Quantum Variational Activation Functions Empower Kolmogorov-Arnold
  Networks
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.
68cbd9024d15e6fae7acb3b2
Jiun-Cheng Jiang
claimed_verified
2025-09-18T13:25:25.267Z
68b93b3a6c86c127a199ad90
/avatars/f370d99b240ce5b9e1bfdbd3130d9ee4.svg
Jiun-Cheng Jiang
user
Jim137
68cbd9024d15e6fae7acb3b3
Morris Yu-Chao Huang
68cbd9024d15e6fae7acb3b4
Tianlong Chen
68cbd9024d15e6fae7acb3b5
Hsi-Sheng Goan
Quantum Variational Activation Functions Empower Kolmogorov-Arnold
  Networks
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.
Quantum variational activation functions (QVAFs) and quantum-inspired Kolmogorov-Arnold networks (QKANs) enhance parameter efficiency and expressivity in quantum machine learning, offering scalability and improved performance in various tasks.
variational quantum circuits Kolmogorov-Arnold networks quantum variational activation functions DARUANs frequency spectrum parameter efficiency expressivity generalization layer extension hybrid QKANs function regression image classification autoregressive generative language modeling NISQ hardware classical quantum simulators