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QuXAI: Explainers for Hybrid Quantum Machine Learning Models

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Q-MEDLEY, an explainer for hybrid quantum-classical models, obtains global feature importance by perturbing classical inputs and re-evaluating the quantum feature map on each perturbation.

desk verdict A sensible DCI+PI adaptation to HQML is undone by an evaluation that never exercises the quantum feature map; the idea deserves a careful rewrite, not a desk reject. read the letter →

arxiv 2505.10167 v3 pith:CF4RIYQ3 submitted 2025-05-15 cs.LG cs.AIquant-ph

Saikat Barua , Mostafizur Rahman , Shehenaz Khaled , Md Jafor Sadek , Rafiul Islam , Shahnewaz Siddique This is my paper · ORCID
classification cs.LGcs.AIquant-ph
keywords quantummachinelearningexplainableAIhybridquantum-classicalalgorithmsfeatureimportancedrop-columnpermutationencodingtrustworthy
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 proposes QuXAI, a framework for explaining hybrid quantum-classical machine learning (HQML) models in which classical features are first mapped into quantum states and then fed to a classical learner. Its central contribution is Q-MEDLEY, an explainer that measures global feature importance by perturbing classical inputs, re-running the quantum feature map on every perturbed input, and averaging drop-column and permutation importance scores. The authors argue that this re-evaluation step is what makes the attributions faithful to the hybrid data flow, rather than treating the whole pipeline as a black box. On amplitude-encoded HQML models over noisy versions of Iris, Wine, and other benchmark datasets, Q-MEDLEY assigns higher importance to original informative features than to synthetic noise and redundancies, and in classical validation settings its rankings agree with Decision Tree and Random Forest ground-truth importances about as well as established explainers. The claim matters because, if correct, it gives practitioners a way to see which original classical inputs drive a quantum-enhanced model's decisions.

What carries the argument

The central object is the Q-MEDLEY explainer, defined for HQML models $M_{\mathrm{HQCL}}(x)=M_{\mathrm{CL}}(f_Q(\Phi_Q(x)))$. For feature $j$, it computes $I_j = \frac{1}{2}(I^{\mathrm{DCI}}_j + I^{\mathrm{PI}}_j)$, where $I^{\mathrm{DCI}}_j$ is the drop in accuracy when the column is neutralized ($x_j \leftarrow 0$) and $I^{\mathrm{PI}}_j$ is the average accuracy drop over $K$ random permutations of that column. The load-bearing adaptation is that evaluation of the perturbed dataset always recomputes the quantum feature map $\Phi_Q(x')$ (amplitudes or kernel matrix) before the classical learner predicts, so perturbations propagate through the quantum stage exactly as real inputs would. The full version also adds adaptive weighting and an interaction-aware permutation importance, which the ablations credit for improved top-3 feature recovery.

What would settle it

Train a kernel-based HQML model on a synthetic dataset whose label is a known function of a single feature, run Q-MEDLEY on it, and check whether that feature receives the top importance score; the paper's own evaluation is almost entirely amplitude-encoded, so a failure on the kernel path would show the claimed generality does not hold.

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Extended reading notes

Core claim

The paper's central claim is that a composite perturbation explainer that explicitly re-evaluates the quantum feature map when inputs are altered can produce reliable global feature-importance rankings for HQML models of the form $M_{\mathrm{HQCL}}(x)=M_{\mathrm{CL}}(f_Q(\Phi_Q(x)))$. For each feature $j$, Q-MEDLEY computes a drop-column importance by neutralizing that feature and a permutation importance by shuffling it $K$ times, then averages the two. The critical design choice is that every perturbed input is passed through the quantum encoding $\Phi_Q$ (or through a recomputed kernel matrix) before the classical learner is asked to score it, so the importance score reflects the feature's influence through the whole hybrid pipeline. The paper reports that on amplitude-encoded models, Q-MEDLEY separates informative from noisy features, and in controlled classical benchmarks it reaches Recall@3 and Spearman correlations comparable to or better than single-method baselines and a tree-ensemble Shapley explainer. Ablations show that adding adaptive weighting of the two components and an interaction-aware permutation step improves top-3 recovery, with the full configuration reaching perfect Recall@3 on some dataset-model pairs.

