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REVIEW 6 major objections 6 minor 33 references

LuKAN: A Kolmogorov-Arnold Network Framework for 3D Human Motion Prediction

T0 review · 6 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

Pith's one-line read The paper claims that a Kolmogorov-Arnold layer using Lucas polynomial activations on wavelet-encoded joint trajectories predicts 3D human motion as accurately as current state-of-the-art baselines while using far fewer parameters.

desk verdict LuKAN is a coherent KAN-plus-DWT architecture worth knowing about, but its superiority claims rest on sub-millimeter MPJPE gaps with no error bars, and the paper overstates its own ablation results. read the letter →

arxiv 2508.04847 v1 pith:UXYKMMPH submitted 2025-08-06 cs.CV

classification cs.CV
keywords 3DhumanmotionpredictionKolmogorov-ArnoldnetworksLucaspolynomialsdiscretewavelettransformMPJPEposeforecastingefficientarchitecturestemporalmodeling
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 introduces LuKAN, an architecture for forecasting future 3D body poses from a short observed history. It encodes each joint trajectory with the discrete wavelet transform, mixes information across joints with two spatial projections, and models temporal dependencies with a Kolmogorov-Arnold layer whose per-edge functions are Lucas polynomials, before reconstructing poses in the time domain. The central claim is that this compact design matches or beats strong baselines such as SiMLPe on Human3.6M, AMASS, and 3DPW while using far fewer parameters and less compute. The authors further argue that Lucas polynomials evaluate more cheaply than the B-spline functions of standard KANs and are better suited to oscillatory motion. If correct, the work offers an efficient KAN-based alternative to transformer-, GCN-, and deep-MLP motion predictors.

What carries the argument

The central object is the KAN layer inside the Temporal Dependency Learner. Each learnable edge function is a weighted combination of Lucas polynomials: $$\varphi_{q,p}(x_p)=\sum_{r=0}^{R}\gamma_{q,p,r}P_r(x_p)$$ with $P_0(x)=2$, $P_1(x)=x$, and the recurrence $P_r(x)=xP_{r-1}(x)+P_{r-2}(x)$. The recurrence makes evaluation linear in the polynomial degree, and the oscillatory shapes of the polynomials are invoked to capture high-frequency motion. Around this layer, a three-level DWT splits each joint trajectory into approximation and detail coefficients, two spatial projection matrices mix information across joints, and IDWT returns the processed coefficients to the time domain.

What would settle it

Run LuKAN and SiMLPe under the same protocol with ten random seeds and report per-horizon MPJPE means with standard deviations or confidence intervals. If the intervals at 720 ms and 1000 ms on Human3.6M overlap or favor SiMLPe, the claimed superiority over the strongest baseline is not supported; likewise, repeat Table 4's Lucas-versus-B-spline comparison and check whether its 2.8 mm gap at 320 ms persists across seeds.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that a KAN layer parameterized by Lucas polynomials, inserted between two spatial projections and fed with three-level Daubechies-4 wavelet coefficients of joint trajectories, can forecast 3D poses at the level of the strongest current baselines. LuKAN reports the best average MPJPE among compared methods at every horizon on Human3.6M (109.3 mm vs 109.4 mm for SiMLPe at 1000 ms) and the best results on 3DPW at most horizons, with close-to-best values on AMASS-BMLrub. The ablations attribute consistent small gains to DWT over DCT encoding and larger gains to Lucas polynomials over B-spline, Chebyshev, Legendre, and Hermite bases. The authors conclude

Load-bearing premise

The load-bearing premise is that the MPJPE values quoted from different papers in Tables 1 and 2 are directly comparable and that the 0.1-0.5 mm differences between LuKAN and SiMLPe are real effects rather than run-to-run noise, since no variance, seeds, or significance tests are provided.

Editorial extensions

If this is right

  • If LuKAN's numbers hold, KAN-based motion predictors become a credible lightweight baseline: the model matches the strongest MLP competitor while using far fewer parameters and a fraction of the compute.
  • Encoding motion in the wavelet domain separates fast joint movements from slow postural drift, so the model can refine high-frequency detail without diffusing it away — the property the authors cite against MotionWavelet.
  • Lucas polynomials' linear recurrence keeps the learnable activations cheap to evaluate, which is what allows a 48-block temporal learner to stay small enough for an 8 GB GPU.
  • The practical gap over SiMLPe is small (0.1-0.2 mm at 720-1000 ms on Human3.6M), so the contribution is better read as competitive accuracy at lower cost than as a large accuracy jump.

