关于由于数字内存计算中的噪声引起的混乱导致的可解决-不可解决过渡
D C Nguyen1, T Chetaille2, Y-H Zhang3
1Department of Physics and Astronomy, University of South Carolina, Columbia, South Carolina 29208, USA.
Chaos (Woodbury, N.Y.)
|January 9, 2026
概括
噪音会影响数字记忆计算机 (DMM) 的性能. 分析数值和物理噪声揭示了与解决问题的成功相关的混乱过渡,功率光谱有助于控制制度.
科学领域:
- 计算神经科学是一种计算神经科学.
- 复杂的系统复杂的系统.
- 机器学习硬件 机器学习硬件
背景情况:
- 数字记忆计算机 (DMM) 是设计用于组合优化的经典动态系统.
- 它们在计算机上的模拟允许在各种条件下进行性能分析.
- 数字错误和物理噪声对DMM性能的影响未得到充分研究.
研究的目的:
- 调查数值错误和物理噪声如何影响DMM性能.
- 了解噪音引起的混乱过渡,从成功的解决问题到失败.
- 将系统动态与解决问题的能力联系起来.
主要方法:
- 模拟DMM与不同的集成时间步骤 (数值噪声) 和随机扰动 (物理噪声).
- 分析功率光谱和利亚普诺夫指数作为噪声强度的函数.
- 将利亚普诺夫指数和功率光谱与DMM实例可解决性相关联.
主要成果:
- 在实例可解决性和集合平均平均最大莱普诺夫指数的符号之间发现了相关性.
- 存在一种制度,DMM具有正的利亚普诺夫指数仍然可以解决问题.
- 功率光谱区分定期 (峰值) 和混乱 (宽带) 行为,提供控制见解.
- 数字和物理噪声对DMM具有质量上相似的影响.
结论:
- 噪音引起的混乱是DMM解决问题的限制的一个关键因素.
- 利亚普诺夫指数和功率光谱是DMM动态和性能的关键指标.
- 功率光谱有可能引导DMM运行到最佳动态模式.
- 了解噪声效应对于设计强大的DMM至关重要.
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