Load-bearing premise

The evaluation treats feature importances derived from classical Decision Tree and Random Forest models trained on the same data as ground truth for what an HQML model should consider important; the authors note this proxy may not capture how feature influence is reshaped by the quantum encoding.

Editorial extensions

If this is right

  • Q-MEDLEY gives global feature importance for amplitude-encoded HQML models without treating the quantum stage as a black box.
  • It can separate original informative features from synthetic noise and redundancies across multiple datasets and ten classical learners.
  • In classical validation, Q-MEDLEY's Recall@3 and Spearman correlations are comparable to or better than DCI, PI, LogRegL1, and a tree-ensemble Shapley explainer.
  • Ablations show the full Q-MEDLEY (adaptive weighting plus interaction-aware PI) achieves the best top-3 feature recovery on several dataset-model pairs, including perfect scores.
  • The framework provides a route for HQML debugging: detecting when noisy or irrelevant features exert disproportionate influence on predictions.

Reading between the lines

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

  • If the classical-proxy validation is not faithful, the reported benchmarks mostly establish Q-MEDLEY as a strong classical explainer; its quantum-specific value remains to be shown on kernel-based HQML and on real quantum hardware with noise.
  • The same perturbation-through-encoding mechanism could be adapted to local, instance-level explanations by restricting perturbations to a single input.
  • Because each permutation requires re-evaluating the feature map, runtime grows linearly with the number of features and repeats; approximating the map's sensitivity analytically could make the explainer scalable to higher-dimensional inputs.
  • Q-MEDLEY scores could serve as a diagnostic for comparing quantum feature maps: maps that preserve the importance structure of the original features would score differently from maps that scramble it.
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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

3 major / 5 minor

Summary. The paper introduces QuXAI, a framework for training and explaining hybrid quantum-classical machine learning (HQML) models of two types: amplitude-encoded models, where classical inputs are mapped by a quantum feature map Phi_Q into state-vector amplitudes, and quantum-kernel models, where a fidelity kernel is fed to a classical learner. The central contribution is Q-MEDLEY, an explainer that computes global feature importance by averaging Drop-Column Importance and Permutation Importance, re-evaluating the quantum feature map for each perturbed input. The paper reports qualitative feature-importance bar charts for amplitude-encoded HQML models on noisy Iris and Wine datasets, quantitative comparisons against DCI, PI, TreeSHAP, and LogRegL1 on classical Decision Tree and Random Forest models, and an ablation study of Q-MEDLEY's components. The authors claim that Q-MEDLEY delineates influential classical features in HQML models, separates them from noise, and competes well with established XAI techniques.

Significance. If validated, Q-MEDLEY would address a real and currently underserved need: model-agnostic global feature attribution for HQML architectures that use quantum feature encoding followed by a classical learner. The paper has genuine strengths: the algorithmic formulation is explicit and reproducible (Eqs. (1)-(6), Algorithms 1-2), the idea of re-evaluating the quantum feature map or kernel after each perturbation is well motivated and correctly formalized, and the code is open-sourced. However, the quantitative evidence as presented does not exercise the quantum-specific path at all: the benchmark experiments in Section 4.2 and the ablations in Section 4.3 explain only classical Decision Tree and Random Forest models trained directly on raw features, with no quantum feature map present. The only experiments that involve a quantum feature map are evaluated by visual inspection. Because the central claimed capability is specifically about HQML models, the current significance is not established by the reported measurements.

