On the Complementarity of Quantum and Classical Features: Adaptive Hybrid Quantum-Classical Feature Fusion for Breast Cancer Classification

Jo\~ao Paulo Papa; Jo\~ao Renato Ribeiro Manesco; Yasmin Rodrigues Sobrinho

arxiv: 2604.22903 · v1 · submitted 2026-04-24 · 💻 cs.CV · cs.AI

On the Complementarity of Quantum and Classical Features: Adaptive Hybrid Quantum-Classical Feature Fusion for Breast Cancer Classification

Yasmin Rodrigues Sobrinho , Jo\~ao Renato Ribeiro Manesco , Jo\~ao Paulo Papa This is my paper

Pith reviewed 2026-05-08 12:21 UTC · model grok-4.3

classification 💻 cs.CV cs.AI

keywords hybrid quantum-classicalfeature fusionbreast cancer classificationquantum machine learningdeep learningBreastMNISTmedical image analysistemperature scaling

0 comments

The pith

A hybrid quantum-classical model with temperature-scaled fusion improves breast cancer image classification over classical baselines.

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

The paper builds a dual-branch pipeline that extracts features from both classical deep networks and quantum circuits for classifying breast cancer images from the BreastMNIST dataset. It introduces three fusion methods and shows that a temperature-scaled variant, which adds a learnable scalar to balance gradients, produces the strongest results when paired with a ResNet backbone and trainable quantum circuit. The approach aims to let the two paradigms supply genuinely different information without one branch dominating training. A sympathetic reader would care because the results point to a concrete way of adding quantum components to medical imaging systems that already use standard neural networks.

Core claim

The authors introduce a dual-branch hybrid architecture that extracts and unifies complementary representations from classical models and quantum circuits using three progressive fusion strategies. The novel Temperature-Scaled Hybrid Fusion (TSHF) incorporates a learnable scalar to dynamically balance hybrid gradient dynamics and resolves optimization asymmetries. When pairing a ResNet backbone with a trainable quantum circuit, TSHF achieves 87.82% accuracy, 91.77% F1-score, and 89.08% AUC-ROC on BreastMNIST, outperforming purely classical baselines and demonstrating that unifying diverse feature representations creates a richer data context for classification.

What carries the argument

Temperature-Scaled Hybrid Fusion (TSHF), which inserts a learnable scalar parameter to balance gradient flow between classical and quantum feature embeddings during joint training.

If this is right

Pairing a ResNet backbone with a trainable quantum circuit through TSHF yields higher classification accuracy than classical-only models on BreastMNIST.
The learnable scalar in TSHF resolves optimization asymmetries between hybrid branches during end-to-end training.
Hybrid models improve both raw accuracy and threshold reliability for potential clinical use.
Static, dynamic, and temperature-scaled fusion can each be tested to find the best balance for a given classical-quantum pairing.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same learnable scalar technique could be tested in other hybrid or multimodal settings to prevent one modality from dominating gradients.
Performance differences may shrink or grow on larger or more diverse medical imaging collections, since the current gains are measured only on BreastMNIST.
If the complementarity assumption holds, the framework offers a practical route to test quantum feature extractors inside existing deep-learning pipelines without replacing the entire system.

Load-bearing premise

The quantum circuit branch supplies information that is genuinely complementary to the classical branch and the fusion strategies can balance the two without creating new optimization instabilities or overfitting on this dataset.

What would settle it

Retraining the identical architecture after replacing the quantum circuit with a classical sub-network of matched parameter count and observing whether the accuracy, F1, and AUC gains disappear.

Figures

Figures reproduced from arXiv: 2604.22903 by Jo\~ao Paulo Papa, Jo\~ao Renato Ribeiro Manesco, Yasmin Rodrigues Sobrinho.

**Figure 1.** Figure 1: Quantum circuit architecture utilized in the proposed quanvolutional layer. view at source ↗

**Figure 2.** Figure 2: Schematic of the hybrid model featuring a non-trainable quantum circuit for the view at source ↗

**Figure 3.** Figure 3: Schematic of the hybrid model featuring a trainable quantum circuit for the view at source ↗

**Figure 4.** Figure 4: Schematic of the SHF strategy, where features are extracted offline and fusion view at source ↗

**Figure 5.** Figure 5: Schematic of the DHF strategy, illustrating the end-to-end gradient flow through view at source ↗

