it falls down is the evaluation. The PJM training set runs through 24 Dec 2018, which is the same calendar window as the Nord Pool test period. That's a temporal overlap that could let the model learn time-specific effects from another market, so the 'zero-shot' label is questionable. Worse, the paper never says what data the Bayesian optimization used for hyperparameter selection. If any of that touched the test window, the reported gains are not zero-shot at all. The baselines have no error bars, so the 13%/24% improvements could easily be noise. There's also a formal slip: Appendix A.1 defines risk as P(F(X) != Y), which is a classification risk, but forecasting is regression. That's not a cosmetic typo — it undermines the theoretical framing. And despite the paper's claim that the adversarial branch learns market-invariant representations, there is no ablation or domain-classifier confusion measurement to show the branch actually does anything. The gains could come from the KAN backbone alone or from hyperparameters.

None of these are fatal to the idea. The combination is worth exploring, and a clean evaluation would be useful. But as it stands, the evidence doesn't establish the claims. I'd tell the authors to fix the temporal split, specify the tuning protocol, add error bars and significance tests, run an ablation of the adversarial branch, and correct the formalism. That version would deserve a serious referee.

This paper is for researchers working on cross-market forecasting or KAN applications. It's not ready for publication in its current form, but the kernel is there. I would not cite it in the next year, and I would not bring it to a reading group as a model of experimental practice. For peer review: I'd desk reject now, but with an invitation to resubmit after a proper revision.

Referee Report

5 major / 6 minor

Summary. The paper proposes a zero-shot time series forecasting model for day-ahead electricity prices that combines Kolmogorov-Arnold Networks (KANs) with a doubly residual N-BEATS-like architecture and an adversarial domain adaptation mechanism using a gradient reversal layer. The model is trained on two of three source markets (PJM, EPEX France, EPEX Belgium) and tested on the unseen Nord Pool market. The authors report MAE and SMAPE comparisons against standard KAN and N-BEATS baselines, claiming approximately 13% and 24% improvements in accuracy. The theoretical framework is described in Appendix A, with additional appendices on zero-shot learning and evaluation metrics.

Significance. If the results were properly validated, the paper would make a useful contribution: combining KANs with the N-BEATS residual stacking is a natural and relatively new idea, and demonstrating zero-shot transfer across electricity markets would have practical value for forecasting in markets with scarce historical data. The paper also correctly identifies the need for domain-invariant representations. However, the significance is severely weakened by the current form of the manuscript: the formal framework contains a fundamental error, the empirical evaluation is missing essential methodological detail, and the main performance claim is not supported by appropriate statistics. The reader cannot currently verify the central zero-shot claim, so the contributions remain at the level of an interesting proposal rather than a validated result.

major comments (5)

[Appendix A.1] Equation (1) defines the target risk as R_Mt(F) = P(F(X) ≠ Y), which is a classification error (0-1 loss). For the regression problem at hand, where Y is a continuous electricity price, the event F(X) ≠ Y essentially always occurs, making this quantity identically 1 and uninformative. The formal framework should instead minimize an expected loss E_{(x,y)∼P_Mt}[L(F(x), y)] for a suitable regression loss L (e.g., MAE or SMAPE). This is not a stylistic slip: the adversarial training justification in the same appendix is expressed in terms of this mis-specified risk, and as written it does not describe the actual optimization objective used in the experiments.
[Section 4] The zero-shot protocol is not verifiable. The paper states that hyperparameters 'are optimized using a Bayesian optimization method' with a tree-structured Parzen estimator, but it never states which data were used for selection. The PJM training set extends to 24 December 2018, which is the same calendar period as the Nord Pool test set (1 January 2018 to 24 December 2018). If any part of the tuning procedure used data from that overlapping period, information about the target market could have influenced model selection, breaking the zero-shot claim. The authors must specify the exact data split used for hyperparameter optimization, report the tuned hyperparameter values, and confirm that no target-market data or same-period source data were used for model selection.
[Table 1] The baseline KAN and N-BEATS results are reported as single point values with no error bars, while only the proposed model is shown with ± intervals. The number of independent runs is not stated, and no statistical significance tests are performed. Consequently, the claimed improvement of 'around 13% and 24%' is not supported by the reported evidence. The authors should report means and standard deviations over multiple seeds for all models, state the number of runs, and apply an appropriate paired test (e.g., Diebold-Mariano or bootstrap) to the forecast errors to demonstrate that the differences are not due to noise.
[Section 2 and Appendix A.1] The central claim that the adversarial framework 'learns market-invariant representations' is not empirically verified. There is no experiment showing that the domain classifier is actually confused, no comparison to a non-adversarial version of the same backbone, and no ablation varying the gradient reversal strength or architecture. Without such experiments, the observed error differences cannot be attributed to the adversarial mechanism; they could be due entirely to the KAN-based residual backbone. The authors should add an ablation and report the domain classifier accuracy on held-out source data to demonstrate that invariance is achieved.
[Section 4] The experimental protocol is under-specified. The sentence 'The values are averaged over different models, each time with a different market as the secondary market' is ambiguous: for each primary market there are two remaining source markets, so it is unclear whether the reported numbers are averages over two models (one per secondary market) or over a different number of configurations, and whether the secondary markets were used individually or jointly. The authors must clarify the number of models averaged, the exact training configurations, and how the reported error bars were computed.

