{"id":"3eb02cc7-c472-4e29-8b65-26fd7a45d2b1","arxiv_id":"2501.19001","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":6,"one_line_summary":"Quantum-SMOTEV2 removes clustering from Quantum-SMOTE and boosts IQR-based angular outliers, reporting modest metric gains on one telecom churn dataset.","lead":"Quantum-SMOTEV2 is a proposed update to the authors' Quantum-SMOTE oversampling method that drops clustering and adds boosting of 'angular outliers' identified by an interquartile range on a swap-test derived angle. The paper reports modest classification gains on a telecom churn dataset, but the defining angular-distance formula is not supported by the paper's own equations and the experiments lack error bars and baselines.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (17) labels a norm-difference as 'angular distance'; the AOL mechanism measures no angle between data point and centroid, so the paper's central distinguishing feature is unsupported.","rationale":"The reader's weakest_assumption identifies exactly the load-bearing flaw: the swap-test quantity in Eqs. (12)-(17) is a function of vector norms, not directions, yet it is used to define angular outliers. I agree this is the most important concern because the manuscript's stated novelty and the mechanism for AOL boosting both rely on this quantity being an angle. If the quantity is not an angle, then the outlier-boosting step is not targeting angular outliers, and the central claim that 'integrating Angular Outliers' improves performance is unsupported. The paper may still contain an empirical heuristic based on norm differences that happens to improve metrics, but that is a different claim from the one made. I also note that the experimental section lacks error bars and code, but the mathematical inconsistency is sufficient to reject the central argument as written. The verdict should remain REJECT, since the defining relation is unsupported and the empirical evidence cannot rescue the stated mechanism.","tokens_in":19765,"tokens_out":3449,"duration_ms":38169,"concrete_test":"Re-run the outlier-detection and boosting pipeline on the same telecom dataset, but compute the angular distance classically as cos⁻¹(DC·MD / (|DC||MD|)) and compare the IQR outlier sets with those obtained from Eq. (13). If the two outlier sets differ materially, the paper's 'angular outliers' are not angular. A minimal falsification: for DC=(1,0) and MD=(0,1), Eq. (13) gives |⟨φ|ψ⟩|² = 0, so Eq. (17) outputs π, whereas the true angle is π/2; this single two-dimensional example directly shows Eq. (17) is not computing the angle between the two vectors.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is that Quantum-SMOTEV2 with Angular Outlier (AOL) boosting improves classification at 30-36% synthetic data because it identifies and boosts outliers in the angular distribution of minority points around a single centroid. That mechanism depends entirely on the quantity called 'angular distance' in Section 3.1. The derivation in Eqs. (12)-(13) gives |⟨φ|ψ⟩|² = (|DC|² - |MD|²)² / (2Z), which depends only on the norms of the centroid and minority vectors, not on their relative direction. There is no term involving DC·MD, so this quantity cannot be the angle between DC and MD. Calling it 'angular distance' in Eq. (17) and using it to define IQR-based Angular Outliers in Section 3.3 is therefore internally inconsistent: the flagged outliers are outliers in a norm-based quantity, not in angular distribution. Since the novelty and the explanation of why AOL helps edge cases rest on this angular interpretation, the empirical tables, even if reproduced, would not support the claim as stated. The issue is not a disagreement with consensus; it is a mismatch between the derivation and the object the algorithm claims to measure.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes Quantum-SMOTEV2, a variant of the authors' earlier Quantum-SMOTE that removes clustering, uses a single data centroid, and adds an 'Angular Outlier' (AOL) boosting step. The method amplitude-encodes the centroid and minority points, runs a compact swap test, interprets the result as an angular distance, and uses that distance both to rotate minority points into synthetic samples and to identify outliers via IQR thresholds. These outliers are then boosted with wider rotations. The authors evaluate the method on a telecom churn dataset with RF, KNN, and NN classifiers, reporting that AOL boosting yields improvements at moderate SMOTE levels (30–36%). The paper's central technical claim is that the swap-test output measures the angle between a minority point and the data centroid, and that angular outliers identified in this way are responsible for the reported