经典和量子学习算法中关于鲁棒性和准确性的基本问题
Fundamental questions on robustness and accuracy for classical and quantum learning algorithms
AI总结：
本文研究了经典和量子学习算法在噪声和对抗性条件下准确性与鲁棒性之间的关系，提出了新的定义并探讨了权衡与避免权衡的条件。
摘要：
本章介绍并探讨了在噪声和对抗性条件下，经典和量子分类算法中准确性与鲁棒性之间关系的一些基本问题。我们介绍了并澄清了各种鲁棒性和准确性定义，包括被污染实例鲁棒性准确性与预测变化鲁棒性，并区分它们与传统准确性与鲁棒性度量。通过理论分析和玩具模型，我们建立了在何种条件下会出现准确性与鲁棒性准确性之间的权衡，并识别出可以避免此类权衡的场景。所开发的框架突显了模型偏差、噪声特征和扰动类型之间的微妙相互作用，包括相关和不相关扰动。我们探讨了这些结果对不兼容噪声、对抗性量子扰动、无免费午餐定理的影响，并建议从动力系统视角未来方法来研究这些问题。
英文摘要：
This chapter introduces and investigates some fundamental questions on the relationship between accuracy and robustness in both classical and quantum classification algorithms under noisy and adversarial conditions. We introduce and clarify various definitions of robustness and accuracy, including corrupted-instance robustness accuracy and prediction-change robustness, distinguishing them from conventional accuracy and robustness measures. Through theoretical analysis and toy models, we establish conditions under which trade-offs between accuracy and robustness accuracy arise and identify scenarios where such trade-offs can be avoided. The framework developed highlights the nuanced interplay between model bias, noise characteristics, and perturbation types, including relevant and irrelevant perturbations. We explore the implications of some of these results for incompatible noise, adversarial quantum perturbations, the no free lunch theorem, and suggest future methods to examine these problems from the lens of dynamical systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
