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Hybrid Quantum-inspired Kolmogorov-Arnold Networks for Privacy-Aware Federated Biosignal Learning

This paper proposes a hybrid quantum-inspired Kolmogorov-Arnold network (HQKAN) for privacy-aware federated ECG classification, demonstrating that it outperforms traditional multilayer perceptrons in accuracy and robustness while significantly reducing trainable parameters and communication costs across diverse client configurations.

Original authors: Chun-Hua Lin, Samuel Yen-Chi Chen, Yu-Chao Hsu, Kuo-Chung Peng, Jiun-Cheng Jiang, Chi-Sheng Chen, Tai-Yue Li, Nan-Yow Chen, En-Jui Kuo, Hsi-Sheng Goan

Published 2026-08-17

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Chun-Hua Lin, Samuel Yen-Chi Chen, Yu-Chao Hsu, Kuo-Chung Peng, Jiun-Cheng Jiang, Chi-Sheng Chen, Tai-Yue Li, Nan-Yow Chen, En-Jui Kuo, Hsi-Sheng Goan

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where your heart's secret diary—the electrical rhythm that beats inside your chest—is locked in a vault at your local hospital, another vault at a wearable watch company, and yet another at a research clinic. These diaries are too precious and private to be copied and pasted into one giant central library, because that would risk exposing your personal health secrets. This is the problem of Federated Learning: a clever way for computers to learn together without ever seeing each other's private data. Instead of sending the raw heartbeats, the computers send only the "lessons learned" (mathematical updates) back and forth.

However, there's a catch. Sending these lessons takes time and bandwidth, like trying to mail a heavy encyclopedia when you only have a small envelope. Also, the data is messy; some clients have thousands of heartbeats, while others have just a few, and some heart conditions are rare "needle-in-a-haystack" events. To solve this, scientists are exploring Quantum-Inspired models. These aren't running on actual quantum computers (which are still very experimental and noisy), but they borrow the mathematical tricks of quantum physics to build models that are incredibly small and efficient. Think of it as using the blueprint of a super-lightweight spaceship to build a bicycle that can still fly. The big question is: Can these tiny, quantum-inspired bicycles carry the heavy load of learning from private heart data better than the standard, heavy trucks we usually use?

The Heart of the Matter: A Race Between a Heavy Truck and a Quantum Bicycle

In this study, the researchers set up a high-stakes race to see if a new type of AI model, called a Hybrid Quantum-inspired Kolmogorov–Arnold Network (HQKAN), could beat the standard workhorse model, a Multilayer Perceptron (MLP), at the job of spotting heart arrhythmias (irregular heartbeats).

The race took place in a "Federated" arena, meaning the models had to learn from data that stayed scattered across different "clients" (simulating different hospitals or devices) without ever moving the raw data. They tested this on two famous heart datasets: MIT-BIH (with five types of heartbeats) and INCART (with three types). The goal was to see who could classify these heartbeats accurately while keeping the "envelope" (the data sent back and forth) as small as possible.

The Heavy Truck vs. The Quantum Bicycle

The standard model, the MLP, is like a heavy, reliable truck. It works well, but it's bulky. To get it to learn, you have to send a massive amount of information back and forth between the server and the clients.

The challenger, the HQKAN, is the "quantum bicycle." It uses a special architecture inspired by quantum mechanics, specifically using something called Data Re-Uploading Activation (DARUAN). Instead of fixed, rigid gears, it uses flexible, learnable functions that can twist and turn to fit the data perfectly. Because of this clever design, the HQKAN is incredibly compact.

The results were surprising and clear: The bicycle won the race.

The Scoreboard: Smaller, Faster, and Smarter

When the researchers ran the simulations with 8, 16, and 32 different clients, the HQKAN consistently outperformed the heavy MLP truck, especially when the data was messy and uneven (a scenario called "non-IID," where some clients have very different data than others).

Here is exactly how much better the HQKAN did, according to the numbers in the paper:

On the MIT-BIH dataset:
- The HQKAN used 37.35% fewer trainable parameters than the MLP.
- It reduced the communication cost (the size of the "envelope" sent over the network) by 24.89%.
- In terms of performance, it achieved higher scores for spotting the rare, tricky heartbeats (the minority classes) and had a lower "Brier score" (a measure of how confident and accurate the predictions were).
On the INCART dataset:
- The HQKAN was even more efficient, using 44.81% fewer trainable parameters.
- It cut the communication cost by 36.41%.
- Just like on the other dataset, it maintained stronger performance even when the clients had very different data distributions.

Why the Bicycle Won

The paper suggests that the HQKAN's secret weapon is its ability to stay robust when the data is fragmented. As the number of clients increased (making the data more scattered), the MLP's performance started to wobble, but the HQKAN held its ground.

For example, on the MIT-BIH dataset with 32 clients, the HQKAN achieved a macro-F1 score (a measure of overall balance between different heartbeat types) of 0.761, while the MLP only managed 0.698. This gap actually grew as the number of clients increased, suggesting that the more fragmented the network becomes, the more the HQKAN shines.

The researchers also looked at how well the models handled "label skew"—a situation where one client might have mostly normal heartbeats and another has mostly rare, dangerous ones. They simulated this using a "Dirichlet distribution" with different concentration parameters (like $\alpha = 0.3$ ). Even in these difficult, skewed scenarios, the HQKAN consistently showed higher AUROC and AUPRC scores (metrics that measure how well a model distinguishes between classes) compared to the MLP.