performance gains.","tokens_in":20042,"tokens_out":5248,"duration_ms":53145,"significance":"If the central mechanism were sound, the paper would offer a practically useful result: quantum oversampling that achieves comparable classification performance with 30–36% synthetic data rather than 50%, without K-means clustering, and with a low-depth swap-test circuit. The authors deserve credit for stating the algorithm in detailed pseudocode, using a public dataset, and reporting many metrics. However, the paper's defining mathematical step is internally inconsistent: the quantity derived in Section 3.1 depends only on the norms of the centroid and minority vectors, not on the angle between their directions. In addition, the swap-test probability formula in Algorithm 3 is algebraically wrong, and the empirical evaluation lacks any comparison against classical SMOTE or the earlier Quantum-SMOTE, has no error bars or repeated runs, and uses hyperparameters tuned on the same evaluation dataset. These problems are load-bearing for the paper's central claim, so the significance of the reported improvements cannot currently be assessed.","major_comments":[{"comment":"The derived quantity is not an angular distance. Equations (12)–(13) give |⟨φ|ψ⟩|² = (|DC|² − |MD|²)²/(2Z) with Z = |DC|² + |MD|², which depends only on the norms of the centroid and minority vectors and contains no term involving the dot product DC·MD. Equation (16) then calls this a Euclidean distance, and Eq. (17) converts it to an angle via 2cos⁻¹(√swap test probability). Neither step is justified: Euclidean distance between two vectors depends on their dot product, and the angle between their directions is determined by ⟨DC|MD⟩, not by ||DC|² − |MD|²|. Consequently, the 'Angular Outliers' defined in Section 3.3 are outliers in a norm-difference quantity, not in an angular distribution. Since the paper's novelty and its explanation for the performance gains rest entirely on this angular interpretation, the central claim is unsupported as stated.","section":"§3.1, Eqs. (12)–(17)"},{"comment":"The swap-test probability is computed incorrectly. For the standard swap test, the probability of measuring the ancilla in |0⟩ is (1 + |⟨ψ|φ⟩|²)/2, so the squared overlap is 2P(0) − 1. The manuscript instead computes 'swap test probability ← 1 − 2 × p0 + p1'; since p0 + p1 = 1, this equals 2 − 3p0, which is negative for identical states (p0 = 1) and gives 0.5 for orthogonal states rather than 0. Because Eq. (17) uses the square root of this quantity, the resulting 'angular distance' is not a valid angle. This compounds the error in Eqs. (12)–(17) and affects every downstream outlier threshold and rotation angle.","section":"Algorithm 3, lines 17–19"},{"comment":"The headline empirical claim is not demonstrated. The abstract states that moderate SMOTE levels (30–36%) achieve what previously required 50% with the original method, but the paper reports no experiment comparing Quantum-SMOTEV2 against classical SMOTE, against the authors' earlier Quantum-SMOTE [5], or against any other oversampling baseline; Tables 2 and 3 only compare with and without AOL within the new method. Moreover, the results appear to come from single runs without error bars or repeated train/test splits, so the large relative F1 improvements for NN at 30–34% (e.g., 68.19% and 91.28% in Table 3), which start from very small absolute values (F1 ≈ 0.05–0.08 in Table 2), may be dominated by variance. The claim that AOL reduces the required SMOTE level from 50% to 30–36% needs a direct comparison and uncertainty quantification.","section":"Section 5, Tables 2 and 3"},{"comment":"The empirical evaluation is vulnerable to post hoc tuning. The key hyperparameters—num_bins, the 1.5 IQR multiplier, the half-threshold rule, the 1.5 boost-angle multiplier, and the splitting factor—are fixed on the same dataset used for evaluation, and no sensitivity analysis or held-out validation is provided. Since most AOL improvements in Table 3 are small in absolute terms (often below 2 percentage points), the possibility that the reported gains depend on these specific choices rather than on a general angular-outlier mechanism cannot be excluded. This is a load-bearing issue for the paper's practical claims.","section":"§3.3.1 and Algorithms 7–8"}],"minor_comments":[{"comment":"The F1-score formula is written as 'F1 = 2 × (Precision × Recall)', which is missing the denominator; it should be F1 = 2PR/(P + R).","section":"§2.1.1, Eq. (4)"},{"comment":"The algorithm numbering is inconsistent: the text refers to 'Quantum-SMOTEV2 (Algo. 5)', but Algorithm 5 is only the synthetic-data creation subroutine, and the complete pipeline spans Algorithms 2–8 with no single numbered algorithm for the