QuIRK: Quantum-Inspired Re-uploading KAN

2025-10-09

AI Summary

To address the high parameter count and low efficiency of Kolmogorov–Arnold Networks (KANs) in modeling periodic functions, this work proposes QuIRK—a quantum-inspired KAN variant. Methodologically, QuIRK replaces conventional B-spline basis functions with single-qubit variational data re-uploading circuits, preserving KAN’s inherent interpretability and enabling closed-form analytical expression extraction. This constitutes the first integration of quantum data re-uploading into the KAN architecture, implemented via GPU-accelerated classical simulation for efficient training. Experimental results demonstrate that QuIRK matches or surpasses standard KANs in multivariate regression tasks—particularly excelling in periodic function approximation—while reducing trainable parameters by 30–50%. Crucially, it retains full support for symbolic expression derivation, thereby jointly optimizing accuracy, computational efficiency, and model interpretability.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

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.

Problem

• Enhancing KAN performance with quantum-inspired re-uploading
• Reducing parameters while maintaining interpretability in networks
• Improving periodic function modeling with classical tractability

Innovation

• Replaces B-Splines with single-qubit quantum models
• Uses fewer parameters than traditional KAN networks
• Remains classically tractable with GPU simulation