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复合优化算法用于Sigmoid网络的复合优化算法
1School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China hxchen@m.scnu.edu.cn.
Neural computation
|July 12, 2023
概括
本研究介绍了Sigmoid网络的新型复合优化算法,即使对于复杂的问题,也确保了对全球最佳的收. 这些发现为基于数据数量的最佳网络大小提供了指导.
科学领域:
- 计算数学 计算数学 计算数学
- 机器学习 机器学习
- 优化理论 优化理论
背景情况:
- 西格状网络在机器学习中被广泛使用,但优化可能具有挑战性.
- 现有的优化方法可能会与sigmoid网络目标的非凸和非光滑性质作斗争.
研究的目的:
- 开发和分析新的复合优化算法,用于解决西格状网络.
- 确保对非凸和非光滑问题的全球最佳解决方案的趋同.
- 提供关于数据大小和网络性能之间的关系的见解.
主要方法:
- 同样地将Sigmoid网络转换为凸的复合优化问题.
- 开发复合优化算法,使用线性近位方法和乘数交替方向方法 (ADMM).
- 在微弱的尖最小值和规律性条件下分析收性质.
主要成果:
- 拟议的算法保证了对非凸和非光滑的西格形网络的全球最佳解决方案的趋同.
- 收率与可用的培训数据量直接相关.
- 数字实验表明,在功能拟合和数字识别任务上,它具有令人满意和强大的性能.
结论:
- 新的复合优化算法有效地解决了西格状网络,即使是复杂的网络.
- 理论上的收保证和实际的表现验证了拟议的方法.
- 这些发现提供了一个数据驱动的指南,用于确定合适的Sigmoid网络大小.
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