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REVIEW 4 major objections 6 minor 14 references

Kolmogorov-Arnold Recurrent Network for Short Term Load Forecasting Across Diverse Consumers

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper proposes a recurrent Kolmogorov–Arnold layer—a hidden state built from a SiLU basis path plus a learnable B-spline path plus a linear memory term—and reports that it beats vanilla RNNs on all ten consumer load datasets and…

desk verdict KARN is a legitimately new recurrent-KAN hybrid with a broad, honest evaluation, but the headline accuracy claims rest on single-split point estimates and several margins are within noise. read the letter →

arxiv 2501.06965 v1 pith:MXDRO3GC submitted 2025-01-12 cs.LG cs.AIeess.SP

Muhammad Umair Danish , Katarina Grolinger This is my paper · ORCID
classification cs.LGcs.AIeess.SP MSC 68T0762M10
keywords short-termloadforecastingKolmogorov-ArnoldnetworksrecurrentneuralsplineactivationsB-splinesenergydemanddiverseconsumertypesgridextension
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

The paper tries to establish that one recurrent architecture, KARN, can forecast the next day's electricity load well across very different consumer types—student residences, detached houses, a house with electric-vehicle charging, a townhouse, and industrial and commercial buildings—without being redesigned for each one. It does this by replacing the fixed neuron activations of an ordinary RNN with learnable spline functions on the edges, so the nonlinearity adapts to each building's consumption pattern. Across ten real datasets, the authors report that KARN beats vanilla RNN everywhere and beats LSTM and GRU in six of ten buildings, with the biggest gains on erratic profiles such as House 2, the EV home, and the retail store. If this is right, utilities could deploy a single adaptable model instead of choosing different forecasters for different customer classes, which would simplify operations and improve accuracy where loads are irregular.

What carries the argument

The load-bearing object is the KARN recurrent layer and its update $h(t)=W^{(h)}h(t-1)+b(t)+S(t)+\text{bias}$. Here $b(t)=w_b(t)\text{SiLU}(x(t))$ is the temporal basis path and $S(t)=w_s(t)\sum_i c_i B_i(x(t))$ is the temporal spline path, with $B_i$ the recursive B-spline basis over knots and $c_i$ learnable coefficients. Grid extension refits coarse-grid spline coefficients on a finer grid by least squares, so capacity can grow without retraining. The mechanism replaces fixed neuron activations with learnable edge splines and couples them to a linear memory term; the paper argues this is why KARN keeps long-term dependencies while avoiding vanishing and exploding gradients. Weight sharing and a locking mechanism keep the spline parameter count tractable.

What would settle it

Run the same ten datasets, or comparable public load series, with several temporal splits and multiple random seeds; if KARN's SMAPE advantage over the best LSTM or GRU in the six buildings falls below the seed-to-seed variance or changes sign, the 'six of ten' claim does not reproduce. Separately, unroll a trained KARN for 100 steps and measure hidden-state gradient norms; exponential growth or decay would contradict the paper's claim that spline activations remove vanishing and exploding gradients.

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Extended reading notes

Core claim

The central claim is that a recurrent layer built on Kolmogorov–Arnold splines, KARN, captures sudden spikes, level shifts, and concept drift in building electricity load better than standard recurrent networks. Its update is $h(t)=W^{(h)}h(t-1)+b(t)+S(t)+\text{bias}$, where $b(t)=w_b(t)\text{SiLU}(x(t))$ is the temporal basis path and $S(t)=w_s(t)\sum_i c_i B_i(x(t))$ is the temporal spline path. This puts the nonlinearity inside learnable edge functions instead of fixed node activations. Across ten real-world datasets—student residences, detached houses, a house with EV charging, a townhouse, and industrial/commercial buildings—the paper reports that KARN beats vanilla RNN in all ten and beats LSTM and GRU in six, with the largest gains on the most erratic load profiles.

Load-bearing premise

The headline result rests on a single 60/20/20 temporal split of ten confidential datasets, with each model tuned by grid search on that split and no repeated runs or significance tests, and the paper itself notes that KARN is sensitive to spline degree and grid size; if the split is favourable or the tuning favours KARN, the reported margins may not reproduce.

