用量子启发方法让KAN模型更少参数、更强性能，尤其适合周期函数。
QuIRK: Quantum-Inspired Re-uploading KAN
- 用单量子比特数据重载电路替代B-Spline，实现函数逼近
- 参数量更少，在周期函数上性能超越传统KAN
- 保持可解释性，能生成闭式解析表达式，适合科学建模
Kolmogorov-Arnold网络（KAN）在科学领域回归任务中表现出色，以远少于传统深度神经网络的可训练参数实现高性能，且因其由一元B-Spline函数构成，具备良好可解释性，可从中推导出广泛问题的闭式方程。本文提出一种受量子启发的KAN变体——量子数据重载KAN（QuIRK），将一元函数逼近器从B-Spline替换为单量子比特数据重载（DR）模型。该设计使模型在参数更少的情况下仍能匹配或超越传统KAN性能，尤其在周期函数建模上表现突出。由于仅使用单量子比特电路，模型仍可通过普通GPU高效模拟，具有经典可计算性。此外，实验表明QuIRK保留了原KAN的可解释性优势，能够生成闭式解。
原文摘要 · Abstract (English)
Kolmogorov-Arnold Networks or KANs have shown the ability to outperform classical Deep Neural Networks, while using far fewer trainable parameters for regression problems on scientific domains. Even more powerful has been their interpretability due to their structure being composed of univariate B-Spline functions. This enables us to derive closed-form equations from trained KANs for a wide range of problems. This paper introduces a quantum-inspired variant of the KAN based on Quantum Data Re-uploading (DR) models. The Quantum-Inspired Re-uploading KAN or QuIRK model replaces B-Splines with single-qubit DR models as the univariate function approximator, allowing them to match or outperform traditional KANs while using even fewer parameters. This is especially apparent in the case of periodic functions. Additionally, since the model utilizes only single-qubit circuits, it remains classically tractable to simulate with straightforward GPU acceleration. Finally, we also demonstrate that QuIRK retains the interpretability advantages and the ability to produce closed-form solutions.
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