{"id":"b9b67178-0125-48ca-8b47-0e4cd273afb4","arxiv_id":"2511.16111","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"A rotation-parameterized graph fractional Fourier transform that reduces exactly to the GFT at zero angle is defined, and its claimed denoising advantage rests on experiments that fit parameters to the clean test signal.","lead":"This paper introduces a graph-signal transform that combines two existing ideas—rotating the graph Fourier basis and applying a fractional power—and fixes a consistency bug where the rotation did not vanish at zero angle. The authors claim the new transform denoises time series, images, and point clouds better than its two predecessors, but their experiments tune the transform parameters on the very clean signals used for evaluation.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The denoising claim is unsupported: Algorithms 1–2 and Eq. (28) fit θ, α, κ, and H using the clean target x on the very signals used for evaluation.","rationale":"The reader's weakest assumption identifies exactly the same load-bearing concern: parameter and filter selection using the clean target x on the evaluation signals. The full-text Algorithms 1 and 2 and Eq. (28) make this explicit. Since the paper's stated significance is empirical superiority in denoising, and the only supporting evidence is in-sample training error, the central claim is not established. I agree with the reader's REJECT verdict for the empirical claim; the theoretical portion may be salvageable in revision but should not be accepted as supporting the abstract's performance claims. No additional concern is needed; the in-sample evaluation is sufficient and decisive. A held-out test, or at minimum a train/test split with the same protocol for all baselines, would settle the matter.","tokens_in":35216,"tokens_out":2842,"duration_ms":32495,"concrete_test":"Re-run the image and point-cloud experiments with a random 50/50 split of 8×8 blocks / local patches. On the training split, run Algorithm 2 (or the same grid search for small signals) using clean x_train to select H, θ, α, κ. Freeze these parameters, then evaluate MSE/PSNR/SSIM on the held-out test split (y_test, x_test). Apply the identical split and protocol to GFRFT and AGFT. If AGFRFT does not consistently beat the baselines on held-out test metrics, the claimed superiority is an in-sample fitting artifact. Report means and standard deviations over at least 5 random splits.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that RP-GFRFT/AGFRFT improves denoising over GFRFT, AGFT, and other baselines. For that claim to hold, the reported MSE/PSNR/SSIM must measure predictive performance on noisy signals whose clean target was not used to choose the parameters. The paper does not do this. Algorithm 1 takes y, x, G as input and selects (θ*, α*, H*) by minimizing MSE against x on the same y. Algorithm 2 does the same with gradient descent, optimizing L = ||F^{-1} H F y − x||^2 in Eq. (28), and the final parameters are selected by tracking the lowest training loss. Tables II–VI report metrics on exactly the same y and x used in that optimization. These are in-sample fitting losses, not denoising results. Because AGFRFT has additional free parameters (θ, κ) relative to GFRFT and AGFT, improved in-sample fit is expected even if the transform has no real denoising advantage. The abstract's claimed empirical superiority is therefore not supported by the experiments. The theoretical construction—degeneracy-friendly rotation and unitary variants—may be salvageable, but the significance stated in the abstract rests on the empirical claim, which collapses without held-out evaluation. Missing error bars, absent code/data, and the RP-GFRFT/AGFRFT naming inconsistency are secondary; the in-sample protocol is the load-bearing issue.