Editorial extensions

If this is right

  • If KARN's results reproduce, a utility could deploy one recurrent architecture across residential, EV-equipped, and commercial customers instead of training separate models for each consumer class.
  • KARN's design gives a concrete mechanism for modelling sudden spikes and level shifts, and the paper's largest reported gains come on exactly such erratic profiles (House 2, the EV home, and the retail store).
  • Because inference time stays low (at most 0.18 minutes on the largest test set) even though training is slower, the model could be used in operational day-ahead forecasting.
  • Grid extension allows model capacity to be increased after training, which offers a path to refine a coarse model on new consumer data without retraining from scratch.

Reading between the lines

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

  • Editorial inference: the six-of-ten headline should be treated as provisional, because the reported evidence is one temporal split per dataset with per-dataset grid search and no repeated runs or significance tests.
  • Editorial inference: ablating the recurrent term in Eq. (4) would show whether the gains come from the spline paths or from the memory term, and the paper does not report that comparison.
  • Editorial inference: grid extension suggests a transfer workflow the paper does not develop—train a coarse model on one consumer type and refine it on another by extending the grid.
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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

4 major / 6 minor

Summary. The paper proposes KARN, a recurrent variant of Kolmogorov-Arnold Networks, in which the hidden-state update combines a SiLU-based temporal basis function, a B-spline temporal spline function, and a linear recurrence on the previous hidden state (Eqs. 1–5). The authors evaluate KARN against vanilla RNN, LSTM, and GRU on ten confidential load datasets spanning student residences, individual houses, and industrial/commercial buildings, using a single 60/20/20 temporal split and per-dataset grid search. They report that KARN outperforms all three baselines in six consumer types and outperforms RNN in all ten, with lower SMAPE on most datasets and competitive inference times. The paper also discusses grid extension, computational complexity, and limitations such as sensitivity to spline-degree and grid-size hyperparameters.

Significance. If the empirical claims were supported by repeated-run statistics and a precisely defined aggregation rule, the contribution would be significant: KARN is a clean architectural extension of KAN to recurrent settings, and the evaluation spans a broader set of consumer types than is typical in load-forecasting papers. The computational-complexity comparison (Tables 9–10) is a useful addition, and the paper clearly states that the data are confidential. However, as it stands, the central claim is not yet falsifiable from the manuscript: all results are single-run point estimates from one split, several decisive margins are small, and the reported win counts are not internally consistent with the tables. No code, data, or significance tests are provided, so the claimed advantage over LSTM/GRU remains unestablished.

