{"id":"66e317b7-d148-4f04-b7e2-4a8e8aec40aa","arxiv_id":"2509.09147","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"JFRFFNet learns the transform orders and filter weights of a joint time-vertex fractional Fourier transform from clean/noisy training pairs, reporting higher output SNR than ten graph baselines on eight datasets.","lead":"This paper trains a neural network built from fractional Fourier transforms on a graph, learning both the transform angles and a filter mask to denoise time-varying graph signals. It reports a few decibels of output SNR improvement over several graph filter and graph network baselines on eight datasets.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Post-hoc selection of the best graph-shift matrix undermines the reported SNR ranking; a validation-based or averaged matrix protocol is needed.","rationale":"The paper's central claim has two components: (i) partial-prior-information denoising and (ii) significant SNR improvements. Component (ii) is the one with quantitative support, and it rests on a comparison protocol that currently selects the best-performing graph-shift matrix per method after seeing test results. That is a multiple-comparison problem: five matrices are tried and the best is reported, so the 'first/second' ranking is an upper envelope, not a stable property. The reader's weakest assumption about clean training data is worth flagging, but it is a terminology/framing issue: Section III-B explicitly discloses clean/noisy training pairs, so the reader can judge the claim. The matrix-selection issue is not disclosed as a limitation and directly affects the validity of every SNR number in Table I. The proposed fix—one fixed matrix or validation-based selection, with error bars—would settle it. This does not change the conditional verdict, since the architecture and math appear coherent and the concerns are addressable.","tokens_in":12064,"tokens_out":8331,"duration_ms":106888,"concrete_test":"Fix the graph-shift matrix to the combinatorial Laplacian for all methods, or select the matrix on the validation split before evaluating on test, and rerun the full Table II comparison with 5 random seeds, reporting mean±std. If JFRFFNet is not first on at least 5 of 8 datasets under this protocol, the reported improvements are attributable to matrix cherry-picking rather than the JFRFT-Wiener architecture.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The strongest quantitative claim is 'best in five datasets, second in three' (Section IV-B), but Table I is built from the best-performing matrix independently for each method ('we present the denoising results for the best-performing matrix'), with different matrices selected for different methods (e.g., lap vs. sna on SST). This is ex-post test-set selection over five graph-shift operators, so the reported margin over GFRFFNet and the ten baselines is the maximum over a family of models rather than the performance of a fixed algorithm. No error bars are reported, so 1–3 dB differences in Table I cannot be assessed for significance. The 'partial prior information' framing in the Abstract is also loose—training uses clean/noisy pairs, not partial statistics—but the matrix-selection issue is the more direct threat to the paper's central performance claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes JFRFFNet, a graph signal denoising method that embeds the joint time-vertex fractional Fourier transform (JFRFT) into a neural network. The transform order pair (α, β) and an element-wise filter matrix H are treated as learnable parameters and updated by backpropagation, while the network itself is structured as JFRFT-domain filtering followed by inverse JFRFT. The method is evaluated on eight real-world time-varying graph datasets and compared with GFRFFNet and ten graph neural network baselines. The authors claim that JFRFFNet significantly improves output SNR and that the approach works with only partial prior information.","tokens_in":12256,"tokens_out":3830,"duration_ms":48290,"significance":"If the performance claims are validated, the proposed architecture would be a useful, interpretable addition to graph signal denoising, particularly because it jointly captures spatial and temporal features through a fractional transform. The main strengths are the explicit formulation of the trainable JFRFT layer, the gradient updates (Eqs. (7)–(8)), and the application to multiple real datasets. However, the evaluation protocol currently does not support the central claims: the reported results are obtained by post-hoc selection of the best graph-shift matrix per dataset, no error bars or significance tests are given, and the 'partial prior information' claim is contradicted by the use of clean/noisy training pairs. These issues are load-bearing for the paper's headline conclusions.","major_comments":[{"comment":"The reported ranking is obtained by selecting, for each method and dataset, the best result among five graph-shift matrices ('we present the denoising results for the best-performing matrix'). This is ex-post test-set selection over a family of models, not the performance of a fixed algorithm. The margins over GFRFFNet and other baselines are therefore maxima over five choices of graph-shift operator, which undermines the claim of 'best in five datasets, second in three'. Please report the full matrix sweep with a fixed selection rule (e.g., validation-based selection), averaged results over matrices, or all per-matrix results. Also specify why the METR adjacency results were discarded.","section":"Section IV-B / Table I"},{"comment":"The Abstract and Conclusion claim that JFRFFNet enables denoising with 'only partial prior information', but Section III-B states that 'The training and validation sets contain both clean and noisy signals'. The loss is MSE against clean signals, so the method requires clean training data. This is not the partial-prior scenario motivated in the Introduction, where complete signal/noise statistics are unavailable. The claim is therefore structurally unsupported. Please either