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a graph spectral transform that combines the graph fractional Fourier transform (GFRFT) with a rotation of the graph Fourier basis, called RP-GFRFT in the arXiv title and AGFRFT in the body. The construction uses a recursively defined, degeneracy-friendly rotation family that reduces to the identity at zero angle, plus two variants (Type I and Type II) whose unitarity, reduction, index-additivity, and invertibility properties are stated with proofs in the appendices. The authors then propose grid-search and gradient-descent algorithms to jointly optimize the fractional order, rotation angle, rotation scale, and a Wiener filter by minimizing the MSE between the filtered output and the clean signal. Experiments on time series, images, and point clouds report improved MSE/PSNR/SSIM over GFRFT, AGFT, and other baselines.","tokens_in":35562,"tokens_out":10123,"duration_ms":107403,"significance":"The theoretical construction is plausible and the degeneracy property is a genuine improvement over the existing AGFT construction, provided the proofs in Appendices A–C are accepted. The properties stated (orthogonality, exact reduction at θ=0, unitarity, invertibility) are natural and useful for a parameterized graph spectral transform. However, the paper's significance as stated in the abstract rests on the empirical claim of improved denoising, and that claim is not supported by the reported protocol: the clean signal is used to select the transform parameters and the filter on the same signals used for evaluation. The reported numbers are therefore in-sample fitting results, not predictive denoising performance. The lack of code, data, error bars, and held-out evaluation further weakens the empirical contribution.","major_comments":[{"comment":"The empirical validation is circular. Algorithm 1 (lines 1, 10) and Algorithm 2 (lines 1, 8) take the clean signal x as an input and select θ, α, κ, H by minimizing ||F^{-1}HF y − x||^2 on the same y that is later evaluated. Eq. (26) and Eq. (28) formalize this in-sample objective. Tables II–VI report MSE/PSNR/SSIM on exactly these fitted signals. Because AGFRFT contains additional free parameters (θ, κ) relative to GFRFT/AGFT, lower in-sample error is a guaranteed artifact of the extra flexibility, not evidence of better denoising. A valid experiment must fix parameters on training data (or use cross-validation) and report performance on held-out noisy signals with multiple noise realizations and error bars.","section":"§IV-A, §IV-B, Eq. (26)-(28), Algorithms 1-2, Tables II-VI"},{"comment":"As written, the optimization admits a trivial zero-loss solution. For any fixed unitary F=F_{θ,α,κ}, the diagonal choice H_ii=(Fx)_i/(Fy)_i for all i with (Fy)_i≠0 achieves F^{-1}HF y=x exactly. The paper does not restrict H to a parametric Wiener form or otherwise regularize the optimization, so the reported nonzero MSE values in Tables V–VI are inconsistent with the stated objective unless an omitted constraint was used. This under-specification further undermines the experimental section and needs to be clarified.","section":"§IV-B, Eq. (28), Algorithm 2"}],"minor_comments":[{"comment":"The arXiv title and the supplied abstract refer to 'RP-GFRFT', while the manuscript header, full-text abstract, and body consistently use 'AGFRFT'. This naming inconsistency must be resolved before any revision.","section":"Title/Abstract/§I"},{"comment":"The claim that yaw/pitch/roll families remain distinct is asserted from the sparsity patterns of J_axis but not actually proved. Distinct generators do not automatically imply distinct matrix families after multiplication by blkdiag and S_M. Please provide a proof or state this as an explicit assumption.","section":"Appendix B, Theorem 1(4)"},{"comment":"The tables are extremely dense and use combined cells for multiple σ values, which makes them difficult to read. Consider splitting them or using a clearer layout. Also, Table V contains a suspicious non-monotonicity (GFRFT Parrot σ=30 PSNR 48.330 > σ=20 PSNR 46.183) that should be checked.","section":"Tables II-IV"},{"comment":"No code or data availability statement is provided, and no error bars or number of noise realizations are reported. This is important for assessing the stability of the claimed improvements.","section":"§V"},{"comment":"The definition of J_roll states i,j=1,...,N−1 but the matrix is claimed to be N×N; clarify how the last row and column are defined.","section":"§III-B"}],"recommendation":"reject","confidential_remarks":"The central theoretical construction may be salvageable, but the empirical claim is load-bearing and the current protocol is in-sample fitting. A full experimental rework with held-out data would be needed; this goes beyond a minor revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First things first: if you only skim one thing, know that the denoising comparison in this paper does not measure what it claims. Algorithms 1 and 2 take the clean signal x as an input and choose θ, α, κ, and the filter H by minimizing MSE against x on the same signals that later appear in Tables II–VI. Those tables are therefore reporting training loss, not predictive denoising performance. Since AGFRFT adds parameters over GFRFT and AGFT, its better in-sample numbers are expected even if the transform has no real denoising advantage. That is the load-bearing flaw.