无限维度的水库计算计算
Lukas Gonon1, Lyudmila Grigoryeva2, Juan-Pablo Ortega3
1Imperial College, Department of Mathematics, London, United Kingdom.
概括
这项研究引入了一个新的类型的动态系统储水库计算,证明近似和泛化使用回声状态网络的边界. 这些发现使得一种新的循环神经网络算法能够避免维度的诅咒.
科学领域:
- 机器学习 机器学习
- 动态系统理论 动态系统理论
- 计算神经科学是一种神经科学.
背景情况:
- 储计算为使用循环神经网络处理时间序列数据提供了一个框架.
- 一般化的巴伦函数代表了一类具有特定近似性质的函数.
- 将这些功能扩展到动态系统对于先进的机器学习应用至关重要.
研究的目的:
- 介绍和分析基于一般化的巴伦函数的新类动态输入/输出系统.
- 在这个新类中建立近似和概括的理论界限.
- 为这些系统开发一个学习算法,它是高效的,避免了维度的诅咒.
主要方法:
- 使用随机生成的回声状态网络 (ESN) 具有线性或ReLU激活功能,用于水库架构.
- 使用随机生成的神经网络,仅在输出层进行训练 (极端学习机器/随机特征网络),用于读取.
- 导出了近似和泛化界限的理论证明.
主要成果:
- 建立了一个新的,丰富的动态系统类别,具有通用近似属性.
- 证明随机生成的ESN可以有效地近似和估计该类内的元素.
- 开发了一种基于神经网络的循环学习算法,具有可证明的融合保证.
结论:
- 拟议的框架为学习复杂动态系统提供了理论基础的方法.
- 开发的算法有效地学习了一般化的巴伦函数类内的输入/输出系统,而不会屈服于维度的诅咒.
- 这项工作促进了对水库计算用于动态系统建模的理解和应用.
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