The Verdict

The paper concludes that you don't have to sacrifice speed or efficiency to get robustness. The HQKAN proves that a compact, communication-efficient model can actually be better at learning from private, scattered heart data than the traditional, bulky models.

It's not a magic cure-all, and these results are based on simulations using existing datasets, but the findings suggest a promising new direction. By borrowing the structural elegance of quantum-inspired math, we might be able to build AI systems that respect our privacy, save our bandwidth, and still catch those rare, dangerous heartbeats with a keen eye. The heavy truck is still useful, but for the future of privacy-aware heart monitoring, the quantum bicycle looks like the vehicle of choice.

Technical Summary: Hybrid Quantum-inspired Kolmogorov–Arnold Networks for Privacy-Aware Federated Biosignal Learning

Problem Statement
Electrocardiogram (ECG) data is critical for arrhythmia screening but presents significant privacy challenges due to its sensitivity and distribution across disparate institutions and devices. While Federated Learning (FL) addresses privacy by keeping raw data local and exchanging only model updates, its application to ECG classification faces three primary hurdles: limited client-side samples, severe class imbalance (e.g., rare arrhythmia types), and non-independent and identically distributed (non-IID) data across clients. These constraints necessitate classifiers that are not only accurate but also communication-efficient and robust to distribution shifts. Furthermore, standard deep learning models often incur high communication overhead due to large parameter counts, which is a bottleneck in FL environments.

Methodology
The authors propose and evaluate a Hybrid Quantum-inspired Kolmogorov–Arnold Network (HQKAN) as a lightweight alternative to the standard Multilayer Perceptron (MLP) for federated ECG classification.

Architecture: The HQKAN utilizes a hybrid autoencoder-like structure comprising a fully connected encoder and decoder, with a Quantum-inspired Kolmogorov–Arnold Network (QKAN) serving as the latent feature processor. Unlike conventional MLPs that use fixed activation functions, QKANs employ Data Re-Uploading ActivatioN (DARUAN) edge functions, which utilize trainable single-qubit circuits to replace fixed spline activations. This design is inspired by quantum machine learning (QML) principles but operates on classical hardware without requiring noisy intermediate-scale quantum (NISQ) devices.
Experimental Setup: The study benchmarks HQKAN against an MLP baseline under the Federated Averaging (FedAvg) protocol. Experiments were conducted on two datasets:
- MIT-BIH: Five-class arrhythmia classification (N, S, V, F, Q) with a highly imbalanced distribution (approx. 113:1 ratio between majority and rarest classes).
- INCART: Three-class classification (N, S, V).
Federated Configuration: Models were trained across varying client counts ( $K \in \{8, 16, 32\}$ ) under both Independent and Identically Distributed (IID) and non-IID settings. The non-IID scenarios were generated using a Dirichlet distribution with concentration parameters ( $\alpha$ ) ranging from 0.1 to 1000 to simulate varying degrees of label skew.
Training Constraints: Both models were trained under identical budgets (30 global rounds, 5 local epochs per round) using AdamW optimization. To address class imbalance, cross-entropy loss was weighted by inverse class frequency. Model selection was based on maximizing the macro-averaged Area Under the Precision-Recall Curve (AUPRC) on a held-out validation set.

Key Contributions and Results
The paper demonstrates that HQKAN offers a parameter-efficient and robust alternative to MLPs in federated biosignal learning.

Parameter and Communication Efficiency:
- On the MIT-BIH dataset, HQKAN reduced trainable parameters by 37.35% (11,581 vs. 18,485 for MLP) and lowered per-round communication costs by 24.89%.
- On the INCART dataset, HQKAN reduced trainable parameters by 44.81% (15,147 vs. 27,443 for MLP) and communication costs by 36.41%.
- These reductions are critical for FL, as the total parameter count directly dictates communication overhead.
Aggregate Performance:
- Across both datasets and all client configurations (IID and non-IID), HQKAN consistently outperformed the MLP baseline in aggregate metrics, including macro-F1, Cohen's $\kappa$ , and Brier score.
- The performance gap widened as the number of clients increased (fragmentation) and under non-IID conditions. For instance, in the 32-client non-IID MIT-BIH setting, HQKAN achieved a macro-F1 of 0.761 compared to 0.698 for MLP, while reducing the Brier score from 0.121 to 0.094.
Minority-Class and Robustness:
- HQKAN showed superior performance on minority classes (e.g., S, V, F in MIT-BIH; S in INCART), achieving higher mean sensitivity and positive predictive value (PPV) in several non-IID scenarios.
- Robustness tests against client heterogeneity (measured by Hellinger distance) revealed that HQKAN maintained higher mean AUROC and AUPRC than MLP across all levels of label skew. Notably, as label skew increased (higher Hellinger distance), the performance of the MLP declined more sharply than that of HQKAN, particularly in AUPRC.

Significance and Claims
The authors conclude that HQKAN provides a compact, communication-efficient, and robust solution for privacy-aware federated learning on biosignal data. The study claims that the robustness required to handle client heterogeneity and data imbalance in federated settings need not come at the expense of model or communication efficiency. By leveraging the structural features of quantum-inspired models (specifically the DARUAN mechanism), HQKAN achieves stronger predictive performance with significantly fewer trainable parameters and lower communication costs compared to conventional MLP baselines. This suggests that hybrid quantum-inspired architectures are a viable and effective pathway for deploying scalable, privacy-preserving medical AI systems.

The Heart of the Matter: A Race Between a Heavy Truck and a Quantum Bicycle

The Heavy Truck vs. The Quantum Bicycle

The Scoreboard: Smaller, Faster, and Smarter

Why the Bicycle Won

The Verdict

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