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arxiv: 2508.01575 · v2 · submitted 2025-08-03 · 💻 cs.LG

KANMixer: a minimal KAN-centered mixer for long-term time series forecasting

Pith reviewed 2026-05-19 01:24 UTC · model grok-4.3

classification 💻 cs.LG
keywords Kolmogorov-Arnold NetworksKANlong-term time series forecastingtime series predictionneural network architecturesbasis functionsmixer modelsforecasting benchmarks
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The pith

A minimal KAN-centered mixer outperforms baselines on most long-term time series forecasting benchmarks while showing that MLP design choices can harm KAN performance.

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

The paper tests whether Kolmogorov-Arnold Networks can replace MLP and Transformer cores in long-term time series forecasting by building a minimal architecture called KANMixer. This model combines multi-scale pooling, a KAN temporal mixing backbone, and prediction heads, then evaluates it on 28 benchmark settings where it records the top MSE in 16 cases and top MAE in 11. Ablation studies reveal that B-spline bases work better than Fourier or Wavelet options, moderate depth is more stable than deeper stacks, the prediction head drives most of the gains, and decomposition priors that help MLP models reduce KAN accuracy. Readers might care because reliable multi-step forecasting supports practical tasks such as energy management and weather prediction, and the results give concrete guidance on how to integrate KANs without heavy auxiliary modules.

Core claim

KANMixer, built from a multi-scale pooling frontend, a KAN-based temporal mixing backbone, and prediction heads, records the best MSE in 16 of 28 benchmark-horizon settings and the best MAE in 11 against nine baselines. Ablations on three datasets establish that B-spline edge functions outperform Fourier and Wavelet alternatives, the prediction head contributes the largest share of gains, moderate depth is preferred over deeper unstable stacks, and decomposition priors that improve MLP results actually degrade KAN performance.

What carries the argument

The KAN-based temporal mixing backbone, which uses adaptive basis functions for granular modulation of nonlinearities inside an otherwise minimal mixer architecture.

If this is right

  • B-spline bases for KAN edge functions deliver higher accuracy than Fourier or Wavelet bases in long-term forecasting.
  • Moderate network depth produces more stable and accurate results than deeper KAN stacks.
  • The prediction head design accounts for a larger share of overall performance gains than the temporal mixing backbone.
  • Decomposition priors that benefit MLP-based models reduce accuracy when applied to KAN backbones.

Where Pith is reading between the lines

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

  • The sensitivity of KAN performance to structural priors may require separate tuning guidelines when moving from MLP to KAN architectures in other sequence tasks.
  • Experiments on datasets that exhibit distribution shift could test whether the reported advantages persist outside the original benchmark collection.
  • Minimal KAN mixers could be adapted to multivariate forecasting or related problems where current MLP or Transformer models struggle with long horizons.
  • Varying the multi-scale pooling component might reveal further interactions between frontend design and KAN nonlinearity.

Load-bearing premise

The 28 benchmark-horizon settings and nine baselines are representative enough that the observed wins generalize beyond the specific datasets and horizons tested.

What would settle it

A new evaluation on time series datasets from domains outside the original benchmarks that shows KANMixer no longer achieves the lowest MSE or MAE would indicate the performance gains do not hold more broadly.

read the original abstract

Long-term time series forecasting (LTSF) underpins critical applications from energy management to weather prediction, yet achieving reliable multi-step-ahead accuracy remains challenging. Existing LTSF approaches, dominated by MLP- and Transformer-based architectures, either rely on simple linear mappings or introduce increasingly complex hand-crafted inductive biases, raising the question of whether a more expressive and principled nonlinear core could offer a better alternative. Therefore, we investigate whether Kolmogorov-Arnold Networks (KANs), a recently proposed model featuring adaptive basis functions capable of granular modulation of nonlinearities, can improve LTSF performance, and under which design choices they are most effective. Specifically, we propose KANMixer, a minimal KAN-centered architecture consisting of a multi-scale pooling frontend, a KAN-based temporal mixing backbone, and prediction heads. By avoiding heavy auxiliary modules, KANMixer enables a clear assessment of KAN components in LTSF. Across 28 benchmark-horizon settings against nine baselines, KANMixer achieves the best MSE in 16 settings and the best MAE in 11. Furthermore, extensive ablations on three representative datasets show that KAN effectiveness depends strongly on the choice of edge function; B-spline bases outperform Fourier and Wavelet alternatives; the prediction head contributes most to the gains; moderate depth is preferred over deeper unstable stacks; and decomposition priors help MLP but harm KAN. Beyond practical guidance for integrating KAN into LTSF, these results reveal an underexplored dependency between structural priors and backbone nonlinearity: design choices that benefit MLP can degrade KAN.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes KANMixer, a minimal KAN-centered mixer architecture for long-term time series forecasting consisting of a multi-scale pooling frontend, a KAN-based temporal mixing backbone, and prediction heads. The central empirical claim is that across 28 benchmark-horizon settings against nine baselines, KANMixer achieves the best MSE in 16 settings and the best MAE in 11. Ablation studies on three datasets indicate that KAN effectiveness depends on edge function choice (B-splines outperforming Fourier and Wavelet), that the prediction head contributes most to gains, that moderate depth is preferred, and that decomposition priors help MLP but harm KAN, revealing a dependency between structural priors and backbone nonlinearity.