major comments (3)
  1. [§4.2–4.3, Figs. 5–6, Table 1] The quantitative evaluation explains only classical Decision Tree and Random Forest models trained directly on raw features, so the quantum feature map Phi_Q of Eqs. (4)–(5) never appears in any measured result. In these experiments, Algorithm 1's PredictAdapted branch (lines 2–3) reduces to identity, and the distinctive re-evaluation of Phi_Q(x') on perturbed inputs (lines 9–16) is never exercised by a reported number. Consequently, the Recall@3 and Spearman results can support at most the generic DCI+PI aggregation, not the paper's central claim that Q-MEDLEY delineates influential classical aspects in HQML models. The authors' own limitation in Section 5.3, that reliance on classical interpretable models as proxies 'may not a perfect reflection of all the intricacies of feature influence in the quantum domain,' understates the gap: the issue is not proxy fidelity but the complete absence of a quantum component from the measured loop.
  2. [§4.3, Table 1] Table 1 shows that the full configuration Q-MEDLEY + AdaptiveWeighting + InteractionPI underperforms the baseline Q-MEDLEY (DCI+PI Avg) on Random Forest for Covtype (0.83 vs. 0.85) and for Diabetes (0.83 vs. 1.00); similarly, Q-MEDLEY with InteractionPI alone underperforms the baseline on RF-Covtype (0.84 vs. 0.85) and RF-Diabetes (0.89 vs. 1.00). This contradicts the Section 4.3 statements that adding components yields 'increasing performance' and that the full configuration 'could obtain the maximum or among the maximum Recall@3 scores.' These differences may be within noise, but no error bars or repeated runs are reported, so the claimed monotonic benefit of the composite structure is not supported by the table.
  3. [§4.1, Figs. 3–4] The only experiments that actually involve a quantum feature map are Figures 3 and 4, but these are assessed exclusively by visual inspection. No quantitative metric, no known ground-truth importance ordering, and no repeated-run variance are reported for these HQML models. Since the noisy and redundant features were synthetically added, a rank-correlation or top-k recall against the known importance structure could be computed for the amplitude-encoded HQML models, as the authors themselves do for the classical models in Section 4.2. Without such a measure, the claim that Q-MEDLEY 'separates their noise' in HQML settings is not quantitatively supported.
minor comments (5)
  1. [§4.2] The text uses 'Remember@3' where the metric is elsewhere called 'Recall@3'; the terminology should be made consistent.
  2. [§1, Contributions] The contribution list describes Q-MEDLEY as a 'global and local feature importance explainer,' but Section 3 defines only the global importance score I_j and no local, instance-level explanation method is described or evaluated anywhere in the manuscript. The claim should be amended to 'global' unless a local method is actually provided.
  3. [§5.3] The limitation paragraph notes that kernel-based HQML results 'were not vast,' but in fact no quantitative kernel-based experiments are reported at all. This should be stated plainly, given that the kernel branch of Algorithm 1 is part of the claimed contribution.
  4. [General] The manuscript contains numerous grammatical and typographical errors ('an framework,' 'purposedly,' 'remonstrating,' 'the abundance of medley scores,' and several incomplete or run-on sentences). A careful copy-edit is needed.
  5. [§3.2–3.3] Details needed for reproducibility are missing for the HQML experiments, including the number of qubits, the specific form of U_j(x_j) in Eq. (4), the simulation backend, and dataset sizes after the noise injection. Since the code is open-sourced, adding these parameters in the text or an appendix would make the experiments independently checkable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Q-MEDLEY's importance scores are defined directly from perturbation-induced accuracy changes, not from parameters fitted to the claims, and the self-citation to KAXAI is not load-bearing.

full rationale

The paper's derivation chain is self-contained for its core method. Q-MEDLEY importance scores are computed by Equations (1)-(3) and Algorithm 1 directly from accuracy differences after feature neutralization and permutation, with no free parameters fitted to the validation ground truth. The only numerical validations in Section 4.2 and Table 1 are performed on classical Decision Tree and Random Forest models, which the paper explicitly acknowledges in Section 5.3 as imperfect proxies for quantum-domain feature influence; this is a limitation of scope, not circular reasoning. The self-citation to KAXAI [26] introduces the MEDLEY concept of combining DCI and PI, but the hybrid-quantum adaptation (re-evaluating the feature map ΦQ for each perturbation, Algorithm 1 lines 2-4 and Section 3.2) is independently specified and implemented, and the claim of explaining HQML models is supported by direct visual inspection of Figures 3-4. No equation is defined in terms of another, and no fitted parameter is renamed as a prediction. Thus, no circular step is found.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The core Q-MEDLEY score is parameter-free once DCI and PI are defined, but the claimed improved variants are underspecified and may carry hidden fitted parameters. The validation relies on an acknowledged proxy assumption about classical ground-truth importances, and the simulation setup assumes no hardware noise.