reframe the contribution as supervised denoising, or provide an experiment in which only partial/statistical prior information is available (e.g., training on noisy targets or using known signal/noise statistics).","section":"Section III-B / Abstract"},{"comment":"The experimental protocol is under-specified: no noise type, noise construction, number of independent runs, standard deviations, or significance tests are reported. Table I gives single SNR values, so the claimed 'significant improvements' (Abstract) cannot be assessed. This is particularly important because many reported differences are 1–3 dB, which may be within run-to-run variability. Please add error bars, significance tests, and a detailed description of the noise-injection procedure.","section":"Section IV-A"}],"minor_comments":[{"comment":"There are typos and grammatical issues, e.g., 'acheives' in the Conclusion. The paper would benefit from careful proofreading.","section":"General"},{"comment":"Table I is very hard to read: multiple rows per dataset are merged into a single line, making it difficult to identify which SNR level corresponds to which baseline. Please reformat the table with clear row separation.","section":"Table I"},{"comment":"The symbol D is used both for the temporal feature dimension (e.g., D in X ∈ R^{N×D}) and for the differentiation operator in the hyper-differential definitions (D^2). This is confusing; please use different notation for the operator.","section":"Equations (1) and (3)"},{"comment":"The relationship between the vectorized gradient update in Eqs. (7)–(8) and the actual forward computation X_1 = F_G^α X (F^β)^⊤ should be spelled out explicitly, including the vectorization convention and how the filter matrix H is initialized and updated. This would improve reproducibility.","section":"Section III-B"},{"comment":"Reference [15] is the authors' own prior work and is central to the JFRFT layer. The letter should clearly state what is new relative to [15] and provide a more explicit comparison, since the current text reads as an application of that work.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The core trainable JFRFT layer and its gradients are taken almost directly from the authors' prior work [15] and from [13]–[14]. The incremental contribution appears to be the application to denoising plus the learnable filter matrix, but the novelty statement is vague. The editor should ask for a clear delineation of what is new in this letter. Additionally, the evaluation protocol with per-dataset best-matrix selection and discarded METR results would need independent validation before the performance claims can be trusted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: JFRFFNet is a sensible combination of a trainable JFRFT layer with a learnable spectral mask for graph signal denoising. The math checks out and the idea is coherent, but the headline performance ranking is weaker than it looks because the best graph matrix is chosen after seeing test results, and the 'partial prior information' framing overstates what the method needs.\n\nWhat's genuinely new is the specific architecture: embedding the JFRFT layer from their prior work [15] into a supervised denoiser with learnable filter coefficients, and showing it beats GFRFFNet and several GNN baselines on eight real datasets. The forward pass and gradient updates are consistent with the JFRFT definition; the paper is honest about the eigendecomposition cost and gives results for multiple graph shift operators in Fig. 2. That is a legitimate, if small, contribution.\n\nThe main problem is Table I. Results are reported for the best-performing matrix per method per dataset, chosen ex post. Since the matrix choice is part of the model, the reported SNR is the maximum over five variants, not the performance of a fixed algorithm. The margin over baselines is usually 1–3 dB, and with no error bars or significance tests, that margin may not be meaningful. The discarded METR adjacency results are reported, which is good, but the protocol for picking the 'best' matrix isn't validated on a hold-out split. Also, the 'partial prior information' claim is loose: the training and validation sets contain clean/noisy pairs, which means you need clean signals to train. That's not 'partial' in the sense motivated in the introduction.\n\nOne more minor point: the paper relies heavily on the authors' own prior work for the trainable layer, but that's not a flaw by itself since [15] is the natural source. The delta over their own GFRFFNet is the real empirical claim, and it seems plausible.\n\nWho this is for: researchers in graph signal processing who care about learned fractional Fourier denoisers. It deserves a serious referee; the idea is not broken and the issues are addressable with error bars, a fixed matrix protocol, and clearer framing. I'd ask for revisions before accepting.","headline":"A coherent but incremental denoising architecture whose performance claims are undermined by post-hoc graph-matrix selection and a loose 'partial prior information' framing.","tokens_in":12763,"tokens_out":2270,"would_cite":false,"duration_ms":23620,"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":"JFRFFNet embeds a Wiener filter into a neural network and learns the transform order pair and filter coefficients by backpropagation, enabling denoising of time-varying graph signals with only partial prior information.","keywords":["graph signal denoising","joint time-vertex fractional Fourier transform","Wiener filter","learnable transform order","graph neural network","spatio-temporal signal processing","backpropagation","partial prior information"],"falsifier":"Train JFRFFNet on a dataset where the training set contains only noisy signals (no clean references) and measure the output SNR; if it fails to improve over the input SNR, the central claim of requiring only partial prior information is refuted. Additionally, the paper itself discards adjacency-based results on the METR dataset due to ill-conditioned eigendecomposition, so a dataset with such a matrix would break