minor comments (6)

[Appendix B] The entire appendix on 'Zero Shot Learning with attributes' discusses class-attribute matrices and seen classes, which has no connection to the time series forecasting problem addressed in this paper. It appears to be leftover material from a different manuscript and should be removed or substantially rewritten to discuss domain adaptation for regression.
[Appendix B.1] In Equation (7), there is a typo: 'l(h(x, y' should be 'l(h(x,y))'. The covariate shift derivation is also not used elsewhere in the paper; if it is kept, it should be explicitly connected to the proposed method.
[Section 4] The phrase 'We observe an improvement of around 13% and 24% in accuracy' is imprecise: the percentages should be computed directly from the table values, the baselines should be named, and 'accuracy' is a misnomer for regression error metrics.
[Figure 2] The caption reads 'The next day forecast presents a comparison' and is awkwardly worded. More importantly, a single qualitative example is not evidence of systematic performance; the quantitative results in Table 1 are the relevant evidence.
[Appendix A.2] Equation (2) uses the notation 'N Ni,j(yb i,j−1, Xb−1)' without defining Xb−1 or clarifying the indexing of the backcast input. All symbols should be defined to make the architecture reproducible.
[Abstract] The phrase 'This addition not only enriches the model's representational capacity' is vague; the abstract would be clearer if it stated the architecture components explicitly.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper's central claims are empirical and rest on an architecture composed of externally cited components; no prediction reduces to a fitted parameter or self-citation.

full rationale

The paper's derivation chain does not contain a circular step of the kind that would force a predicted quantity to equal its input by construction. The proposed model is a combination of KAN layers (cited from external prior work) and the N-BEATS doubly residual stacking principle (also external). No step in the derivation defines the model in terms of the target Nord Pool labels, nor does any fitted parameter get renamed as a zero-shot prediction. The adversarial domain adaptation objective (Appendix A.1, Eq. 1) is formally mis-specified: it defines the target risk as P(F(X) != Y), which is a classification risk for a regression task with continuous Y. This is a correctness and clarity flaw, not a circularity, because the actual training and evaluation use regression losses (MAE/SMAPE) and the reported numbers are not equal to Eq. 1 by construction. Similarly, the use of Bayesian optimization is not described in terms of which data were used for hyperparameter selection; if the target market's test period informed model selection, the zero-shot protocol would be compromised. That would be data leakage/protocol invalidity, not circularity, because the model's output is not a mathematical restatement of the tuning target. The paper cites no prior work by the same authors as load-bearing evidence, and no uniqueness theorem is imported from the authors' own publications. The performance comparison against standard KAN and N-BEATS baselines is an external empirical benchmark, so the central claim retains independent content. Thus, under the specified criteria, the honest finding is that there is no significant circularity.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new physical or mathematical entities. It combines existing building blocks (KAN, N-BEATS residuals, gradient reversal) and tunes hyperparameters, so the main free parameters are the undisclosed hyperparameter choices and the untested assumptions inherited from KAN and DANN.

free parameters (1)

