AI 中文总结
本研究探讨量子高斯过程回归中量子核的表达性与过拟合平衡问题，通过实证表明小规模过拟合可导致性能崩溃，并提出需仔细选择正则化以优化主动学习性能。
AI 中文摘要
主动学习是机器学习的一种范式，可用于通过从主动查询的训练点训练代理模型来建模昂贵的黑盒函数。该框架的性能在很大程度上取决于代理模型的选择。当代理模型为高斯过程回归（GPR）时，其性能主要由底层核的表达性决定。在本工作中，我们研究了使用量子核改变基于GPR的主动学习计算动态的特殊性，重点关注通过超参数调优对正则化的敏感性。虽然通用的、无结构的核在大规模下遭受指数浓度问题，但我们实证表明，即使在小规模下，过拟合也能使GPR性能崩溃。核正则化可用于抵消这种效应，但由于量子保真度核的平滑性，必须仔细选择正则化以平衡表达性与过拟合。我们的定性结果可迁移到为避免指数浓度而设计的受限量子核的实际应用中，并展示了在近期量子设备上可能对核训练有价值的噪声类型。
英文摘要
Active learning is a paradigm of machine learning that can be utilized to model expensive black-box functions by training a surrogate model from actively queried training points. The performance of this framework depends heavily on the choice of the surrogate model. When the surrogate is Gaussian Process Regression (GPR), its performance is largely determined by the expressivity of the underlying kernel. In this work, we investigate the peculiarities of using a quantum kernel to change the computational dynamics of active learning with GPR, focusing on the sensitivity to regularization by hyperparameter tuning. While generic, unstructured kernels suffer from exponential concentration at large scale, we empirically demonstrate that even at small scale overfitting can collapse GPR performance. Kernel regularization can be used to counteract this effect, but due to the smoothness of the quantum fidelity kernel, regularization must be carefully chosen to balance expressivity and overfitting. Our qualitative results transfer to the practical application of restricted quantum kernels designed to avoid exponential concentration and also present the kinds of noise that may be valuable to kernel training in near-term quantum devices.