free parameters (2)
  • Adaptive weighting coefficients = not reported
    Table 1 and Section 4.3 attribute improved Recall@3 to AdaptiveWeighting and InteractionPI, but Section 3 defines no formulas or fitting procedure for these components. If the weights are selected per dataset or learned to maximize the reported metric, they are free parameters.
  • Permutation repeats K = 5
    Permutation Importance is evaluated with K=5 in Figures 5 and 6 and in the ablation study. The sensitivity of the results to K is not reported, and K is a hand-chosen experimental constant that could affect the stability of the importance scores.
assumptions (3)
  • domain assumption Trained classical model intrinsic importances (e.g., Gini importance) are a valid ground truth for feature importance in HQML models.
    Used in Sections 4.2 and 4.3 for Recall@3 and Spearman validation; authors acknowledge in Section 5.3 that this proxy may not capture quantum-domain feature influence.
  • domain assumption Accuracy on the reference dataset is a sufficient fidelity measure for feature attribution.
    Equations (1)-(3) define importance as changes in accuracy; alternative metrics (F1, calibration, loss) could yield different attributions, and no sensitivity analysis is given.
  • domain assumption The simulated amplitude-encoded quantum feature map faithfully represents the quantum processing without hardware noise.
    All HQML experiments appear to use classical simulation of statevector amplitudes; real quantum hardware noise and finite-shot sampling are not included, despite noise being a stated motivation.

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Pith. "Pith review of QuXAI: Explainers for Hybrid Quantum Machine Learning Models." pith.science (2026). https://pith.science/paper/CF4RIYQ3

@misc{pith2026250510167,
  author       = {Pith},
  title        = {Pith review of: QuXAI: Explainers for Hybrid Quantum Machine Learning Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CF4RIYQ3}},
  note         = {Machine review of arXiv:2505.10167}
}
read the original abstract

The emergence of hybrid quantum-classical machine learning (HQML) models opens new horizons of computational intelligence but their fundamental complexity frequently leads to black box behavior that undermines transparency and reliability in their application. Although XAI for quantum systems still in its infancy, a major research gap is evident in robust global and local explainability approaches that are designed for HQML architectures that employ quantized feature encoding followed by classical learning. The gap is the focus of this work, which introduces QuXAI, an framework based upon Q-MEDLEY, an explainer for explaining feature importance in these hybrid systems. Our model entails the creation of HQML models incorporating quantum feature maps, the use of Q-MEDLEY, which combines feature based inferences, preserving the quantum transformation stage and visualizing the resulting attributions. Our result shows that Q-MEDLEY delineates influential classical aspects in HQML models, as well as separates their noise, and competes well against established XAI techniques in classical validation settings. Ablation studies more significantly expose the virtues of the composite structure used in Q-MEDLEY. The implications of this work are critically important, as it provides a route to improve the interpretability and reliability of HQML models, thus promoting greater confidence and being able to engage in safer and more responsible use of quantum-enhanced AI technology. Our code and experiments are open-sourced at: https://github.com/GitsSaikat/QuXAI

Figures

Figures reproduced from arXiv: 2505.10167 by the authors.

Figure 1
Figure 1. Citation network map illustrating the relationships and thematic clustering of key research papers relevant to [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Overall workflow of the QuXAI framework, illustrating the sequential stages from data preparation, through [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Q-MEDLEY scores for ten different amplitude-encoded HQML models trained on the Noisy Iris dataset. [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Q-MEDLEY scores for ten different amplitude-encoded HQML models trained on the Noisy Wine dataset. [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Recall@3 comparison of explainers (DCI, PI (k=5), Q-MEDLEY, TreeSHAP) on the Noisy Iris dataset for [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: Spearman Rank Correlation heatmap comparing feature importance rankings from different explainers (DCI, [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

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