**Figure 6.** Figure 6: Schematic of the TSHF strategy, featuring the learnable scalar view at source ↗

**Figure 7.** Figure 7: Sample images from the BreastMNIST, INbreast, and BUS-UCLM datasets used view at source ↗

**Figure 8.** Figure 8: F1-Score learning curves for classical and quantum baseline models on BreastM view at source ↗

**Figure 9.** Figure 9: ROC curves for classical and quantum baseline models, showing classification view at source ↗

**Figure 10.** Figure 10: F1-Score learning curves comparison across the three proposed hybrid fusion view at source ↗

**Figure 11.** Figure 11: Combined F1-Score learning curves for final performance overview on BreastM view at source ↗

**Figure 12.** Figure 12: ROC curves comparison across the three proposed hybrid fusion strategies on view at source ↗

**Figure 13.** Figure 13: UMAP feature space comparison for hybrid fusion strategies using a ResNet-18 view at source ↗

read the original abstract

The integration of quantum machine learning with classical deep learning offers promising avenues for medical image analysis by mapping data into high-dimensional Hilbert spaces. However, effectively unifying these distinct paradigms remains challenging due to common optimization asymmetries. In this paper, a novel hybrid quantum-classical architecture for breast cancer diagnosis based on a dual-branch feature-extraction pipeline is proposed. Our framework extracts and unifies complementary representations from classical models and quantum circuits, exploring both trainable and deterministic (non-trainable) quantum paradigms. To integrate these embeddings, three progressive feature fusion strategies are introduced: Static Hybrid Fusion (SHF) for offline extraction, Dynamic Hybrid Fusion (DHF) for end-to-end co-adaptation, and a novel Temperature-Scaled Hybrid Fusion (TSHF). The TSHF strategy incorporates a learnable scalar, inspired by multimodal learning, that dynamically balances hybrid gradient dynamics and resolves optimization bottlenecks. Empirical validation on the BreastMNIST dataset confirms our hypothesis that unifying diverse feature representations creates a richer data context. The TSHF strategy, specifically when pairing a ResNet backbone with a trainable quantum circuit, achieved a peak accuracy of 87.82%, F1-score of 91.77%, and an AUC-ROC of 89.08%, outperforming purely classical baselines. These results demonstrate that the proposed hybrid framework improves classification accuracy and threshold reliability, providing a stable, high-performance architecture for the clinical deployment of quantum-enhanced diagnostic tools.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper adds a learnable temperature scalar to hybrid quantum-classical fusion and reports peak gains on BreastMNIST, but single-run numbers without variance or tests leave the complementarity claim unconvincing.

read the letter

The main takeaway is that a temperature-scaled fusion (TSHF) between a ResNet branch and a trainable quantum circuit reaches 87.82% accuracy, 91.77% F1, and 89.08% AUC on BreastMNIST, beating the classical baseline. The authors also compare static and dynamic fusion variants and test both trainable and fixed quantum circuits. That is the concrete new piece: the learnable scalar meant to balance gradient scales across the two branches, borrowed from multimodal work but applied here to resolve optimization asymmetry in a medical imaging task. The paper does a clean job laying out the three fusion strategies and showing that the hybrid setup can improve threshold reliability on this dataset. The experiments are straightforward and use a public benchmark, which makes the comparison easy to follow. The soft spot is the evaluation. The numbers are given as single peaks with no means, standard deviations, or statistical tests across seeds. BreastMNIST is small, and the hybrid model adds parameters and training degrees of freedom, so run-to-run fluctuation or overfitting cannot be ruled out. The abstract also omits circuit depth, simulation details, and hyperparameter choices, which makes it hard to judge whether the reported complementarity is robust. This paper is aimed at researchers already working on hybrid quantum-classical models for computer vision or medical imaging. A reader in that niche can pick up the fusion variants and see how the temperature trick performs in practice, but the work will not shift broader understanding of quantum features. It deserves a serious referee because the idea is specific, the dataset is public, and the empirical claim is falsifiable once the missing statistics and ablations are supplied. I would send it to review with a request for multi-seed results and clearer implementation details.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes a dual-branch hybrid quantum-classical architecture for breast cancer classification on BreastMNIST. Classical backbones (e.g., ResNet) and quantum circuits (trainable or deterministic) extract features that are fused via Static Hybrid Fusion (SHF), Dynamic Hybrid Fusion (DHF), or the novel Temperature-Scaled Hybrid Fusion (TSHF) that introduces a learnable scalar to balance gradient dynamics and resolve optimization asymmetries. The central claim is that TSHF with a ResNet backbone and trainable quantum circuit yields peak performance of 87.82% accuracy, 91.77% F1-score, and 89.08% AUC-ROC, outperforming purely classical baselines.

