提出噪声下量子模型的依赖数据泛化界,提升对量子机器学习可泛化性的理解。
Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise
- 基于量子费舍尔信息矩阵构建数据相关泛化界
- 揭示参数空间体积与训练规模对泛化能力的影响
- 适合研究量子机器学习鲁棒性与模型复杂度的学者
量子机器学习为解决复杂问题提供了变革性方法,但近端量子设备中的固有噪声阻碍了其实际应用。这一障碍使得难以理解量子电路模型的泛化能力。在噪声环境下设计稳健的量子机器学习模型,需要超越经典容量度量的、关于复杂性和泛化性的原则性理解。本研究探讨了噪声影响下参数化量子机器学习模型的泛化特性。我们提出了一个基于量子费舍尔信息矩阵的数据依赖泛化界。通过统计学习理论,将参数空间体积与训练样本规模关联,以估计训练后模型的泛化能力。我们通过量子费舍尔信息矩阵特征值定义的局部参数邻域和有效维度,系统刻画了量子模型的复杂性。此外,分析了该界紧致性,并讨论了模型表达能力与泛化性能之间的权衡。
原文摘要 · Abstract (English)
Quantum machine learning offers a transformative approach to solving complex problems, but the inherent noise hinders its practical implementation in near-term quantum devices. This obstacle makes it difficult to understand the generalizability of quantum circuit models. Designing robust quantum machine learning models under noise requires a principled understanding of complexity and generalization, extending beyond classical capacity measures. This study investigates the generalization properties of parameterized quantum machine learning models under the influence of noise. We present a data-dependent generalization bound grounded in the quantum Fisher information matrix. We leverage statistical learning theory to relate the parameter space volumes and training sizes to estimate the generalization capability of the trained model. We provide a structured characterization of complexity in quantum models by integrating local parameter neighborhoods and effective dimensions defined through quantum Fisher information matrix eigenvalues. We also analyze the tightness of the bound and discuss the tradeoff between model expressiveness and generalization performance.
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