full method. Reorganizing and labeling the pipeline as one coherent algorithm would improve clarity.","section":"§4.1.2 and Algorithms 2–8"},{"comment":"Several figure captions list subfigures as '(a), (c), (d)' when only three subfigures are present; the labels should be corrected to '(a), (b), (c)'.","section":"Supplementary figures, e.g., Figs. 18, 20, 22, 24, 26, 28, 30, 32, 34"},{"comment":"The text in Section 4.1 describes the cell-to-cell churn dataset and cites [10], a different 'Telco Customer Churn' Kaggle dataset, while [7] is the reference given in the Introduction for the cell-to-cell data. The data provenance should be made unambiguous, since the two datasets have different sizes and features.","section":"References [7] and [10]"}],"recommendation":"reject","confidential_remarks":"The paper has a plausible motivating idea, and the authors have made an effort to present the algorithm in detail. However, the central mathematical derivation is not merely incomplete; it identifies a norm-difference quantity as an angular distance, and the swap-test probability formula is algebraically wrong. These are internal inconsistencies, not disagreements with an existing consensus, and they invalidate the paper's key contribution as written. The empirical section would also need substantial rework—direct baselines, repeated runs with error bars, and sensitivity analysis—before the performance claims could be evaluated. I would not advise the editor to invite a minor revision; the authors would need to re-derive the angular-distance computation, rerun the experiments, and add the missing comparative evidence. If that is done, a substantially revised manuscript could be considered anew."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The one thing to know: the stress-test note is right. The paper's defining novelty—Angular Outlier (AOL) boosting—rests on a quantity that is not an angle. In Section 3.1, Eqs. (12)-(17), the swap-test inner product evaluates to (|DC|^2 - |MD|^2)^2 / (2Z), which depends only on the norms of the centroid and the minority point, never on their relative direction. Calling that an angular distance and then running IQR outlier detection on it means the outliers are outliers in a norm-difference, not in any angular distribution. The paper even labels the same quantity as Euclidean distance in Eq. (16), which is also incorrect. This is not a subtle concern; it is load-bearing and internally inconsistent.\n\nWhat is actually new: removing the clustering step from the authors' earlier Quantum-SMOTE and adding IQR-based outlier boosting around a single centroid is a legitimate, if modest, extension. The pseudocode in Algorithms 2-8 is detailed and would let someone reimplement the steps. That is more than many quantum-ML papers offer.\n\nThe soft spots are substantial. The empirical section is single runs with no error bars, no comparison against classical SMOTE, and no comparison against the original Quantum-SMOTE with clustering. The improvements from AOL are mostly small (well under 5% for RF and KNN; the large NN F1 gains are relative to a baseline of 0.041 and are driven by a few synthetic points). Hyperparameters like num_bins, the 1.5 IQR multiplier, and the 1.5 boost multiplier appear chosen post hoc on the same dataset. The abstract's claim of 'significant enhancements at 30-36%' is not supported by the evidence as presented.\n\nThis paper is not ready for peer review. A serious referee would catch the Eq. (17) issue quickly, and the empirical design would need to be redone with proper baselines and repeated runs. The authors should fix the derivation and show that the quantity they actually compute has the properties they claim. Until then, I would not cite it or spend a reading group on it.","headline":"The angular-outlier mechanism is built on an algebraic error: the quantity called angular distance is a norm difference, and the empirical evidence lacks baselines and error bars, so the central claim does not hold up.","tokens_in":666,"tokens_out":948,"would_cite":false,"duration_ms":38644,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Quantum-SMOTEV2 claims that boosting points the algorithm labels as angular outliers lets classifiers reach 50%-level performance with only 30–36% synthetic data, and removes the K-means clustering step of the earlier Quantum-SMOTE.","keywords":["Quantum SMOTE","class imbalance","swap test","angular outliers","quantum machine learning","oversampling","telecom churn","synthetic data"],"falsifier":"Compute the swap-test probability for two minority points that have the same Euclidean norm but point in opposite directions from the centroid: the formula gives identical 'angular distances' for both, so the