{"id":"86585cc0-021d-4d50-a1cd-fd12cc33a8aa","arxiv_id":"2508.04847","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"LuKAN matches state-of-the-art 3D human motion prediction accuracy using a KAN with Lucas polynomial activations and wavelet encoding, with marginal measured gains.","lead":"A new model called LuKAN uses Kolmogorov-Arnold networks with Lucas polynomial functions and wavelet transforms to forecast 3D human poses from past motion. It matches the best existing predictors on standard benchmarks while staying compact, though the reported accuracy gains over the strongest baseline are very small.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Superiority claims rest on sub-noise MPJPE gaps: no repeated runs or significance tests, and the DWT ablation contradicts its own 'consistent improvement' text.","rationale":"The paper presents a coherent architecture and standard benchmark results, so the reader's conditional verdict is appropriate. The load-bearing assumption is that 0.1–0.5 mm differences are meaningful. That assumption fails because no uncertainty is reported and because the same protocol produces opposite-sign gaps on AMASS. The Table 3 inconsistency reinforces the concern: the DWT contribution is claimed to be consistently better while the reported numbers show it worse at several short horizons on Human3.6M. A multi-seed rerun with paired tests is the minimal check that separates 'superior' from 'competitive.' If the gaps vanish, the paper's central claim should be softened, but the architecture could still merit publication as an efficient baseline.","tokens_in":18965,"tokens_out":8642,"duration_ms":94716,"concrete_test":"Re-run LuKAN and SiMLPe on Human3.6M, AMASS-BMLrub, and 3DPW under the paper's protocol with at least 5 seeds; report mean±std MPJPE per horizon and a paired significance test (Wilcoxon signed-rank on per-sequence errors) for LuKAN vs SiMLPe. Independently re-run the DWT vs DCT ablation (Table 3) with the same seeds and check whether the claim 'DWT consistently outperforms DCT' holds for all horizons on Human3.6M. If the 720/1000 ms gaps are within one standard deviation or p>0.05, revise the conclusion to 'competitive' and correct the Table 3 narrative.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim of 'competitive or superior ... with significantly fewer parameters' depends on the reported MPJPE gaps being real and stable. They are not demonstrably so. LuKAN's advantages over SiMLPe on Human3.6M are 0.1–0.4 mm (e.g., 109.3 vs 109.4 mm at 1000 ms; 89.9 vs 90.1 mm at 720 ms), and on 3DPW it ties or edges ahead by 0.1–0.2 mm. On AMASS-BMLrub, LuKAN is worse than SiMLPe at 320–1000 ms (34.4 vs 34.3, 40.8 vs 40.5, 50.9 vs 50.5, 57.6 vs 57.3, 62.7 vs 62.4, 66.4 vs 65.7). No variance, seeds, or significance tests are reported, and the baselines are not rerun under identical conditions. The ablation evidence is also internally inconsistent: Table 3's text says DWT 'demonstrates consistent improvements over DCT across all datasets,' but on Human3.6M DWT is worse than DCT at 160 ms (21.5 vs 21.4), 320 ms (46.2 vs 45.8), and 400 ms (57.2 vs 56.8). If these sub-millimeter differences are seed noise, the conclusion collapses from 'superior' to 'competitive,' and the DWT/Lucas-specific advantages lose support. The architecture may still be a useful efficient baseline, but the paper's own numbers do not yet establish the stronger claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":19365,"tokens_out":6793,"duration_ms":74934,"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":[{"comment":"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'.","section":"Section 4.2, Tables 1 and 2"},{"comment":"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.","section":"Section 4.3, Table 3"},{"comment":"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.","section":"Section 4.4 and Conclusion"},{"comment":"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.","section":"Section 3.3 and Section 4.4, Eqs. (5), (7)"},{"comment":"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.","section":"Supplementary Table 6 and Section 4.1"},{"comment":"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.","section":"Section 4.3, Table 4"}],"minor_comments":[{"comment":"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.","section":"Supplementary Section F"},{"comment":"Typo: 'In it important to mention' should be 'It is important to mention'.","section":"Section 3.3"},{"comment":"Typo: 'test it on on the AMASS-BMLrub' has a duplicated 'on'.","section":"Section 4.2"},{"comment":"Axis labels contain 'uni00A0' unicode artifacts. Also, the plotted parameter counts for each method should be given numerically in the text or caption.","section":"Figure 3 (supplementary)"},{"comment":"There are duplicated paragraphs and repeated Figure 2 instances in the main body; the final version should be cleaned.","section":"Full text"},{"comment":"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.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The reported effect sizes are very small, and the paper does not provide multiple-seed variance or runtime measurements. I would not publish the current claims as 'superior' or 'significantly fewer parameters' without those data. The architecture is plausible and the direction is publishable after the requested revisions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read the paper over the weekend. The architecture work is solid: a KAN layer with Lucas polynomial activations, DWT temporal encoding, two spatial projections, and residual blocks. As far as I know, that exact combination is new, and the ablations on polynomial bases and DWT vs. DCT are genuinely informative. The model is also simple and plausible as an efficient baseline. I give them credit for that.