Reading between the lines

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

  • Because no variance or significance tests are reported, this review's inference is that the head-to-head with SiMLPe should be read as statistical parity until multi-seed results appear; the architecture's value would then be efficiency, not accuracy.
  • The paper's own supplementary discussion (Section F) concedes that robustness on large-scale noisy or incomplete motion data and real-time suitability are untested; that concession narrows the efficiency claim to the evaluated benchmarks.
  • The Table 4 ablation suggests the polynomial basis, not the wavelet encoding, drives most of the gain: Lucas over B-spline is 2.8 mm at 320 ms, while DWT over DCT is 0.4 mm in the same setting.
  • The same recipe — DWT, polynomial KAN, IDWT — is a generic learned filter-bank forecaster; transferring it to vehicle trajectories or physiological signals would be a natural test the paper does not attempt.
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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

6 major / 6 minor

Summary. The paper proposes LuKAN, a Kolmogorov-Arnold Network architecture for 3D human motion prediction. The model applies a discrete wavelet transform (DWT) to the input motion sequence, projects the coefficients into an embedding space, processes them with B blocks of a KAN layer whose activations are Lucas polynomials, and reconstructs the time-domain prediction via inverse DWT. Experiments on Human3.6M, AMASS-BMLrub, and 3DPW report MPJPE against several baselines, with ablations on temporal encoding, polynomial basis, and embedding dimension. The central claim is that LuKAN is competitive or superior to state-of-the-art methods while having significantly fewer parameters and lower computational cost. Code is provided.

Significance. If the performance and efficiency claims survive scrutiny, LuKAN is a plausible lightweight KAN-based baseline for 3D motion prediction. The architecture is simple, the ablation covers relevant design choices, and the public code is a practical asset. However, the empirical support is currently fragile: the reported accuracy advantages over the strongest baseline are mostly in the 0.1–0.5 mm range with no uncertainty quantification, and the efficiency claim is not measured. The paper is best viewed as a promising empirical study whose claims need to be tightened before publication.

