{"id":"221239ec-86cb-4d29-8e12-62a5566f70f8","arxiv_id":"2506.16602","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"SlepNet replaces graph Fourier harmonics with learned Slepian harmonics concentrated in learned subgraphs and reports classification and representation gains on fMRI and traffic data.","lead":"This paper introduces SlepNet, a graph neural network that learns which subgraphs matter and uses Slepian harmonics, signals concentrated in those subgraphs, to classify spatiotemporal data. The authors report accuracy gains over graph Fourier and wavelet baselines on fMRI and traffic datasets, though the reported gains are weakened by model selection on the test set.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Reported results are obtained by selecting the best epoch on the test set, so Table 1 does not measure generalization; the central outperformance claim is unsupported as reported.","rationale":"The paper's strongest claim is empirical: SlepNet outperforms conventional GNNs and graph signal processing constructs across five datasets. That claim is carried by Table 1. Appendix G explicitly says the reported model is the epoch with the highest test accuracy during 300 epochs of training, with an 80/20 train/test split and no validation set. This is test-set model selection, not a valid generalization estimate. The protocol is load-bearing because every headline number is a maximum over 300 evaluations of the test set; the margin over baselines could be inflated or even spurious. The reader's identified weakest assumption—how the continuous mask is converted to the discrete node-selection matrix SV—is a genuine correctness issue in the architecture, but even if that discretization were cleanly resolved, the empirical claim would still be unverified under this evaluation protocol. The ablation inconsistency (K=500 outperforms the K=100 used in the main table) adds further uncertainty about whether Table 1 even reflects the best configuration. I therefore agree with the reader's REJECT verdict and see no change needed, though my primary load-bearing concern differs from the reader's stated weakest assumption. The proposed retest with a validation split is straightforward because the paper releases code and specifies the training setup concretely.","tokens_in":879,"tokens_out":938,"duration_ms":41734,"concrete_test":"Re-run the full evaluation with a fixed random split into train/validation/test (e.g., 70/15/15), select epochs and hyperparameters (including K and kappa) using validation accuracy only, and report test accuracy for SlepNet-I, SlepNet-II, and every baseline under the identical protocol. Repeat for all five datasets with the same seeds; if SlepNet remains at or near the top of Table 1 with a comparable margin, the concern resolves. If the margin collapses or reverses, the strongest claim is not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that SlepNet outperforms conventional GNNs/GSP baselines rests on Table 1, whose numbers are selected from test-set performance. Appendix G states: \"We trained the model for 300 epochs on every dataset, saved and recorded the results of the model with highest test accuracy during training\" and \"The datasets used are split into 80% training and 20% testing sets for each run.\" There is no validation split and no epoch-selection rule independent of test labels. Taking the maximum test accuracy over 300 epochs is test-set model selection; it optimizes the reported metric on the evaluation data and biases every entry upward, with the bias growing with the number of epochs. Because no baseline is protected from this bias, the margins in Table 1 cannot be interpreted as evidence of superiority. This is load-bearing: if the protocol is corrected, the rank ordering and margins may change, and the paper's main contribution is empirical. A secondary inconsistency compounds this: the main Table 1 uses K=100 Slepian vectors, while the authors' own ablation (Table 6) shows K=500 gives substantially higher accuracy (e.g., PVDM 92.94% vs 84.70%), so the headline result is not even the best configuration the paper reports. The mask-discretization issue raised by the reader is a real correctness concern, but it is secondary to the evaluation-protocol problem for the central empirical claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"SlepNet is a graph convolutional network that replaces graph Fourier harmonics with Slepian harmonics, which are designed to concentrate signal energy on a learned subgraph. The architecture consists of an attention-based mask that selects node clusters and a Slepian spectral filtering