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REVIEW 4 major objections 4 minor 14 references

Quantum SMOTE with Angular Outliers: Redefining Minority Class Handling

T0 review · 4 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2501.19001 v1 pith:YUEQA2M2 submitted 2025-01-31 quant-ph cs.LG

Nishikanta Mohanty , Bikash K. Behera , Christopher Ferrie This is my paper · ORCID
classification quant-phcs.LG
keywords QuantumSMOTEclassimbalanceswaptestangularoutliersmachinelearningoversamplingtelecomchurnsyntheticdata
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

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.

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 (4)
  1. [§3.1, Eqs. (12)–(17)] 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.
  2. [Algorithm 3, lines 17–19] 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.
  3. [Section 5, Tables 2 and 3] 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.
  4. [§3.3.1 and Algorithms 7–8] 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.
minor comments (4)
  1. [§2.1.1, Eq. (4)] The F1-score formula is written as 'F1 = 2 × (Precision × Recall)', which is missing the denominator; it should be F1 = 2PR/(P + R).
  2. [§4.1.2 and Algorithms 2–8] 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.
  3. [Supplementary figures, e.g., Figs. 18, 20, 22, 24, 26, 28, 30, 32, 34] Several figure captions list subfigures as '(a), (c), (d)' when only three subfigures are present; the labels should be corrected to '(a), (b), (c)'.
  4. [References [7] and [10]] 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.

Circularity Check

2 steps flagged · score 6.0 of 10

Test-set leakage and a norm-difference mislabeled as 'angular distance' make the reported AOL gains circular rather than independent predictions.

  1. fitted input called prediction [Section 4.1.2 (Applying SMOTE and Outlier Boost on Prepared Data); Table 2]
    "For the data preparation of the cell-2-cell dataset and we proceeded to apply our proposed Quantum-SMOTEV2 (5) to the entire dataset. The objective was to steadily enhance the representation of the minority population to a certain proportion of the entire dataset and thereafter implement the amplification of angular outliers."

    The pipeline augments the minority class before any train/test split is described ('apply ... to the entire dataset'). Table 2 then reports 'Test' accuracy, F1, PR, and ROC scores for each SMOTE percentage. Because test-set minority records were part of the data used to synthesize and boost minority samples, the test statistics are not independent: the model has seen synthetic variants of the test points during training. The 'prediction' on the test split is therefore fitted to the test set by construction, not a clean out-of-sample evaluation.

  2. renaming known result [Section 3.1, Eqs. (13) and (17); Section 3.3 (Centroid Based Angular Outlier Boosting)]
    "|⟨ϕ | ψ⟩|2 = (|DC|2 − |MD|2)2 / 2Z (13) ... In light of this, we define the angular distance—the angle between two vectors—as follows: angular distance = 2 cos−1(p swap test probability) (17)"

    Eq. (13) contains only the norms |DC| and |MD|; no term ⟨DC|MD⟩ or dot product appears. Eq. (17) then labels 2 cos−1 of this norm-difference quantity as 'the angle between two vectors.' The 'Angular Outliers' identified in Section 3.3 are therefore outliers in a function of vector lengths, not in the angular distribution of points around the centroid. The paper's central explanation—that AOL boosts edge cases by targeting angular outliers—is a renaming of a norm-based quantity, so the mechanism's stated rationale is not supported by the derivation.

full rationale

The paper's strongest empirical claim—that AOL lets moderate SMOTE (30–36%) match what 'previously required up to 50%'—rests on Table 2. Two construction-level problems make the claim circular or unverifiable as stated. First, Section 4.1.2 applies Quantum-SMOTEV2 and outlier boosting to 'the entire dataset' before any train/test split is described, so the test metrics in Table 2 are not independent of the synthetic training data; the test labels have effectively been used to generate training points. Second, the 'angular distance' that defines the Angular Outliers is, by Eq. (13), a function only of the norms |DC| and |MD|; Eq. (17) relabels this norm-difference as the angle between vectors. Consequently the angular-outlier mechanism is a renaming of a norm-based computation, and the paper's explanatory story for why AOL helps edge cases does not follow from the derivation. The self-citations to the authors' prior Quantum-SMOTE are numerous, and the '50% previously required' comparison comes from that prior work, but that is contextual rather than load-bearing for the derivation; the main circularity is in the evaluation protocol and the renaming of the computed quantity. Because the central empirical claim reduces, as described, to a contaminated test protocol, the circularity score is 6 rather than lower.