the method.","tokens_in":11930,"feed_emoji":"📡","tokens_out":4191,"duration_ms":45192,"temperature":0.7,"pith_summary":"The paper tries to establish that a classical model-based denoiser for time-varying graph signals—Wiener filtering in the joint time-vertex fractional Fourier (JFRFT) domain—can be turned into a trainable neural layer whose transform-order pair and filter coefficients are learned from data. If true, this would let practitioners denoise graph signals without knowing the signal and noise statistics in advance, needing only a modest set of clean/noisy training pairs. The central claim is that this data–model co-driven approach beats both the purely model-based Wiener filter and a graph neural network baseline across eight real-world datasets, ranking first or second in every case.","feed_headline":"Denoise graph signals with a learned fractional Wiener filter","feed_subtitle":"JFRFFNet learns transform orders and filter coefficients by backpropagation, ranking first or second on all eight test datasets.","key_machinery":"The JFRFT matrix F^{α,β}_J = F^β ⊗ F^α_G, the Kronecker product of the discrete fractional Fourier matrix and the graph fractional Fourier matrix, serves as the core trainable transform. The paper derives exact derivatives of this matrix with respect to the fractional orders α and β, making the transform a fully differentiable layer. The Wiener filter is then approximated by a learnable pointwise (Hadamard) filter matrix H in the JFRFT domain, and both the orders and H are updated by backpropagation through forward and inverse transforms.","core_discovery":"The central discovery is that the JFRFT-domain Wiener filter can be embedded as a differentiable layer, with the two transform orders (α, β) and the diagonal filter matrix as learnable parameters. Because the JFRFT matrix is defined through matrix exponentials of graph and temporal fractional Fourier operators, the paper derives exact derivatives of the layer with respect to α and β and uses them in gradient descent. This turns a filter that previously required complete prior knowledge of signal and noise covariances into a network that learns the right transform domain and filter shape from paired clean/noisy examples. Experiments show that this joint spatio-temporal learnable filter consis","pith_inferences":["The 'partial prior information' claim is narrower than it appears: the training set still needs clean reference signals, so the method exchanges analytic prior knowledge for labeled data. A true partial-information version would need a self-supervised or blind denoising loss, which the paper does not explore.","The three-layer stacking suggests that repeated application of the JFRFT filter in different fractional domains may act like a small learnable filter bank; testing with more layers or with shared versus per-layer orders would clarify what the network actually learns.","The O(N^3) eigendecomposition cost is the main computational bottleneck; replacing it with a fast approximate GFRFT could make the method practical for large graphs without changing the architecture.","The learned transform orders initialized at (0.5, 0.5) could be compared across datasets to see whether certain graph types prefer specific fractional domains, offering a diagnostic tool for graph signal structure."],"forward_implications":["On eight real-world time-varying graph datasets, JFRFFNet achieves higher output SNR than GFRFFNet and ten graph baselines, ranking first on five datasets and second on three.","The learned transform-order pair and filter coefficients replace the grid search and analytic covariance computations of classical JFRFT Wiener filtering, adapting to each graph and dataset.","Because the transform layer is fully differentiable, the architecture can be trained end-to-end with any differentiable loss, not just denoising objectives.","Joint learning of spatial (graph) and temporal (time series) features is shown to yield consistent gains over spatial-only filtering, demonstrating the value of the JFRFT domain.","The method requires only partial prior information in the sense that it uses the graph topology and a training set of clean/noisy pairs, rather than explicit noise statistics."],"fun_headline_variants":["Learn the transform order to denoise graph signals","Graph denoising via a learned fractional Wiener filter","Backprop through fractional Fourier for better graph denoising","Partial prior? JFRFFNet learns to denoise graph signals","Learn the right fractional domain for graph denoising"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The method needs a training set containing both clean and noisy versions of the signal; if only noisy signals are available, there is no supervision signal and the claimed 'partial prior information' advantage disappears.","fun_headline_variants_meta":{"raw":{"variants":["Learn the transform order to denoise graph signals","Graph denoising via a learned fractional Wiener filter","Backprop through fractional Fourier for better graph denoising","Partial prior? JFRFFNet learns to denoise graph signals","Learn the right fractional domain for graph denoising"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000799,"raw_usage":{"total_tokens":3314,"prompt_tokens":672,"completion_tokens":2642,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":416,"completion_tokens_details":{"reasoning_tokens":2563}},"tokens_in":416,"tokens_out":2642,"duration_ms":22123,"temperature":1.0,"reasoning_tokens":2563,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T19:35:08.464142+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train JFRFFNet on a dataset where the training set contains only noisy signals (no clean references) and measure the output SNR; if it fails to improve over the input SNR, the central claim of requiring only partial prior information is refuted. Additionally, the paper itself discards adjacency-based results on the METR dataset due to ill-conditioned eigendecomposition, so a dataset with such a matrix would break the method.","supporting_citations":[],"review_version":1}