outlier test cannot distinguish direction. A reader could also compare the paper's Eq. (17) ranking with a ranking by true cosine similarity on the same prepared data; if the rankings differ, the claimed angular quantity is not the angle.","tokens_in":19584,"feed_emoji":"⚛️","tokens_out":5627,"duration_ms":44536,"temperature":0.7,"pith_summary":"This paper claims that a quantum version of SMOTE can generate synthetic minority-class samples without K-means clustering, and that adding a boosting step for points the algorithm labels 'angular outliers' lets Random Forest, K-Nearest Neighbours, and Neural Network classifiers reach their full performance at 30–36% synthetic data rather than the 50% the earlier Quantum-SMOTE needed. The central idea is to measure each minority point's relation to the dataset centroid by a swap-test inner product, read it as an angle, and rotate points by a fraction of that angle to create new samples. Points far from the centroid in this angular sense are then boosted with wider rotation angles. If the claim holds, the method saves computational effort and improves edge-case classification without clustering and without raising SMOTE proportions. The paper's experimental evidence is a single telecom churn dataset, so the claim's generality rests on that one demonstration.","feed_headline":"Quantum SMOTE hits 50%-level results with just 36% synthetic data","feed_subtitle":"Angular Outlier boosting lets RF, KNN, and NN classifiers reach target metrics at 30–36% synthetic data instead of 50%.","key_machinery":"The load-bearing object is the compact swap test used as a purported angular-distance oracle. The circuit amplitude-encodes the centroid $|DC\\rangle$ and a minority point $|MD\\rangle$, forms the states $|\\psi\\rangle$ and $|\\phi\\rangle$, and reads out $|\\langle\\phi|\\psi\\rangle|^2 = (|DC|^2 - |MD|^2)^2 / (2Z)$, which the paper calls the swap-test probability. Equation (17) then defines angular distance as $2\\cos^{-1}(\\sqrt{\\text{swap-test probability}})$, and Algorithm 1 chooses a rotation angle as a random fraction of that value (divided by the splitting factor), applied via single-qubit $R_X$ gates to the amplitude-encoded minority point. The angular-outlier stage computes an IQR threshold on these angular distances across the minority class, and Algorithm 8 boosts underrepresented bins with wider rotation angles. The machinery's role is to generate synthetic points near a single centroid and selectively densify the tails of the angular distribution.","core_discovery":"Quantum-SMOTEV2 replaces the cluster-centroid machinery of its predecessor with a single dataset centroid, computes an 'angular distance' from each minority point to that centroid via a compact swap test, and rotates minority points by a random fraction of that angle to synthesize new points. After synthesis, points whose angular distances fall beyond 1.5×IQR of the angular-distance distribution are designated Angular Outliers, and underrepresented bins among them are augmented using the same rotation circuit with wider angles to avoid duplicates. On the cell-to-cell telecom churn dataset, applying this outlier boost yields the paper's headline result: F1, PR-AUC, and ROC-AUC improvements at 30–36% synthetic minority fractions that previously required 50% minority with the original method, with the largest relative gains in F1 score for the neural network (91.28% improvement at 34% synthetic data). The paper states this as evidence that angular outliers represent critical edge cases whose targeted boosting improves classification.","pith_inferences":["The 'angular distance' of Eq. (17) is a function of the vector norms only, so the outlier ranking is really a ranking by distance from the centroid (or norm), not by direction; if that is the case, the improvements attributed to 'angular' outliers would also be available to any norm- or distance-based outlier method, and the quantum swap test is not doing angular work.","A direct head-to-head test would be to run the same boosting protocol but substitute the true cosine angle between the centroid and each minority point; if the results match the swap-test version, the norm dependence is confirmed, and if they diverge, the paper's quantity must encode some other information.","The dataset is a single churn table with likely correlated categorical features; the 30–36% sweet spot could be an artefact of that dataset's geometry rather than a general property, so applying the same two-stage protocol to other imbalanced benchmarks (fraud, medical) would tell whether the AOL gain transfers."],"forward_implications":["If the angular-outlier boost is the cause of the gains, then users of Quantum-SMOTE can lower their synthetic-data