量子變分激活函數賦能科爾莫戈羅夫-阿諾德網路
Quantum Variational Activation Functions Empower Kolmogorov-Arnold Networks
September 17, 2025
作者: Jiun-Cheng Jiang, Morris Yu-Chao Huang, Tianlong Chen, Hsi-Sheng Goan
cs.AI
摘要
變分量子電路（VQCs）是量子機器學習的核心，而最近在科爾莫戈羅夫-阿諾德網絡（KANs）方面的進展則凸顯了可學習激活函數的強大能力。我們通過引入量子變分激活函數（QVAFs）來統一這兩個方向，這些函數通過稱為數據重上傳激活網絡（DARUANs）的單量子比特數據重上傳電路實現。我們展示了在數據預處理中具有可訓練權重的DARUAN，其頻譜隨著數據重複次數呈指數增長，從而實現了與基於傅里葉的激活函數相比的參數規模指數級減少，且不損失表達能力。將DARUAN嵌入KANs中，產生了量子啟發的KANs（QKANs），它們保留了KANs的可解釋性，同時提高了參數效率、表達能力和泛化能力。我們進一步引入了兩種新技術來增強可擴展性、可行性和計算效率，例如層擴展和混合QKANs（HQKANs），作為大規模模型中前饋網絡的多層感知器（MLPs）的即插即用替代方案。我們提供了理論分析和在函數回歸、圖像分類和自回歸生成語言建模方面的廣泛實驗，展示了QKANs的效率和可擴展性。DARUANs和QKANs為在噪聲中尺度量子（NISQ）硬件和經典量子模擬器上推進量子機器學習提供了一個有前景的方向。
English
Variational quantum circuits (VQCs) are central to quantum machine learning,
while recent progress in Kolmogorov-Arnold networks (KANs) highlights the power
of learnable activation functions. We unify these directions by introducing
quantum variational activation functions (QVAFs), realized through single-qubit
data re-uploading circuits called DatA Re-Uploading ActivatioNs (DARUANs). We
show that DARUAN with trainable weights in data pre-processing possesses an
exponentially growing frequency spectrum with data repetitions, enabling an
exponential reduction in parameter size compared with Fourier-based activations
without loss of expressivity. Embedding DARUAN into KANs yields
quantum-inspired KANs (QKANs), which retain the interpretability of KANs while
improving their parameter efficiency, expressivity, and generalization. We
further introduce two novel techniques to enhance scalability, feasibility and
computational efficiency, such as layer extension and hybrid QKANs (HQKANs) as
drop-in replacements of multi-layer perceptrons (MLPs) for feed-forward
networks in large-scale models. We provide theoretical analysis and extensive
experiments on function regression, image classification, and autoregressive
generative language modeling, demonstrating the efficiency and scalability of
QKANs. DARUANs and QKANs offer a promising direction for advancing quantum
machine learning on both noisy intermediate-scale quantum (NISQ) hardware and
classical quantum simulators.