Significance. If the performance gains are shown to be statistically robust, the work would demonstrate a practical route to leveraging quantum feature spaces for medical imaging while addressing training instabilities common in hybrid models. The TSHF mechanism, inspired by multimodal scaling, offers a concrete, low-overhead technique that could generalize beyond this dataset.

major comments (2)

[Abstract / Empirical validation] Abstract and empirical validation: the reported peak metrics (87.82% accuracy, 91.77% F1, 89.08% AUC) are single-run values with no means, standard deviations, multi-seed averages, or paired statistical tests. On a small dataset (~780 training images) where hybrid models introduce additional parameters and optimization degrees of freedom, this omission is load-bearing for the outperformance claim and prevents distinguishing complementarity from run-to-run fluctuation.
[Methodology (quantum circuit)] Quantum branch description: no information is given on qubit count, circuit depth, ansatz, gate set, or simulation method (exact vs. approximate, backend). Without these, it is impossible to assess whether the quantum features are genuinely complementary or to reproduce the claimed hybrid advantage.

minor comments (1)

[Abstract] The abstract introduces SHF, DHF, and TSHF but does not provide even one-sentence characterizations of each; adding brief definitions would improve readability for readers unfamiliar with the fusion variants.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment below and will revise the manuscript accordingly to strengthen the empirical validation and reproducibility.

read point-by-point responses

Referee: [Abstract / Empirical validation] Abstract and empirical validation: the reported peak metrics (87.82% accuracy, 91.77% F1, 89.08% AUC) are single-run values with no means, standard deviations, multi-seed averages, or paired statistical tests. On a small dataset (~780 training images) where hybrid models introduce additional parameters and optimization degrees of freedom, this omission is load-bearing for the outperformance claim and prevents distinguishing complementarity from run-to-run fluctuation.

Authors: We agree that single-run metrics are insufficient to substantiate the outperformance claims, particularly on the small BreastMNIST training set and with the added optimization complexity of hybrid models. In the revised manuscript we will repeat all experiments over multiple random seeds, report mean and standard deviation for accuracy, F1-score and AUC-ROC, and include paired statistical tests (e.g., t-tests) against the classical baselines. This will provide the necessary evidence that the observed gains reflect genuine complementarity rather than stochastic variation. revision: yes
Referee: [Methodology (quantum circuit)] Quantum branch description: no information is given on qubit count, circuit depth, ansatz, gate set, or simulation method (exact vs. approximate, backend). Without these, it is impossible to assess whether the quantum features are genuinely complementary or to reproduce the claimed hybrid advantage.

Authors: We acknowledge that the original manuscript omitted the required technical specifications for the quantum branch. The revised version will explicitly state the qubit count, circuit depth, ansatz, gate set, and simulation backend/method employed, thereby enabling reproducibility and allowing readers to evaluate the degree of feature complementarity. revision: yes

Circularity Check

0 steps flagged

No circularity: results are empirical performance metrics on public dataset

full rationale

The paper proposes hybrid architectures (SHF, DHF, TSHF) and reports peak accuracy/F1/AUC numbers from training on BreastMNIST. No derivation chain, first-principles equations, or predictions are claimed; the central claims are measured outcomes of model training and evaluation. No self-definitional loops, fitted parameters renamed as predictions, or load-bearing self-citations that reduce the reported metrics to tautologies. The architecture choices and fusion strategies are independent design decisions whose value is assessed externally via classification performance.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that quantum and classical feature spaces are complementary and that the learnable temperature scalar can balance their gradients. No new physical entities are postulated; the quantum circuit is treated as a standard variational ansatz.

free parameters (1)

learnable temperature scalar in TSHF
A scalar parameter introduced to dynamically balance hybrid gradient dynamics during end-to-end training.

axioms (2)

domain assumption Quantum circuits can extract features complementary to classical CNNs for image classification tasks
Invoked when claiming that unifying representations creates a richer data context.
standard math Standard supervised classification loss and backpropagation apply without modification to the hybrid model
Implicit in the end-to-end training of DHF and TSHF.

pith-pipeline@v0.9.0 · 5572 in / 1412 out tokens · 24491 ms · 2026-05-08T12:21:49.537828+00:00 · methodology

discussion (0)

Reference graph

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