layer, with a neural eigenmapping approximation for scalability. The authors evaluate SlepNet on three fMRI datasets (OCD-PVDM, OCD-RA, ASD-ABIDE) and two traffic datasets (PEMS03, PEMS07), reporting that it outperforms GNN and graph-wavelet baselines in classification, that its learned masks recover ground-truth subgraphs in synthetic settings, and that its embeddings yield more structured temporal trajectories and better downstream classification. The paper includes ablations over the number of Slepian vectors, visualizations of learned brain masks, and a two-tier evaluation scheme.","tokens_in":17664,"tokens_out":2784,"duration_ms":31470,"significance":"If the empirical claims held, SlepNet would be a useful addition to graph-signal-processing tools for spatiotemporal neural data, offering a principled way to localize spectral filters to learned subgraphs. The synthetic mask-recovery experiment, the public code release, and the neural eigenmapping idea are concrete strengths. However, the central classification claim is undermined by the evaluation protocol described in Appendix G: models are selected on the test set, so the reported accuracies do not measure generalization. Because the paper's main contribution is empirical, this flaw is load-bearing and prevents the claimed outperformance from being established. The method description also leaves an important implementation detail unresolved regarding discretization of the attention mask.","major_comments":[{"comment":"The evaluation protocol selects the model with the highest test accuracy during 300 epochs of training, with no validation split and no independent early-stopping rule. This is test-set model selection: the reported numbers are optimistically biased, with the bias increasing in the number of epochs, and the margins in Table 1 cannot be interpreted as evidence that SlepNet outperforms the baselines. Since Table 1 is the central empirical claim, this issue is load-bearing.","section":"Appendix G (Experimental Details) and Table 1"},{"comment":"Table 1 reports SlepNet-I with K=100 Slepian vectors, but Table 6 shows K=500 yields substantially higher accuracy (e.g., 92.94% vs. 84.70% on OCD-PVDM). The headline results are therefore not the best configuration the authors themselves report, and the choice of K=100 for the main comparison is unexplained; this inconsistency further weakens the presentation of the central claim.","section":"Table 1 and Table 6 (Ablation Studies)"},{"comment":"The paper states that attention weights are sigmoidal or hard-Tanh values, but it never specifies how these continuous weights are converted into the 0/1 diagonal node-selection matrix S_V that defines the Slepian basis. If the mask is thresholded or rounded, the Slepian basis used in the forward pass is not the one that gradients see; if it is kept soft, S_V is not a valid selection matrix. This ambiguity affects the formal definition of the method and needs to be resolved.","section":"Section 4.1 (Attention-based Mask Learning Module)"}],"minor_comments":[{"comment":"There are several typos and grammatical slips, including 'laerned', 'sucessfully', 'interpretiblity', and 'resovled'; the manuscript would benefit from a careful proofreading pass.","section":"Throughout"},{"comment":"The claim that the learned mask recovers ground-truth subgraphs with 100% accuracy is stated without a quantitative metric or confidence interval; please specify how accuracy is computed and report variability over runs.","section":"Section 5.1 and Figure 4"},{"comment":"The right panel of Figure 3 reports performance of neural eigenmap predictions on unseen nodes, but the text does not define the error metric or the experimental setup; please clarify what quantity is plotted.","section":"Section 4.2.1 and Figure 3"},{"comment":"The dataset table lists only the number of timepoints and subjects, not the graph sizes (number of nodes per subject) or the number of graph instances after temporal snapshotting; adding these details would improve reproducibility.","section":"Appendix D, Table 5"},{"comment":"The paper does not report any statistical significance tests comparing SlepNet with the baselines; given the small subject counts in the fMRI datasets and the overlapping standard deviations for some comparisons, significance tests or confidence intervals for the differences should be provided.","section":"Tables 1 and 3"}],"recommendation":"reject","confidential_remarks":"The test-set model selection in Appendix G is a fundamental problem for a paper whose main contribution is empirical. In my view this warrants rejection despite the interesting architectural idea and the code release, because the reported results cannot be taken as evidence of generalization. If the authors rerun the full comparison with a proper validation-based epoch selection, the manuscript could be resubmitted as a substantially revised version."