major comments (6)
  1. [Section 4.2, Tables 1 and 2] The claim of 'consistently lower' MPJPE and 'superior' performance is not supported at the reported precision. On Human3.6M, LuKAN's advantage over SiMLPe is 0.1–0.4 mm (e.g., 89.9 vs 90.1 mm at 720 ms; 109.3 vs 109.4 mm at 1000 ms). On AMASS-BMLrub, LuKAN is worse than SiMLPe at every horizon from 320 ms to 1000 ms (e.g., 57.6 vs 57.3 at 720 ms; 66.4 vs 65.7 at 1000 ms). No variance, number of runs, or significance tests are reported, and the baselines are not rerun under identical conditions. These gaps are likely within run-to-run noise. Please report mean ± std over multiple seeds and either demonstrate statistical significance or soften the conclusion to 'competitive'.
  2. [Section 4.3, Table 3] The ablation text states that DWT 'demonstrates consistent improvements over DCT across all datasets,' but the same table shows DWT worse than DCT on Human3.6M at 160 ms (21.5 vs 21.4), 320 ms (46.2 vs 45.8), and 400 ms (57.2 vs 56.8). This internal inconsistency directly weakens the paper's motivation for DWT. The claim should be revised to acknowledge that DWT is favorably comparable or better on most settings but not uniformly consistent, or the experiments need to be rerun with error bars to establish consistency.
  3. [Section 4.4 and Conclusion] The computational-efficiency claim ('significantly fewer parameters and lower computational cost') is not substantiated by measurements. The complexity analysis is asymptotic only, and no parameter count, FLOPs, inference time, or throughput is reported for LuKAN or any baseline. The supplementary Figure 3 is a qualitative scatter plot without numerical parameter counts. Please provide actual measured parameter counts and runtime comparisons under a consistent protocol.
  4. [Section 3.3 and Section 4.4, Eqs. (5), (7)] The complexity formulas need dimension bookkeeping. Equation (7) operates on an (La + Ld) × D tensor, and the KAN layer is described as applied along the temporal dimension. However, Section 4.4 reports time complexity O(BDRL^2) and parameter complexity O(BRL^2). These formulas imply the KAN weights are shared across the D embedding channels, but sharing is not stated in Eq. (5). If the KAN weights are not shared, the parameter complexity is O(BD R L^2), not O(BR L^2). Please clarify the sharing pattern and recompute the complexity accordingly.
  5. [Supplementary Table 6 and Section 4.1] The embedding dimension D=200 is selected as the best performer on Human3.6M, but the paper does not state whether this is a validation or test split. If D is chosen from the same test table used to report final results, the reported MPJPE is optimistically biased. Similarly, B=48 is fixed without a sensitivity study. Please clarify the hyperparameter selection procedure or perform selection on a validation split.
  6. [Section 4.3, Table 4] The claim that Lucas polynomials yield 'significant improvements' over other polynomial bases is largely supported by sub-millimeter differences against the next-best basis, Hermite (e.g., 46.2 vs 46.3 mm at 320 ms; 57.2 vs 57.3 mm at 400 ms; 109.3 vs 110.1 mm at 1000 ms). With single-run MPJPE, these gaps are not distinguishable from noise. Please report variance or significance tests, and temper the language unless the advantage is statistically robust.
minor comments (6)
  1. [Supplementary Section F] The Limitations paragraph explicitly states that robustness on large-scale and noisy motion data requires further investigation. This should be reflected in the abstract/conclusion, which currently overstates generality.
  2. [Section 3.3] Typo: 'In it important to mention' should be 'It is important to mention'.
  3. [Section 4.2] Typo: 'test it on on the AMASS-BMLrub' has a duplicated 'on'.
  4. [Figure 3 (supplementary)] Axis labels contain 'uni00A0' unicode artifacts. Also, the plotted parameter counts for each method should be given numerically in the text or caption.
  5. [Full text] There are duplicated paragraphs and repeated Figure 2 instances in the main body; the final version should be cleaned.
  6. [References] Reference [26] has 'Maching Learning' instead of 'Machine Learning'; reference [9] has 'Fenga' rather than 'Feng'; the title in [25] should be in sentence case.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: LuKAN is an empirical architecture paper whose claims rest on test-set MPJPE comparisons, not on equations fitted to the target result or on load-bearing self-citation.

full rationale

The paper's chain is architectural construction plus empirical evaluation, not a derivation whose output equals an input by construction. The KAN layer is defined by a learnable combination of Lucas polynomials (Eq. 5) whose recurrence is cited to an external source [25]; the DWT/IDWT pair (Eqs. 2-3) is an invertible transform applied to input trajectories, and the spatial projections (Eqs. 4, 8) are learned linear maps trained with the loss in Eq. 10 on standard training splits. Predictions are then evaluated on held-out test data (Human3.6M S5, AMASS-BMLrub, 3DPW), so the reported MPJPE values are not fitted quantities renamed as predictions. Hyperparameter choices such as embedding dimension D=200 and number of blocks B=48 are selected via ablations on the same benchmarks; this is model selection, not definitional circularity, and the paper does not present those choices as independent predictions. No load-bearing self-citation appears: the cited Kolmogorov-Arnold theorem, KAN papers, and Lucas polynomial recurrence are all external prior work, and no uniqueness theorem from the authors is invoked to force the architecture. The strongest concern—that the advantage over SiMLPe is often 0.1-0.4 mm without variance or significance tests, and that Table 3's DWT-vs-DCT comparison is not consistently better on Human3.6M short horizons—is a statistical robustness and reporting concern, not a circularity concern. The supplementary limitation statement that robustness on large-scale, noisy, or incomplete data 'requires further investigation' also acknowledges an empirical gap rather than a circular step. Therefore no circular step can be quoted or reduced to the paper's own inputs, and the honest finding is no significant circularity.