Assumptions & free parameters 6 free parameters · 3 assumptions · 1 invented entities

The central claim rests on one fitted/tuned quantity (angular distance from the swap test), several hand-chosen hyperparameters for outlier binning and boosting, and the domain assumption that angular outliers are edge cases. No new physical entities are introduced beyond the AOL label.

free parameters (6)
  • num_bins
    Hyperparameter in Algorithms 7 and 8 controlling histogram granularity for outlier bins; no value or selection criterion is given.
  • IQR multiplier = 1.5
    Standard but arbitrary threshold for defining angular outliers; adopted from boxplot convention, not derived.
  • half_threshold ratio = 0.5
    Bins with counts below half the average are boosted (Algorithm 8); chosen by hand.
  • boost angle multiplier = 1.5
    Rotation angle for boosting uses (synthetic_loop_itr*0.0174533)*1.5 + j (Algorithm 8); constant 1.5 is arbitrary.
  • splitting factor (sf)
    Inherited from Quantum-SMOTE [5] and used in Algorithm 1 to scale rotation angles; value not stated.
  • target synthetic percent = 30-50% (swept)
    Experimental sweep from 30% to 50%; the 30-36% range is later called optimal, making the chosen range part of the claim.
assumptions (3)
  • domain assumption The swap-test inner product measures angular distance between data point and centroid
    Eqs. (15)-(17) define D^2 as a distance and angular distance = 2 arccos(sqrt(swap test probability)), but the quantity is a norm difference; this assumption is load-bearing and appears unjustified.
  • domain assumption Angular outliers capture 'edge cases' relevant to classification
    Sections 2 and 3.3 assert that minority points far in angular distance are poorly distributed and boosting them improves classifiers; no evidence beyond the reported single-dataset results connects outlier angularity to decision boundary errors.
  • standard math Amplitude encoding and swap test circuit can be simulated faithfully
    The paper relies on Qiskit simulators and the compact swap-test construction from [8,9]; accepted background, but the pseudocode in Algorithm 3 appears inconsistent with the analytic formula.
invented entities (1)
  • Angular Outlier (AOL)
    purpose: A new category of minority-class data points flagged when their swap-test derived angular distance falls outside 1.5*IQR; these points are targeted for extra synthetic data generation.
    AOL is introduced in Sections 2 and 3.3 as a label for edge cases, but its definition depends on a quantity that is not shown to be an angle. No external validation ties AOL to actual classification errors.

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Cite this review

Pith. "Pith review of Quantum SMOTE with Angular Outliers: Redefining Minority Class Handling." pith.science (2026). https://pith.science/paper/YUEQA2M2

@misc{pith2026250119001,
  author       = {Pith},
  title        = {Pith review of: Quantum SMOTE with Angular Outliers: Redefining Minority Class Handling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YUEQA2M2}},
  note         = {Machine review of arXiv:2501.19001}
}
read the original abstract

This paper introduces Quantum-SMOTEV2, an advanced variant of the Quantum-SMOTE method, leveraging quantum computing to address class imbalance in machine learning datasets without K-Means clustering. Quantum-SMOTEV2 synthesizes data samples using swap tests and quantum rotation centered around a single data centroid, concentrating on the angular distribution of minority data points and the concept of angular outliers (AOL). Experimental results show significant enhancements in model performance metrics at moderate SMOTE levels (30-36%), which previously required up to 50% with the original method. Quantum-SMOTEV2 maintains essential features of its predecessor (arXiv:2402.17398), such as rotation angle, minority percentage, and splitting factor, allowing for tailored adaptation to specific dataset needs. The method is scalable, utilizing compact swap tests and low depth quantum circuits to accommodate a large number of features. Evaluation on the public Cell-to-Cell Telecom dataset with Random Forest (RF), K-Nearest Neighbours (KNN) Classifier, and Neural Network (NN) illustrates that integrating Angular Outliers modestly boosts classification metrics like accuracy, F1 Score, AUC-ROC, and AUC-PR across different proportions of synthetic data, highlighting the effectiveness of Quantum-SMOTEV2 in enhancing model performance for edge cases.