Model hyperparameters (number of stacks, blocks, hidden units, spline order, learning rate, etc.) = not reported
The paper states hyperparameters were optimized using Bayesian optimization (TPE) but does not list the chosen values or the validation data used. The reported performance depends on these choices, and whether the target market influenced them is unknown.

assumptions (3)

standard math Kolmogorov-Arnold representation theorem
Invoked in Section 2 to motivate KANs. The theorem guarantees exact representation of multivariate continuous functions by sums of univariate functions, but the practical KAN implementation only approximates it; the theorem is not used to derive the architecture.
domain assumption Adversarial domain-invariance via gradient reversal produces domain-invariant features
Heuristic from Ganin et al. (ref 4) used in Appendix A.1. There is no guarantee that fooling a domain classifier yields representations that transfer to an unseen market; it is an empirical assumption.
ad hoc to paper Covariate shift assumption S(y|x) = T(y|x) for reweighting
Appendix B.1 derives a reweighting scheme under this assumption, but the assumption and reweighting are never used in the experiments or the main method, indicating the passage is disconnected from the paper.

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Cite this review

Pith. "Pith review of Zero Shot Time Series Forecasting Using Kolmogorov Arnold Networks." pith.science (2026). https://pith.science/paper/SDD5L24C

@misc{pith2026241217853,
  author       = {Pith},
  title        = {Pith review of: Zero Shot Time Series Forecasting Using Kolmogorov Arnold Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SDD5L24C}},
  note         = {Machine review of arXiv:2412.17853}
}

read the original abstract

Accurate energy price forecasting is crucial for participants in day-ahead energy markets, as it significantly influences their decision-making processes. While machine learning-based approaches have shown promise in enhancing these forecasts, they often remain confined to the specific markets on which they are trained, thereby limiting their adaptability to new or unseen markets. In this paper, we introduce a cross-domain adaptation model designed to forecast energy prices by learning market-invariant representations across different markets during the training phase. We propose a doubly residual N-BEATS network with Kolmogorov Arnold networks at its core for time series forecasting. These networks, grounded in the Kolmogorov-Arnold representation theorem, offer a powerful way to approximate multivariate continuous functions. The cross domain adaptation model was generated with an adversarial framework. The model's effectiveness was tested in predicting day-ahead electricity prices in a zero shot fashion. In comparison with baseline models, our proposed framework shows promising results. By leveraging the Kolmogorov-Arnold networks, our model can potentially enhance its ability to capture complex patterns in energy price data, thus improving forecast accuracy across diverse market conditions. This addition not only enriches the model's representational capacity but also contributes to a more robust and flexible forecasting tool adaptable to various energy markets.

Figures

Figures reproduced from arXiv: 2412.17853 by the authors.

**Figure 2.** The next day forecast presents a comparison between the KAN, N-BEATS and Proposed [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** This representative example shows some of the functions learned by the KAN network [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Schematic of our Domain Adaptation Framework. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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TFKAN places Kolmogorov-Arnold Networks directly on FFT coefficients alongside a time-domain KAN branch, improving long-term forecast accuracy on seven benchmark datasets.

Reference graph

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

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@esa ( ) , n @biblabelnum##1 ##1

\@ifclassloaded aguplus natbib The aguplus class already includes natbib coding, so you should not add it explicitly Type <Return> for now, but then later remove the command natbib from the document \@ifclassloaded nlinproc natbib The nlinproc class already includes natbib coding, so you should not add it explicitly Type <Return> for now, but then later r...

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Ziming Liu, Yixuan Wang, Sachin Vaidya, Fabian Ruehle, James Halverson, Marin Solja c i \'c , Thomas Y Hou, and Max Tegmark. KAN: Kolmogorov-Arnold Networks . arXiv preprint arXiv:2404.19756 , 2024

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Yaroslav Ganin, Evgeniya Ustinova, Hana Ajakan, Pascal Germain, Hugo Larochelle, Fran c ois Laviolette, Mario Marchand, and Victor Lempitsky. Domain-adversarial training of neural networks . The journal of machine learning research , 17(1):2096--2030, 2016

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Hyperopt: A python library for optimizing the hyperparameters of machine learning algorithms

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