target from 50% to around 30–36%, reducing the number of generated samples and the cost of running the swap-test and rotation circuits.","Removing the clustering step means the method applies to datasets where K-means is unstable, without losing Quantum-SMOTE's original hyperparameters (rotation angle, minority percentage, splitting factor) and with one new hyperparameter, the number of bins.","The reported improvements are model-dependent: KNN and NN gain most from outlier boosting while RF gains are modest, so the method is most useful for instance-based and neural classifiers rather than as a universal booster.","The procedure avoids CNOT and ZZ gates in the rotation step, keeping circuits shallow and thereby less exposed to decoherence, which matters if the circuits are moved from simulators to quantum hardware."],"supporting_citations":[{"why":"Classical SMOTE baseline that Quantum-SMOTE and this variant aim to improve; supplies the oversampling task and the KNN/Euclidean-distance approach that the quantum method replaces.","marker":"[4]"},{"why":"The predecessor Quantum-SMOTE whose rotation-angle, minority-percentage, and splitting-factor machinery Quantum-SMOTEV2 inherits, and whose performance at 50% is the baseline for the 30–36% claim.","marker":"[5]"},{"why":"The cell-to-cell telecom churn dataset used in the experiments, the sole evidence for the performance gains.","marker":"[7]"},{"why":"The dissimilarity-measure construction that the paper adapts to compute the inner product and so-called angular distance in the compact swap test.","marker":"[9]"},{"why":"The telecom churn dataset referenced in the case-study section as the public data source for the evaluation.","marker":"[10]"},{"why":"The Qiskit-based description of compact swap-test circuits used for the distance calculation, supporting the qubit-count claim.","marker":"[8]"}],"fun_headline_variants":["Angular Outliers cut SMOTE's synthetic data need from 50% to 36%","Quantum SMOTE hits target metrics with 36% synthetic data via angular outliers","Outlier-aware SMOTE needs only 36% synth data for 50% results","Angular Outlier boost matches 50% performance with 36% synthetic data"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole angular-outlier mechanism rests on the assumption that the swap-test output measures the angle between a minority point and the centroid; the derived quantity actually depends only on the lengths of the two vectors, so the ranking that drives boosting may not be angular at all.","fun_headline_variants_meta":{"raw":{"variants":["Angular Outliers cut SMOTE's synthetic data need from 50% to 36%","Quantum SMOTE hits target metrics with 36% synthetic data via angular outliers","Outlier-aware SMOTE needs only 36% synth data for 50% results","Angular Outlier boost matches 50% performance with 36% synthetic data"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000828,"raw_usage":{"total_tokens":3641,"prompt_tokens":988,"completion_tokens":2653,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":604,"completion_tokens_details":{"reasoning_tokens":2563}},"tokens_in":604,"tokens_out":2653,"duration_ms":18324,"temperature":1.0,"reasoning_tokens":2563,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T21:40:20.973135+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the swap-test probability for two minority points that have the same Euclidean norm but point in opposite directions from the centroid: the formula gives identical 'angular distances' for both, so the outlier test cannot distinguish direction. A reader could also compare the paper's Eq. (17) ranking with a ranking by true cosine similarity on the same prepared data; if the rankings differ, the claimed angular quantity is not the angle.","supporting_citations":[{"cited_title":"Available from: https://www.kaggle.com/datasets/ jpacse/datasets-for-churn-telecom","cited_arxiv_id":null,"evidence_quote":"The cell-to-cell telecom churn dataset used in the experiments, the sole evidence for the performance gains."},{"cited_title":"Quantum Block-Matching Algorithm Using Dissimilarity Measure","cited_arxiv_id":null,"evidence_quote":"The dissimilarity-measure construction that the paper adapts to compute the inner product and so-called angular distance in the compact swap test."},{"cited_title":"Available from: https://www.kaggle.com/datasets/ blastchar/telco-customer-churn","cited_arxiv_id":null,"evidence_quote":"The telecom churn dataset referenced in the case-study section as the public data source for the evaluation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The Qiskit-based description of compact swap-test circuits used for the distance calculation, supporting the qubit-count claim."}],"review_version":1}