Significance. If the empirical results hold under proper statistical validation, the work would provide useful practical guidance for integrating KANs into LTSF and highlight non-transferable design choices from MLP to KAN models. The minimal architecture enables a focused assessment of KAN components, which is a strength, and the ablation insights on basis functions and prior interactions could stimulate further research on adaptive basis networks for sequential data.

major comments (2)
  1. [Results] The central claim (abstract and results tables) that KANMixer achieves the best MSE in 16 of 28 settings reports only point estimates. No error bars, standard deviations from multiple seeds, or statistical significance tests are provided, despite known sensitivity of time-series models to initialization, data ordering, and optimizer noise. This directly affects whether the win count can be interpreted as reliable superiority.
  2. [Ablation Studies] Ablation studies conclude that decomposition priors help MLP but harm KAN and that B-spline bases are preferred. These findings rest on experiments on three datasets but lack details on hyperparameter search, exact data splits, or how the decomposition is integrated with KAN layers, limiting the load-bearing strength of the broader claim about structural priors and nonlinearity.
minor comments (2)
  1. [Abstract] The abstract refers to '28 benchmark-horizon settings' without naming the specific datasets and horizons, which would aid reader context and reproducibility.
  2. [Methods] Notation for KAN basis functions and the multi-scale pooling operation could be introduced with a short equation or diagram in the methods section for readers less familiar with KANs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for the detailed and constructive feedback on our manuscript. We address each of the major comments below and have made revisions to strengthen the paper where appropriate.

read point-by-point responses
  1. Referee: [Results] The central claim (abstract and results tables) that KANMixer achieves the best MSE in 16 of 28 settings reports only point estimates. No error bars, standard deviations from multiple seeds, or statistical significance tests are provided, despite known sensitivity of time-series models to initialization, data ordering, and optimizer noise. This directly affects whether the win count can be interpreted as reliable superiority.

    Authors: We agree that the absence of error bars and statistical tests limits the interpretability of the win counts. While our original experiments followed the single-run reporting convention prevalent in the LTSF literature, we recognize the value of multi-seed validation. In the revised manuscript, we will report results averaged over 5 random seeds with standard deviations for the main comparison table, and include a note on the statistical significance where applicable. This revision will be incorporated to provide a more reliable assessment of KANMixer's performance. revision: yes

  2. Referee: [Ablation Studies] Ablation studies conclude that decomposition priors help MLP but harm KAN and that B-spline bases are preferred. These findings rest on experiments on three datasets but lack details on hyperparameter search, exact data splits, or how the decomposition is integrated with KAN layers, limiting the load-bearing strength of the broader claim about structural priors and nonlinearity.

    Authors: Thank you for highlighting the need for greater detail in the ablation studies. To address this, the revised manuscript will include an expanded description of the experimental setup for the ablations: specifically, we will detail the hyperparameter search ranges and selection criteria, provide the exact data split ratios and indices for the three datasets used in the ablations, and clarify the integration of decomposition (e.g., series decomposition is applied as a preprocessing step prior to the multi-scale pooling and KAN mixer). These additions will support the reproducibility of our findings on the interaction between priors and backbone choice. revision: yes

Circularity Check

0 steps flagged

No circularity: purely empirical architecture proposal and benchmark comparison

full rationale

The paper proposes KANMixer as an architectural design (multi-scale pooling + KAN temporal mixer + heads) and evaluates it via direct MSE/MAE comparisons on 28 benchmark-horizon settings against nine baselines, plus ablations on edge functions, depth, and decomposition. No derivation chain exists that reduces a claimed prediction or uniqueness result to a fitted parameter or self-citation by construction. The central claims are empirical win counts and ablation observations; these are falsifiable against external data and do not rely on any self-referential definition or imported uniqueness theorem. Self-citations, if present for the original KAN work, are not load-bearing for the reported performance numbers.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions about benchmark validity and the expressivity of KAN basis functions; no new entities are postulated and the only free parameters are ordinary training hyperparameters.

free parameters (2)
  • KAN depth and width
    Chosen via ablation; moderate depth preferred.
  • Basis function type
    B-spline, Fourier, or Wavelet selected after comparison.
axioms (1)
  • domain assumption KANs with adaptive basis functions can represent nonlinearities more granularly than fixed-activation MLPs
    Invoked to motivate the architecture choice.

pith-pipeline@v0.9.0 · 5854 in / 1282 out tokens · 30526 ms · 2026-05-19T01:24:08.660223+00:00 · methodology

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