量子神经触点内核的可表达性诱导的度
Li-Wei Yu1, Weikang Li2, Qi Ye2
1Nankai University, Chern Institute of Mathematics, Tianjin, 300071, CHINA.
Reports on progress in physics. Physical Society (Great Britain)
|October 3, 2024
概括
量子神经网络中的高可表达性会导致量子触点内核值集中到零,影响训练. 这种度问题即使在局部编码中仍然存在,为量子电路设计提供了洞察力.
科学领域:
- 量子机器学习就是量子机器学习.
- 理论计算机科学 理论计算机科学
背景情况:
- 量子触角内核方法分析量子机器学习 (QML) 模型在无限宽限.
- 这些方法对于设计量子电路架构和理解量子神经网络中的训练错误融合至关重要.
研究的目的:
- 为了研究量子触角内核模型的可表达性和值度之间的关系.
- 分析全球和本地量子编码对内核值度的影响.
主要方法:
- 对全球和本地损失函数进行严格的数学证明.
- 广泛的数值模拟来验证理论发现.
主要成果:
- 全球和本地量子编码中的高可表达性导致量子触点内核值的指数集中到全球损失函数的零.
- 这种度问题仍然存在,但对于局部损失函数而言,其部分得到了缓解.
结论:
- 量子神经触角核的度是一个基本特征,仅仅通过使用具有高表达性的本地编码无法避免.
- 结果为设计有效的广度量子变量电路模型提供了关键的见解.
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