用算法稳定性分析量子神经网络泛化能力，揭示噪声的潜在优势。
Stability and Generalization of Quantum Neural Networks
- 引入经典学习理论中的算法稳定性分析量子神经网络
- 在真实数据集上验证理论，发现噪声有助于提升泛化性能
- 提出依赖优化过程的更精细泛化界，适合研究量子机器学习者
量子神经网络（QNNs）在快速发展的量子机器学习领域中扮演关键角色。尽管其经验表现良好，但关于其泛化能力的理论研究仍不充分，主要局限于均匀收敛方法。本文利用经典学习理论中的先进工具——算法稳定性，研究QNN的泛化特性。首先通过均匀稳定性建立了高概率泛化界，揭示了影响QNN泛化性能的关键因素，并为设计与训练提供实践指导。接着探讨了近期内存量子（NISQ）设备上QNN的泛化行为，指出量子噪声可能带来益处。此外，我们指出先前分析给出的是最坏情况下的泛化保证，进而基于平均稳定性建立了依赖优化过程的改进泛化界。多个真实数据集上的数值实验支持了理论结论。
原文摘要 · Abstract (English)
Quantum neural networks (QNNs) play an important role as an emerging technology in the rapidly growing field of quantum machine learning. While their empirical success is evident, the theoretical explorations of QNNs, particularly their generalization properties, are less developed and primarily focus on the uniform convergence approach. In this paper, we exploit an advanced tool in classical learning theory, i.e., algorithmic stability, to study the generalization of QNNs. We first establish high-probability generalization bounds for QNNs via uniform stability. Our bounds shed light on the key factors influencing the generalization performance of QNNs and provide practical insights into both the design and training processes. We next explore the generalization of QNNs on near-term noisy intermediate-scale quantum (NISQ) devices, highlighting the potential benefits of quantum noise. Moreover, we argue that our previous analysis characterizes worst-case generalization guarantees, and we establish a refined optimization-dependent generalization bound for QNNs via on-average stability. Numerical experiments on various real-world datasets support our theoretical findings.
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