论文标题
散射变换及其神经激活概括引起的中央和非中心定理
Central and Non-central Limit Theorems arising from the Scattering Transform and its Neural Activation Generalization
论文作者
论文摘要
通过分析复杂和非平稳的时间序列的动机，我们研究了包括广泛的神经激活功能的散射变换（ST）的概括，这称为神经激活ST（NAST）。总体而言，NAST是一个转换，包括``神经加工单元''的序列，每个序列都将高通滤波器应用于上一层的输入，然后在上一个层的组成中作为非线性函数作为下一个神经元的输出。在这里，非线性函数模型神经元如何被输入信号激发。除了显示非膨胀，水平翻译不可分性和对局部变形的不敏感性之外，高斯过程的统计特性具有各种依赖性和（非）平稳性结构及其与所选高通滤波器的相互作用，并提供了与所选高通滤波器的相互作用，并提供了探索和中心（Clt Theorem and Central Lives limem and（Clt）和非clt theorem and clt Theorem and Cltt theorem and clt Theorem and Cltt and clt and clt and clt and clt and clt and callt。还提供了数值模拟。结果解释了NAST过程如何复杂且非平稳的时间序列，并在非零病例下基于NAST的统计推断铺平了一种方法。
Motivated by analyzing complicated and non-stationary time series, we study a generalization of the scattering transform (ST) that includes broad neural activation functions, which is called neural activation ST (NAST). On the whole, NAST is a transform that comprises a sequence of ``neural processing units'', each of which applies a high pass filter to the input from the previous layer followed by a composition with a nonlinear function as the output to the next neuron. Here, the nonlinear function models how a neuron gets excited by the input signal. In addition to showing properties like non-expansion, horizontal translational invariability and insensitivity to local deformation, the statistical properties of the second order NAST of a Gaussian process with various dependence and (non-)stationarity structure and its interaction with the chosen high pass filters and activation functions are explored and central limit theorem (CLT) and non-CLT results are provided. Numerical simulations are also provided. The results explain how NAST processes complicated and non-stationary time series, and pave a way towards statistical inference based on NAST under the non-null case.