major comments (4)
  1. [Section 4.1 and Tables 4–8] The headline comparison rests on single-run point estimates from one temporal split. No confidence intervals, standard deviations, or paired significance tests are reported. Several decisive margins are small (House 4 SMAPE: 39.39% vs 39.75%; Office: 3.55% vs 3.77%; Retail: 7.17% vs 7.56%), and the same tables show LSTM or GRU winning on other metrics for those datasets. A paired test (e.g., Diebold–Mariano or a bootstrap over sliding test windows) and repeated random initializations are required before the claimed advantage over LSTM/GRU can be accepted.
  2. [Sections 2.2, 3.3, and 5.4 (Eq. 4)] The claim that KARN avoids vanishing and exploding gradients because activations are placed on edges is not supported. Equation (4) is linear in h(t-1), so backpropagation through time multiplies gradients by powers of W^(h); the spectral radius of W^(h) governs gradient decay or explosion just as in a linear RNN. The splines in Eq. (3) act on the input, not on the recurrent path, so they do not by themselves stabilize the recurrence. The paper provides no gradient-norm measurements or analysis. Either provide such evidence or soften the claim.
  3. [Section 5.4, abstract, conclusion, and Tables 4–8] The 'six out of ten' claim is not reproducible from the tables. If SMAPE is the criterion, KARN beats all three baselines in seven datasets (House 1, House 2, House 3, House 4, Medical clinic, Retail store, Office). If all three metrics must be lower, KARN beats all three baselines in only four datasets (House 1, House 2, Medical clinic, Office), because GRU has lower RMSE on House 3, LSTM has lower RMSE on House 4 and Retail, LSTM has lower SMAPE on Residence 1 and Manufacturing, and GRU has lower SMAPE on Residence 2. The aggregation rule for 'outperforms' must be stated explicitly, and the count must be corrected accordingly.
  4. [Section 4.3 and Tables 3–8] The hyperparameter search does not establish an equal-budget comparison. KARN has additional hyperparameters (spline degree k, grid points, grid extension) that are not present in the baselines, while the paper reports that KARN always used the MAE loss, baselines selected between MAE and MSE, and grid extension was applied only for houses. No information is given about the number of configurations evaluated per model, the validation scores used for final model selection, or whether the per-dataset choices (e.g., grid extension for House 3) were made without inspecting test results. Without this information, the comparison may favor KARN by construction.
minor comments (6)
  1. [Section 5.3, paragraph after Table 8] The sentence 'KARN demonstrated superior performance in most scenarios, achieving the lowest SMAPE values for the office building 3.55%, retail store 7.17%, and manufacturing building 8.52%' is contradicted by Table 7, which gives LSTM the lowest manufacturing SMAPE at 7.67%. This appears to be a typo for Medical clinic (3.71%) and should be corrected.
  2. [Figure 15 caption] The caption states 'for all consumers, KARN achieves the lowest SMAPE,' which is contradicted by Tables 6 and 7 (Residence 1: LSTM 9.12% vs KARN 9.40%; Residence 2: GRU 8.14% vs KARN 8.93%; Manufacturing: LSTM 7.67% vs KARN 8.52%).
  3. [Sections 5.1, 5.2, and Figures 2, 4, 8, 10] Several figure references are incorrect: Section 5.1 refers to 'actual versus predicted values in Fig. 2,' but Fig. 2 is a House 2 load plot; Section 5.2 says Residence 2 results are shown in 'Fig. 4,' but Fig. 4 is also House 2. Additionally, Section 5.2 begins with 'Case Study 1 focuses on two student residence buildings,' which should be Case Study 2.
  4. [Equations (2)–(5) and Section 3.3] The notation for weights is inconsistent: Eq. (2) uses w_b(t), Eq. (4) uses W^(h), and the text refers to 'learnable weight metrics' instead of 'weight matrices.' The dimensions of w_b(t), w_s(t), and the spline coefficient c_i are not specified. Also, the phrase 'bials(y)' after Eq. (5) appears to be a typo for 'bias(y).'
  5. [Tables 4–5] The MAE and RMSE values for houses (e.g., 0.36, 0.39, 0.45) appear to be on a scaled or normalized scale, while Tables 6–8 are in kW. The paper should state explicitly which metric values are computed on scaled data and report unscaled errors or provide scaling factors.
  6. [Section 6] The statement that KARN achieved 'approximately 11% lower SMAPE values than LSTM' for House 2 and the Retail Store is not supported: House 2 relative SMAPE reduction is about 41% (32.53% to 19.29%), and Retail is about 5% (7.56% to 7.17%). The comparison should be restated with the correct relative or absolute differences.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: KARN is evaluated on held-out test splits and its recurrent-KAN equations are independent definitions; self-citations are contextual.

full rationale

The paper makes an empirical rather than a derivational claim: the KARN update equations (2)-(5) define the model, and the reported SMAPE/MAE/RMSE improvements are computed on a temporally held-out 20% test split after grid search on the validation split. No parameter fitted to the test set is later renamed as a prediction, and no load-bearing result is imported from the authors' prior work. The self-citations (Danish and Grolinger 2024; L'Heureux et al. 2022; Skala et al. 2023; Fekri et al. 2023) appear only as related-work or standard-metric references and do not carry the KARN superiority claim. The KAN citations (Liu et al. 2024) are external and supply the spline/KAN machinery, not the recurrent comparison. The vanishing-gradient advantage is asserted rather than proven, and the single-split/no-significance-test protocol weakens the empirical conclusion, but those are correctness and rigor concerns, not circularity. Thus no step reduces Eq. (2)-(4) to its inputs or equates a fit with a prediction.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claims rest on standard spline math, on assumptions about data representativeness and the sufficiency of a single split, and on an unanalyzed claim about gradient behavior in the new architecture. The main hand-set choices are the hyperparameters listed above; the learned weights themselves are ordinary fitted parameters.