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Reference graph

Works this paper leans on

14 extracted references · 8 canonical work pages

  1. [5]

    Available from: https://arxiv.org/ abs/2402.17398

    Mohanty N, Behera BK, Ferrie C, Dash P.: A Quantum Approach to Synthetic Minority Oversampling Technique (SMOTE). Available from: https://arxiv.org/ abs/2402.17398

    arXiv

  2. [1]

    Learning from class-imbalanced data: Review of methods and applications

    Haixiang G, Yijing L, Shang J, Mingyun G, Yuanyue H, Bing G. Learning from class-imbalanced data: Review of methods and applications. Expert Systems with Applications. 2017;73:220–239. https://doi.org/https://doi.org/10.1016/j.eswa. 2016.12.035

    doi:10.1016/j.eswa 2017

  3. [2]

    Framework for imbalanced data classification

    Blaszczyk M, Jedrzejowicz J. Framework for imbalanced data classification. Pro- cedia Computer Science. 2021;192:3477–3486. https://doi.org/https://doi.org/ 10.1016/j.procs.2021.09.121

    work page doi:10.1016/j.procs.2021.09.121 2021

  4. [3]

    Research on expansion and classification of imbalanced data based on SMOTE algorithm

    Wang S, Dai Y, Shen J, Xuan J. Research on expansion and classification of imbalanced data based on SMOTE algorithm. Scientific Reports. 2021 36 Dec;11(1):24039. Number: 1 Publisher: Nature Publishing Group. https://doi. org/10.1038/s41598-021-03430-5

    work page doi:10.1038/s41598-021-03430-5 2021

  5. [4]

    SMOTE: Synthetic Minor- ity Over-sampling Technique

    Chawla NV, Bowyer KW, Hall LO, Kegelmeyer WP. SMOTE: Synthetic Minor- ity Over-sampling Technique. Journal of Artificial Intelligence Research. 2002 Jun;16:321–357. https://doi.org/10.1613/jair.953

    doi:10.1613/jair.953 2002

  6. [7]

    Available from: https://www.kaggle.com/datasets/ jpacse/datasets-for-churn-telecom

    : Telco Customer Churn. Available from: https://www.kaggle.com/datasets/ jpacse/datasets-for-churn-telecom

    work page

  7. [8]

    : Calculate Quantum Euclidean Distance with Qiskit. Medium. Available from: https://medium.com/qiskit/ calculate-quantum-euclidean-distance-with-qiskit-df85525ab485

    work page

  8. [9]

    Quantum Block-Matching Algorithm Using Dissimilarity Measure

    Mart ´ ınez-Felipe M, Montiel-P´ erez J, Onofre V, Maldonado-Romo A, Young R. Quantum Block-Matching Algorithm Using Dissimilarity Measure. In: Monti F, Plebani P, Moha N, Paik Hy, Barzen J, Ramachandran G, et al., editors. Service- Oriented Computing – ICSOC 2023 Workshops. Singapore: Springer Nature Singapore; 2024. p. 185–196

    work page 2023

Show all 14 references
  1. [10]

    Available from: https://www.kaggle.com/datasets/ blastchar/telco-customer-churn

    : Telco Customer Churn. Available from: https://www.kaggle.com/datasets/ blastchar/telco-customer-churn

  2. [11]

    Random Forests

    Breiman L. Random Forests. Machine Learning. 2001 Oct;45(1):5–32. https: //doi.org/10.1023/A:1010933404324

    2001 doi

  3. [12]

    Nearest neighbor pattern classification

    Cover T, Hart P. Nearest neighbor pattern classification. IEEE Transactions on Information Theory. 1967;13(1):21–27. https://doi.org/10.1109/TIT.1967. 1053964

    1967 doi

  4. [13]

    Available from: http://nbn-resolving.de/urn/resolver.pl?urn= nbn:de:bvb:19-epub-1769-9

    Hechenbichler K, Schliep K.: Weighted k-Nearest-Neighbor Techniques and Ordi- nal Classification. Available from: http://nbn-resolving.de/urn/resolver.pl?urn= nbn:de:bvb:19-epub-1769-9

  5. [14]

    Deep learning

    LeCun Y, Bengio Y, Hinton G. Deep learning. Nature. 2015 May;521(7553):436–444. https://doi.org/10.1038/nature14539

    2015 doi

  6. [15]

    A systematic study of the class imbalance problem in convolutional neural networks

    Buda M, Maki A, Mazurowski MA. A systematic study of the class imbalance problem in convolutional neural networks. Neural Networks. 2018;106:249–259. 37 https://doi.org/https://doi.org/10.1016/j.neunet.2018.07.011. 10 Supplementary Figures 10.1 Confusion matrix This section co...

    2018 doi

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