\n\nNow the soft spots, and they're load-bearing. Every claim of superiority over SiMLPe rests on differences of 0.1–0.4 mm on Human3.6M and 3DPW, and on AMASS-BMLrub LuKAN is actually worse than SiMLPe at every horizon from 320 to 1000 ms. They report single runs, no variance, no significance tests, and they don't rerun baselines under identical conditions. A 0.1 mm gap on MPJPE is within run-to-run noise on these benchmarks. The conclusion's phrase \"competitive or superior\" is defensible; \"superior\" is not.\n\nThe DWT ablation has an internal contradiction. The text says DWT \"demonstrates consistent improvements over DCT across all datasets,\" but Table 3 shows DWT worse than DCT on Human3.6M at 160, 320, and 400 ms. The AMASS and 3DPW results favor DWT, so the overall choice may still be right, but the claim as written is false.\n\nThe efficiency claims are also unmeasured. The complexity analysis is only big-O notation, and parameter counts are shown in a scatter plot with no actual numbers or wall-clock times. With B=48 blocks and D=200, I'd like to see a runtime table before accepting \"significantly fewer parameters and lower computational cost.\" Also, the best embedding dimension D=200 is selected from a sweep on the test set; that's a mild form of test-set adaptation, not fatal, but worth disclosing.\n\nOne more thing: the paper has clear production issues, including duplicated paragraphs in the supplementary and repeated figure blocks in the main text. That doesn't change the science, but it signals a rushed submission.\n\nIf they add variance over multiple seeds, rerun SiMLPe and maybe one or two other baselines under the same protocol, and tone down the language, this could be a useful subfield contribution. The competitive claim is plausible; the superior claim isn't supported. I'd send it for review because the architecture and ablations deserve referee attention, but I'd expect major revision.","headline":"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.","tokens_in":19828,"tokens_out":1876,"would_cite":false,"duration_ms":23493,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["3D human motion prediction","Kolmogorov-Arnold networks","Lucas polynomials","discrete wavelet transform","MPJPE","pose forecasting","efficient architectures","temporal modeling"],"falsifier":"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.","tokens_in":18867,"feed_emoji":"🏃","tokens_out":11589,"duration_ms":119327,"temperature":0.7,"pith_summary":"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.","feed_headline":"Lucas-wavelet KAN matches 3D motion baselines with fewer parameters","feed_subtitle":"DWT and Lucas polynomials replace heavy transformer blocks in a compact pose forecaster tested on three benchmarks","key_machinery":"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.","core_discovery":"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","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Defines the KAN layer with learnable edge functions that LuKAN adapts, replacing spline functions with Lucas polynomials.","marker":"[18]"},{"why":"Presents SiMLPe, the MLP baseline that LuKAN compares against and reports slightly lower MPJPE on Human3.6M.","marker":"[11]"},{"why":"Introduces the DCT-based trajectory-dependency network that motivates the frequency-encoding branch and supplies baselines.","marker":"[21]"},{"why":"Provides the motion-attention baseline and the evaluation protocol used for AMASS and 3DPW splits.","marker":"[22]"},{"why":"MotionWavelet, the wavelet-based diffusion predictor LuKAN contrasts with for retaining high-frequency detail.","marker":"[9]"},{"why":"Supplies the Lucas polynomial recurrence used for cheap evaluation of the KAN activations.","marker":"[25]"},{"why":"Analyzes expressiveness and spectral bias of KANs, the motivation for replacing MLP cores with KAN layers.","marker":"[30]"},{"why":"Human3.6M dataset used for the main short- and long-term MPJPE comparisons.","marker":"[12]"},{"why":"AMASS dataset used for training and the BMLrub test evaluation.","marker":"[20]"},{"why":"3DPW dataset used to test generalization from AMASS-trained models.","marker":"[29]"}],"fun_headline_variants":["Lucas-wavelet KAN matches 3D pose baselines in leaner model","KAN with Lucas polynomials achieves top MPJPE on Human3.6M","DWT and Lucas-KAN: efficient 3D motion forecaster","Lean Lucas-KAN rivals larger 3D pose models","Wavelet-encoded Lucas polynomials for compact 3D pose prediction"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Lucas-wavelet KAN matches 3D pose baselines in leaner model","KAN with Lucas polynomials achieves top MPJPE on Human3.6M","DWT and Lucas-KAN: efficient 3D motion forecaster","Lean Lucas-KAN rivals larger 3D pose models","Wavelet-encoded Lucas polynomials for compact 3D pose prediction"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001072,"raw_usage":{"total_tokens":4334,"prompt_tokens":763,"completion_tokens":3571,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":507,"completion_tokens_details":{"reasoning_tokens":3474}},"tokens_in":507,"tokens_out":3571,"duration_ms":36354,"temperature":1.0,"reasoning_tokens":3474,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T23:43:43.041643+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}