free parameters (6)
  • Spline degree (k) = 2 (grid search over 1, 2, 3)
    Selected via grid search for KARN; affects the polynomial order of B-splines and model capacity.
  • Grid size (G) = 2 to 14 grid points; extended to 10 for House 3
    Tuned per dataset; grid extension applied only to individual houses, introducing per-dataset model configuration.
  • Hidden layer size = 64 units for most datasets, 128 for townhouse and office
    Result of grid search over 64, 128, 256.
  • Number of recurrent layers = 1
    Grid search found one layer optimal for all models.
  • Loss function = MAE for KARN across all datasets
    Chosen via hyperparameter optimization; MSE did not yield optimal performance.
  • Optimizer = SGD for most, Adam for House 1, AdamW in search space
    Selected per model and dataset by grid search.
assumptions (5)
  • standard math The Kolmogorov-Arnold representation theorem justifies replacing linear weights with univariate spline functions
    Invoked in Section 3 as the theoretical foundation of KARN, though the implemented architecture is an approximation and the theorem itself is not used constructively.
  • standard math B-spline recursion and grid extension minimize the coarse-to-fine discrepancy as described
    Equations (6)-(9) rely on standard spline theory; the least-squares coefficient update is assumed valid for the empirical distribution p(x).
  • domain assumption A 24-hour sliding window with five features is a sufficient input representation for next-day load forecasting
    Section 4.1 fixes the window and feature set without ablation experiments.
  • domain assumption The ten confidential datasets are representative of diverse consumer types and a single 60/20/20 split supports the comparative conclusions
    Section 4.1 defines the split; no public data or repeated evaluation is provided.
  • ad hoc to paper The linear recurrence in Eq. (4) avoids vanishing and exploding gradients because activations are on edges
    Claimed in Sections 2.1 and 5.4 without gradient analysis; the recurrence is linear in h(t-1) and can still cause gradient growth or decay depending on the spectral properties of W(h).

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Cite this review

Pith. "Pith review of Kolmogorov-Arnold Recurrent Network for Short Term Load Forecasting Across Diverse Consumers." pith.science (2026). https://pith.science/paper/MXDRO3GC

@misc{pith2026250106965,
  author       = {Pith},
  title        = {Pith review of: Kolmogorov-Arnold Recurrent Network for Short Term Load Forecasting Across Diverse Consumers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MXDRO3GC}},
  note         = {Machine review of arXiv:2501.06965}
}
read the original abstract

Load forecasting plays a crucial role in energy management, directly impacting grid stability, operational efficiency, cost reduction, and environmental sustainability. Traditional Vanilla Recurrent Neural Networks (RNNs) face issues such as vanishing and exploding gradients, whereas sophisticated RNNs such as LSTMs have shown considerable success in this domain. However, these models often struggle to accurately capture complex and sudden variations in energy consumption, and their applicability is typically limited to specific consumer types, such as offices or schools. To address these challenges, this paper proposes the Kolmogorov-Arnold Recurrent Network (KARN), a novel load forecasting approach that combines the flexibility of Kolmogorov-Arnold Networks with RNN's temporal modeling capabilities. KARN utilizes learnable temporal spline functions and edge-based activations to better model non-linear relationships in load data, making it adaptable across a diverse range of consumer types. The proposed KARN model was rigorously evaluated on a variety of real-world datasets, including student residences, detached homes, a home with electric vehicle charging, a townhouse, and industrial buildings. Across all these consumer categories, KARN consistently outperformed traditional Vanilla RNNs, while it surpassed LSTM and Gated Recurrent Units (GRUs) in six buildings. The results demonstrate KARN's superior accuracy and applicability, making it a promising tool for enhancing load forecasting in diverse energy management scenarios.

Discussion (0). Continue with ORCID to comment.

Reference graph

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Reviewed August 10, 2026 · model on record in the stance chip above.