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nHere's my read of SlepNet. The architecture is genuinely new: first GCN that uses graph Slepian harmonics as convolution bases, with a learned subgraph mask and a neural eigenmapping to avoid repeated eigendecompositions. The synthetic mask-recovery experiment (three ring, ER, embedded subgraph) is clean and shows the model can find ground-truth subgraphs. That part is worth building on.\n\nThe problem is the headline empirical claim. Appendix G says they trained 300 epochs, saved and recorded the model with highest test accuracy, with an 80/20 train/test split and no validation set. That is test-set model selection: they chose the epoch that scored best on the evaluation labels. It inflates every reported number and makes Table 1 uninterpretable as a comparison. The bias grows with epoch count and affects baselines too, but not symmetrically enough to trust the margins. This is load-bearing because the paper's main contribution is outperformance.\n\nThere are secondary issues. Table 1 uses K=100 Slepian vectors, but their own ablation (Table 6) shows K=500 gives much higher accuracy (PVDM 92.9 vs 84.7). If the best configuration is K=500, why report K=100? The choice looks arbitrary. Also, the mask-learning section says a sigmoid 'forces the value to be 0 or 1', which it doesn't, and never says how the continuous attention is converted into the discrete node-selection matrix SV that defines the Slepian basis. If they round, gradients don't reach the basis; if they don't, SV is not a true selection. They need to spell this out. Proposition 1 is essentially a restatement of the Slepian concentration criterion with a likely typo (W vs B); it doesn't add theoretical weight.\n\nThe citation pattern looks fair; the self-citations are to their own T-PHATE and scattering work used as baselines/tools, which is normal. Code is released, which helps follow-up.\n\nWho this is for: researchers in graph signal processing and neuroimaging who want a localized spectral convolution and are willing to fix the evaluation themselves. Not for anyone who wants to trust the reported accuracies.\n\nMy verdict: the idea deserves a serious referee, not a desk reject. The evaluation protocol must be corrected (validation-based early stopping or nested CV, and report K=500 or explain the choice). If that comes out in revision, the method might hold up. As is, the empirical claims are not supported.","headline":"SlepNet is a genuinely new architecture, but the reported outperformance is built on test-set model selection and is not supported as written.","tokens_in":18160,"tokens_out":2669,"would_cite":false,"duration_ms":25763,"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":"SlepNet replaces global graph Fourier harmonics with Slepian harmonics concentrated on a learned subgraph, and reports higher classification accuracy across three fMRI and two traffic datasets plus more resolvable trajectory embeddings.","keywords":["graph neural networks","Slepian harmonics","graph signal processing","spectral graph convolution","fMRI classification","subgraph learning","neural eigenmapping","spatiotemporal trajectories"],"falsifier":"At inference time, round the learned mask to 0/1, recompute the Slepian basis from that discrete subgraph, and rerun the classifier; if the accuracy falls to the Spectral GCN baseline, or if the gradients used in training cannot be matched to the rounded basis, then the network is not actually learning Slepian harmonics. As a second check, retraining with a random mask that keeps accuracy high would show the mask is not doing the localization work claimed.","tokens_in":1668,"feed_emoji":"🧠","tokens_out":2269,"duration_ms":97408,"temperature":0.7,"pith_summary":"This paper proposes SlepNet, a graph neural network whose spectral filters are built from Slepian harmonics instead of the usual graph Fourier harmonics. Slepian harmonics are basis vectors that concentrate a band-limited signal's energy inside a chosen set of nodes, and SlepNet learns that set of nodes with an attention mask during training. The paper reports that the SlepNet family reaches the top classification accuracy on three fMRI datasets (OCD and ASD) and two traffic datasets, beating conventional GNNs and graph-wavelet constructions. It also reports that SlepNet's learned embeddings separate