Quantum Variational Activation Functions Empower Kolmogorov-Arnold Networks

Quantum-inspired Kolmogorov–Arnold Networks (QKAN): Scalable, Efficient, and Expressive Neural Architectures

We present Quantum-inspired Kolmogorov–Arnold Networks (QKANs), a new neural architecture that unifies quantum variational circuits with learnable activation functions to deliver faster, more parameter-efficient, and highly expressive models. At the core of QKAN are Quantum Variational Activation Functions (QVAFs) implemented via single-qubit DatA Re-Uploading ActivatioNs (DARUANs). DARUANs exhibit an exponentially growing frequency spectrum with repeated data uploads, enabling dramatic reductions in parameter count compared to classical Fourier-based activations while preserving expressive power.

By embedding DARUANs into Kolmogorov–Arnold Networks (KANs), QKANs retain the interpretability of classical KANs while achieving superior generalization, efficiency, and scalability. To further enhance large-scale usability, we introduce Hybrid QKANs (HQKANs) as drop-in replacements for MLPs in deep architectures, including GPT-style models, reducing computational cost and memory usage without sacrificing performance.

We provide rigorous theoretical analysis and demonstrate QKAN’s effectiveness across regression, image classification, and autoregressive generative modeling tasks. Our fully open-source code and preprint make it easy for the community to experiment with quantum-inspired neural architectures.