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

Central claim rests on architecture hyperparameters and standard signal-processing assumptions, not on new physical entities. The most notable unstated choices are D=200 and B=48, plus the unreported polynomial degree R. No independent benchmarks are used outside the paper's own experiments.

free parameters (5)
  • embedding dimension D = 200
    Spatial projection width; selected by ablation on Human3.6M (Table 6) using test-set MPJPE.
  • Lucas polynomial degree R = not reported
    Defined in Eq. (5) and used in complexity O(BDRL^2), but its value is not stated anywhere.
  • number of temporal blocks B = 48
    Set in implementation details; no ablation in main text.
  • wavelet type and decomposition levels = Daubechies 4, 3 levels
    Chosen transform configuration; no sensitivity analysis.
  • pose and velocity loss balance = 1.0
    Eq. (10) sums pose and velocity L2 terms with equal weight; no tuning reported.
assumptions (4)
  • domain assumption Kolmogorov-Arnold representation theorem applies to the motion-prediction functions being approximated
    Invoked in Section 3 to motivate KANs; the theorem is about exact representation, not learnability with Lucas polynomials on this data.
  • domain assumption Lucas polynomials form a sufficiently expressive basis for the needed univariate functions
    Eq. (5) assumes each edge function is a finite weighted sum of Lucas polynomials; convergence for motion trajectories is not analyzed.
  • standard math DWT followed by IDWT reconstructs the trajectory after coefficient modification
    DWT/IDWT is invertible for unmodified coefficients with proper boundary handling, but the network modifies coefficients and boundary effects are not discussed (Section 3.1).
  • domain assumption Joint indices are consistently aligned across Human3.6M (22 joints), AMASS (23), and 3DPW (18) under the standard protocol
    The model fixes K=3J and evaluates across datasets with different J; alignment is delegated to protocol [22] (Section 4.1).

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Cite this review

Pith. "Pith review of LuKAN: A Kolmogorov-Arnold Network Framework for 3D Human Motion Prediction." pith.science (2026). https://pith.science/paper/UXYKMMPH

@misc{pith2026250804847,
  author       = {Pith},
  title        = {Pith review of: LuKAN: A Kolmogorov-Arnold Network Framework for 3D Human Motion Prediction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UXYKMMPH}},
  note         = {Machine review of arXiv:2508.04847}
}
read the original abstract

The goal of 3D human motion prediction is to forecast future 3D poses of the human body based on historical motion data. Existing methods often face limitations in achieving a balance between prediction accuracy and computational efficiency. In this paper, we present LuKAN, an effective model based on Kolmogorov-Arnold Networks (KANs) with Lucas polynomial activations. Our model first applies the discrete wavelet transform to encode temporal information in the input motion sequence. Then, a spatial projection layer is used to capture inter-joint dependencies, ensuring structural consistency of the human body. At the core of LuKAN is the Temporal Dependency Learner, which employs a KAN layer parameterized by Lucas polynomials for efficient function approximation. These polynomials provide computational efficiency and an enhanced capability to handle oscillatory behaviors. Finally, the inverse discrete wavelet transform reconstructs motion sequences in the time domain, generating temporally coherent predictions. Extensive experiments on three benchmark datasets demonstrate the competitive performance of our model compared to strong baselines, as evidenced by both quantitative and qualitative evaluations. Moreover, its compact architecture coupled with the linear recurrence of Lucas polynomials, ensures computational efficiency.

Figures

Figures reproduced from arXiv: 2508.04847 by the authors.

Figure 1
Figure 1. Overview of Model Architecture. LuKAN processes input 3D motion data by applying DWT to encode temporal information. A spatial projection is applied both before and after the Temporal Dependency Learner block (repeated B times). Each block consists of a KAN layer, LayerNorm, and a residual skip connection. The inverse DWT (IDWT) reconstructs the motion in the time domain, outputting a sequence of predicted 3D poses.… view at source ↗
Figure 2
Figure 2. Visual comparison results of our model and the SiMLPe baseline on two ac￾tions: Directions (top) and Eating (bottom). Predicted poses from our model are depicted in red and blue, while those from SiMLPe are shown in yellow and green. Ground truth poses, represented by dashed lines, are overlaid with the predictions to highlight deviations [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Comparison of performance and model complexity. Our model is bench￾marked against state-of-the-art methods, including LTD [21], Hisrep [22], MSR-GCN [6], ST-DGCN [19], CIST-GCN [24], MotionMixer [3], and SiMLPe [11]. Performance is as￾sessed using the Mean Per Joint Position Error (MPJPE), where lower values indicate supe￾rior prediction performance. All evaluations are performed on the Human3.6M dataset. D Experime… view at source ↗

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