Quantum-inspired activation functions and quantum Chebyshev-polynomial network

• URL: http://arxiv.org/abs/2404.05901v3
• Date: Wed, 23 Oct 2024 13:28:28 GMT
• Title: Quantum-inspired activation functions and quantum Chebyshev-polynomial network
• Authors: Shaozhi Li, M Sabbir Salek, Yao Wang, Mashrur Chowdhury,
• Abstract summary: We investigate functional expressibility of quantum circuits integrated within a convolutional neural network (CNN) We develop a hybrid quantum Chebyshev-polynomial network (QCPN) based on the properties of quantum activation functions. Our findings suggest that quantum-inspired activation functions can reduce model depth while maintaining high learning capability.
• Score: 6.09437748873686
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Driven by the significant advantages offered by quantum computing, research in quantum machine learning has increased in recent years. While quantum speed-up has been demonstrated in some applications of quantum machine learning, a comprehensive understanding of its underlying mechanisms for improved performance remains elusive. Our study address this problem by investigating the functional expressibility of quantum circuits integrated within a convolutional neural network (CNN). Through numerical experiments on the MNIST, Fashion MNIST, and Letter datasets, our hybrid quantum-classical CNN model demonstrates superior feature selection capabilities and substantially reduces the required training steps compared to classical CNNs. Notably, we observe similar performance improvements when incorporating three other quantum-inspired activation functions in classical neural networks, indicating the benefits of adopting quantum-inspired activation functions. Additionally, we developed a hybrid quantum Chebyshev-polynomial network (QCPN) based on the properties of quantum activation functions. We demonstrate that a three-layer QCPN can approximate any continuous function, a feat not achievable by a standard three-layer classical neural network. Our findings suggest that quantum-inspired activation functions can reduce model depth while maintaining high learning capability, making them a promising approach for optimizing large-scale machine-learning models. We also outline future research directions for leveraging quantum advantages in machine learning, aiming to unlock further potential in this rapidly evolving field.

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