similar brain-signal patterns better than baseline embeddings, producing temporally coherent trajectories useful for downstream tasks.","feed_headline":"Slepian harmonics let a GCN beat standard GNNs on five datasets","feed_subtitle":"Harmonics focus signal energy on learned brain subgraphs, sharpening classification and trajectory clarity.","key_machinery":"The central object is the Slepian basis $Z$: eigenvectors of the concentration matrix $C=S_B^TU^TS_VUS_B$, which are graph Fourier harmonics bandlimited to the first $K$ Laplacian eigenvectors and maximally concentrated on a node subset selected by $S_V$. SlepNet learns $S_V$ through a sigmoidal or hard-Tanh attention mask over $\\kappa=60$ spectral clusters, forms $Z$, and filters signals as $Z(\\Theta Z^Tx)$. A neural eigenmapping network, trained by regression on eigendecompositions of a subset of nodes, approximates the Slepian harmonics to avoid the $O(N^3)$ cost of full eigendecomposition. This basis carries the argument because it provides spatially localized, canonical spectral filters, which the paper argues global Fourier harmonics and graph wavelets cannot provide.","core_discovery":"The central claim is that replacing the graph Fourier basis with Slepian harmonics, which are bandlimited functions optimally concentrated on a learned subgraph, improves both classification and representation of spatiotemporal signals on graphs. Concretely, the paper defines a graph convolution as $\\tilde{x}=Z(\\Theta Z^Tx)$, where $Z$ contains Slepian harmonics restricted to selected nodes, the selection comes from cluster-level attention weights, and both the mask and the diagonal filters $\\Theta$ are learned end-to-end. Across the five datasets, one of the two SlepNet variants achieves the top accuracy in every case, with the strongest numbers being 84.70 percent on OCD-PVDM, 90.65 percent on OCD-RA, 74.13 percent on ASD-ABIDE, and 56.56 percent on PEMS03, compared with a best baseline of 62.62, 69.76, 57.68, and 56.31 percent respectively. The paper also claims that the learned mask recovers ground-truth informative subgraphs on synthetic graphs with 100 percent accuracy, and that SlepNet's embedding trajectories have high curvature and support better secondary classification of subject sex than baseline embeddings.","pith_inferences":["The paper leaves open whether the learned mask is genuinely discrete when defining $S_V$; if a continuous mask is used in training but a rounded mask at inference, the network may not actually be optimizing the Slepian basis it claims to use.","The same mask-plus-Slepian design could be applied to other signal-on-graph problems where the informative support is unknown, such as EEG source localization or anomaly detection in sensor networks, but the paper only demonstrates fMRI and traffic data.","The differing performance of the energy-concentration and embedded-distance Slepian variants across datasets suggests that the choice of Slepian criterion is itself a tunable modeling decision; an adaptive or mixed criterion might further improve results.","Because the mask operates at the level of $\\kappa=60$ spectral clusters, the learned subgraph is coarse; a hierarchical or finer-grained mask could test whether cluster granularity is a bottleneck for localization accuracy."],"forward_implications":["If SlepNet's reported accuracy holds, spectral GNNs for neuroimaging can be built around learned subgraph localization rather than global graph Fourier harmonics, yielding gains on disease classification tasks.","The learned Slepian embeddings are resolved enough to be reused for an untrained secondary task, such as classifying subject sex from OCD data, indicating the representation itself carries signal beyond the original classifier.","The mask learned on fMRI data highlights the parietal lobe, dorsolateral prefrontal cortex, and left temporal regions, which the paper ties to prior OCD findings, so the method offers interpretable region discovery rather than a black-box score.","The neural eigenmapping approximation makes Slepian computation practical for graphs beyond roughly 1000 nodes, since full eigendecomposition scales as $O(N^3)$ while the approximating network has lower and more stable runtime.","Ablations show that increasing the number of Slepian basis vectors from 5 to 500 monotonically improves classification accuracy, so the model's expressivity is directly tied to spectral bandwidth."],"supporting_citations":[{"why":"Defines graph Slepians as eigenvectors of the concentration matrix $C$, which is the mathematical construction SlepNet's basis is built from.","marker":"[11]"},{"why":"Defines