\n\nNow the legitimate part. The paper constructs a family of rotation matrices that reduce exactly to the identity at zero angle, fixing a real defect in the recursive AGFT constructions. It then combines that with fractional powers to define two unitary transforms, and proves the expected properties—reduction, invertibility, smoothness. The proofs are short but standard; I did not spot a gap in the core algebra. As a theoretical addendum to GFRFT, it is a modest but real contribution.\n\nWhere the paper falls short, in order:\n\n1. The empirical protocol. I already called this; it is not a detail. Without held-out evaluation, the abstract's claim of improved denoising is unsupported.\n2. Minor but real: no code or data, no error bars, and a naming inconsistency (abstract says RP-GFRFT, the full text says AGFRFT). The table says \"Periodicity: Yes\" for the corrected AGFT without proof; that is small but should be fixed.\n3. The theory is not deep; the rotation family is a patch on existing constructions. That alone would not justify publication in a top venue, but it is enough for a workshop or a methods paper if the experiments are redone honestly.\n\nBottom line: the transform deserves a serious referee, and I would send it out, but the current empirical section should not be accepted as evidence. A revision with proper train/test splits, parameter selection on a validation set, and comparison against equally flexible baselines could make the denoising claim defensible. As it stands, I would not cite this version for the performance numbers.","headline":"The transform construction is coherent and the zero-angle fix is real, but the denoising results are training losses, not predictions.","tokens_in":36065,"tokens_out":2522,"would_cite":false,"duration_ms":26412,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["94A12","05C50","15A16"],"pacs":[],"model":"deepseek-v4-flash","headline":"A new graph spectral transform unifies fractional order and rotation angle by fixing the zero-angle degeneracy flaw of angular graph Fourier transforms.","keywords":["graph fractional Fourier transform","angular graph Fourier transform","rotation matrix family","degeneracy-friendly rotation","graph signal denoising","optimal filtering","unitary transform","parameter optimization"],"falsifier":"Split each denoising experiment into training and test signals: optimize (θ, α, κ, H) on one noisy-clean pair (or one subset) and evaluate on a held-out noisy observation. If the MSE advantage of AGFRFT over GFRFT and AGFT largely disappears on held-out signals, the claimed denoising superiority is an artifact of in-sample parameter fitting.","tokens_in":35036,"feed_emoji":"🔄","tokens_out":4173,"duration_ms":41958,"temperature":0.7,"pith_summary":"The paper proposes a graph Fourier transform that carries two dials at once: a fractional order α and a rotation angle θ of the spectral basis. Its central fix is a rotation matrix family that returns exactly the identity at θ=0, so the transform reduces to the plain graph fractional Fourier transform at zero angle—something existing angular graph Fourier transforms fail to do. On top of this degeneracy-friendly rotation family, the paper defines two variants (I-AGFRFT and II-AGFRFT), proves they are unitary, invertible, and smooth in both parameters, and uses the parameters as learnable degrees of freedom in an optimal filtering pipeline. Experiments on time series, images, and point clouds report lower MSE and higher PSNR/SSIM than GFRFT, AGFT, and baseline filters.","feed_headline":"One rotation family fixes zero-angle flaw in graph Fourier transforms","feed_subtitle":"The new AGFRFT reduces to GFT at zero angle and beats GFRFT and AGFT in denoising","key_machinery":"The degeneracy-friendly rotation matrix family in SO(N) is the central object. It is built recursively: for even N=2M the rotation is a product of a block-diagonal combination of the lower-dimensional rotation and its diamond double-flip, a block Givens rotation S_M(ϕ), and an exponential map exp(ϕJ) with axis-dependent skew-symmetric J. The diamond flip and the exponential perturbation make the family reduce to the identity at θ=0 