一个通用网络策略,用于光速计算调节的最佳运输
Yong Shi1, Lei Zheng2, Pei Quan3
1School of Economics and Management, University of Chinese Academy of Sciences, Beijing, 100190, China; Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences, Beijing, 100190, China; Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing, 100190, China.
概括
本研究引入了一种新的神经网络策略来估计运输矩阵,大大降低了最佳运输 (OT) 计算的计算成本. 与Sinkhorn算法等传统方法相比,该方法提供了更好的准确性和效率.
科学领域:
- 机器学习 机器学习
- 计算数学 计算数学 计算数学
- 优化优化 优化优化
背景情况:
- 最佳运输 (OT) 测量了概率分布之间的差异.
- 通过Sinkhorn算法进行透调节的OT对于神经网络来说是计算密集的.
- 高精度要求导致大计算图,消耗大量时间和内存.
研究的目的:
- 开发一个新的网络策略来估计OT中的运输矩阵.
- 为了减少神经网络中的OT计算的计算复杂性和内存足迹.
- 创建一种适用于任意成本函数和变化的边际分布的方法.
主要方法:
- 一个新的网络策略来估计运输矩阵,绕过Sinkhorn算法.
- 在日志域中使用双形式实现,以防止数值不稳定.
- 对于近似输入的理论误差估计.
主要成果:
- 与基于Sinkhorn的方法相比,显著减少了计算图形大小.
- 证明适用于任意成本函数和变化的边际分布.
- 在广泛的实验中,在计算成本和准确性方面表现优于基线方法.
结论:
- 拟议的网络战略为机器学习中的OT计算提供了一个更有效,更准确的替代方案.
- 该方法是稳固的,可以适应各种成本函数和数据分布.
- 对强大的OT和重心计算的扩展是可行的和有效的.
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