the Spectral GCN that uses graph Fourier harmonics, the convolution design SlepNet replaces and a key baseline in the accuracy tables.","marker":"[5]"},{"why":"Provides the first-order GCN baseline and the standard spectral GNN design against which SlepNet is compared.","marker":"[6]"},{"why":"Supplies the graph-wavelet baseline and the claimed limitation that wavelets are non-canonical and leak energy at subgraph boundaries, motivating Slepians.","marker":"[7]"},{"why":"Gives matrix backpropagation for eigenvectors and eigenvalues of symmetric matrices, which is what makes learning through the Slepian basis differentiable.","marker":"[19]"},{"why":"Establishes neural eigenmapping for computing eigenvectors, the technique SlepNet adapts to approximate Slepian harmonics without full eigendecomposition.","marker":"[21]"},{"why":"Provides T-PHATE, the manifold embedding used to visualize SlepNet trajectories and support the claim of more resolvable signal patterns.","marker":"[28]"},{"why":"Supplies the PeMS traffic sensor data used for the two day-of-week classification benchmarks.","marker":"[53]"}],"fun_headline_variants":["SlepNet's Slepian harmonics outperform standard GNNs on five datasets","Slepian harmonics concentrate energy on learned subgraphs for better GCN","SlepNet learns subgraph-focused Slepian basis, besting GNNs on 5 datasets","SlepNet: Slepian basis for subgraph-focused graph neural networks","SlepNet's learned subgraph focus sharpens graph signal classification"],"cache_read_input_tokens":20352,"weakest_assumption_plain":"SlepNet assumes that the continuous cluster-attention scores can be converted into the discrete yes-or-no choice of which nodes define the subgraph, and that this conversion can still be trained by gradient descent; the paper does not specify how the rounding happens or how gradients pass through it.","fun_headline_variants_meta":{"raw":{"variants":["SlepNet's Slepian harmonics outperform standard GNNs on five datasets","Slepian harmonics concentrate energy on learned subgraphs for better GCN","SlepNet learns subgraph-focused Slepian basis, besting GNNs on 5 datasets","SlepNet: Slepian basis for subgraph-focused graph neural networks","SlepNet's learned subgraph focus sharpens graph signal classification"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001047,"raw_usage":{"total_tokens":4470,"prompt_tokens":1087,"completion_tokens":3383,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":703,"completion_tokens_details":{"reasoning_tokens":3278}},"tokens_in":703,"tokens_out":3383,"duration_ms":21671,"temperature":1.0,"reasoning_tokens":3278,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T19:22:58.037920+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"At inference time, round the learned mask to 0/1, recompute the Slepian basis from that discrete subgraph, and rerun the classifier; if the accuracy falls to the Spectral GCN baseline, or if the gradients used in training cannot be matched to the rounded basis, then the network is not actually learning Slepian harmonics. As a second check, retraining with a random mask that keeps accuracy high would show the mask is not doing the localization work claimed.","supporting_citations":[{"cited_title":"When Slepian meets Fiedler: Putting a focus on the graph spectrum","cited_arxiv_id":null,"evidence_quote":"Defines graph Slepians as eigenvectors of the concentration matrix $C$, which is the mathematical construction SlepNet's basis is built from."},{"cited_title":"Spectral networks and deep locally connected networks on graphs","cited_arxiv_id":null,"evidence_quote":"Defines the Spectral GCN that uses graph Fourier harmonics, the convolution design SlepNet replaces and a key baseline in the accuracy tables."},{"cited_title":"BLIS-Net: Classifying and Analyzing Signals on Graphs","cited_arxiv_id":"2310.17579","evidence_quote":"Supplies the graph-wavelet baseline and the claimed limitation that wavelets are non-canonical and leak energy at subgraph boundaries, motivating Slepians."},{"cited_title":"Matrix backpropagation for deep networks with structured layers","cited_arxiv_id":null,"evidence_quote":"Gives matrix backpropagation for eigenvectors and eigenvalues of symmetric matrices, which is what makes learning through the Slepian basis differentiable."},{"cited_title":"Busch, Jessie Huang, Andrew Benz, Tom Wallenstein, Guillaume Lajoie, Guy Wolf, Smita Krishnaswamy, and Nicholas B","cited_arxiv_id":null,"evidence_quote":"Provides T-PHATE, the manifold embedding used to visualize SlepNet trajectories and support the claim of more resolvable signal patterns."}],"review_version":2}