while keeping yaw, pitch, and roll distinct in high dimensions; this exact reduction carries the paper's consistency claims.","core_discovery":"The central claim is that fractional order and angular rotation can be unified in one graph spectral transform without sacrificing theoretical consistency. The key is a recursively built rotation family R(θ) in SO(N) with R(0)=I_N, constructed from block Givens rotations, a 'diamond' double-flip, and axis-dependent skew-symmetric matrices fed through the matrix exponential. This guarantees exact reduction: at θ=0 the AGFRFT becomes GFRFT, and at α=1 it becomes a corrected AGFT. Two variants are defined—Type I as (F_θ)^α and Type II as F^α R(θ)^H—and the paper proves unitarity, reversibility, smooth parameter dependence, and (for Type I) index additivity. The paper then treats θ, α, and the f","pith_inferences":["Because the rotation family is built only from identity-preserving blocks, the same construction could be dropped into any GFRFT-based algorithm to add angular control without breaking its zero-angle behavior.","The reported superiority is measured by optimizing the filter and parameters on the very signals used for evaluation; a test on held-out noisy signals would be needed to confirm the gains are predictive rather than in-sample fitting.","The two variants trade off: Type I has cleaner algebraic structure, while Type II is simpler to implement but needs commutation for index additivity; applications needing fractional-order composition should prefer Type I.","The exponential-map perturbation could be explored as a general mechanism for parameterizing smooth families of graph filters with guaranteed identity reduction."],"forward_implications":["At zero rotation angle, AGFRFT reduces exactly to GFRFT, so any angular rotation is a true generalization rather than a different transform.","Type I AGFRFT inherits index additivity, letting fractional orders compose additively at fixed angle; Type II does not unless a commutation condition holds.","The transform is unitary and invertible for both variants, preserving energy and allowing exact reconstruction via negative fractional order.","The whole pipeline—rotation matrix, fractional matrix power, and filter—is differentiable in (θ, α, κ), enabling gradient-based joint optimization for large graphs.","Reported experiments show consistent MSE/PSNR/SSIM gains over GFRFT and AGFT on temporal, image, and point-cloud denoising."],"fun_headline_variants":["Zero-angle fix unites rotation and fractional order in graph transforms","Graph transform rotates eigenvectors, fixes fractional Fourier degeneracy","Rotation-parameterized graph transform: exact GFT at zero angle","New graph transform unifies fractional order and rotation, clears zero-angle bug","RP-GFRFT unifies rotation and fractional order, beats baselines in denoising"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The denoising evaluation optimizes the transform parameters and filter with the clean target signal in the loss on the same signals being evaluated, so the reported improvements over baselines are in-sample fitting results rather than demonstrated generalization to unseen noisy signals.","fun_headline_variants_meta":{"raw":{"variants":["Zero-angle fix unites rotation and fractional order in graph transforms","Graph transform rotates eigenvectors, fixes fractional Fourier degeneracy","Rotation-parameterized graph transform: exact GFT at zero angle","New graph transform unifies fractional order and rotation, clears zero-angle bug","RP-GFRFT unifies rotation and fractional order, beats baselines in denoising"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001363,"raw_usage":{"total_tokens":5399,"prompt_tokens":813,"completion_tokens":4586,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":557,"completion_tokens_details":{"reasoning_tokens":4507}},"tokens_in":557,"tokens_out":4586,"duration_ms":33407,"temperature":1.0,"reasoning_tokens":4507,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T21:12:18.571641+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Split each denoising experiment into training and test signals: optimize (θ, α, κ, H) on one noisy-clean pair (or one subset) and evaluate on a held-out noisy observation. If the MSE advantage of AGFRFT over GFRFT and AGFT largely disappears on held-out signals, the claimed denoising superiority is an artifact of in-sample parameter fitting.","supporting_citations":[],"review_version":1}