Mathematical Sciences: RUI: Applications of Wavelet Analysis to Neural Networks

数学科学：RUI：小波分析在神经网络中的应用

• 批准号: 9404513
• 负责人: Hrushikesh Mhaskar
• 金额: $ 6万
• 依托单位: California State L A University Auxiliary Services Inc.
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-10-01 至 1998-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9404513&HistoricalAwards=false
• 关键词: Mathematical; Sciences; RUI; Applications; Wavelet

The investigator studies the approximation capabilities of afeedforward neural network for approximating functions in different function classes in terms of the activation function used, the number of layers, and the number of neurons. Particular emphasis is placed on dimension-independent bounds and localized approximation by networks. In particular, the research establishes strong connections between the theory of wavelets and neural networks. Applications to the construction of universal time series predictors and pattern classifiers also are studied. The project connects the theory of wavelets with that of neural networks. Both of these theories have numerous applications in such areas as data compression, prediction of time series, target classification, pattern recognition, and signal processing. Both topics of study have therefore flourished during the recent past, for the most part, independently of each other. There do exist certain similarities between the two theories stemming from the fact that they both deal with mathematically similar processes of approximation. The investigator explores these similarities further. In particular, he studies the inherent capabilities and limitations of universal mapping networks and develops efficient training paradigms. A remarkable feature of the networks to be studied is the ease with which the same network can be trained and retrained to perform a variety of tasks using a theoretically guaranteed minimal number of neurons.

研究人员研究了前馈神经网络在使用的激活函数、层数和神经元数量方面逼近不同函数类别中的函数的逼近能力。 特别强调与维度无关的边界和网络的局部逼近。 特别是，该研究在小波理论和神经网络之间建立了紧密的联系。 还研究了构建通用时间序列预测器和模式分类器的应用。 该项目将小波理论与神经网络理论联系起来。 这两种理论在数据压缩、时间序列预测、目标分类、模式识别和信号处理等领域都有广泛的应用。 因此，这两个研究主题在最近一段时间里都蓬勃发展，并且在很大程度上是相互独立的。 这两种理论之间确实存在某些相似之处，因为它们都处理数学上相似的近似过程。 研究人员进一步探讨了这些相似之处。 特别是，他研究了通用地图网络的固有功能和局限性，并开发了有效的训练范例。 要研究的网络的一个显着特征是可以轻松地训练和再训练同一网络，以使用理论上保证的最小数量的神经元执行各种任务。