人工神经网络(Artificial Neural Network,即ANN),它从信息处理角度对人脑神经元网络进行抽象,建立某种简单模型,按不同的连接方式组成不同的网络。在工程与学术界也常直接简称为神经网络或类神经网络。神经网络是一种运算模型,由大量的节点(或称神经元)之间相互联接构成。每个节点代表一种特定的输出函数,称为激励函数(activation function)。每两个节点间的连接都代表一个对于通过该连接信号的加权值,称之为权重,这相当于人工神经网络的记忆。网络的输出则依网络的连接方式,权重值和激励函数的不同而不同。而网络自身通常都是对自然界某种算法或者函数的逼近,也可能是对一种逻辑策略的表达。

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人工神经网络与其他学科领域联系日益紧密,人们通过对人工神经网络层结构的探索和改进来解决各个领域的问题。根据人工神经网络相关文献进行分析,综述了人工神经网络算法以及网络模型结构的发展史,根据神经网络的发展介绍了人工神经网络相关概念,其中主要涉及到多层感知器、反向传播神经网络、卷积神经网络以及递归神经网络,描述了卷积神经网络发展当中出现的部分卷积神经网络模型和递归神经网络中常用的相关网络结构,分别综述了各个人工神经网络算法在相关领域的应用情况,总结了人工神经网络的未来发展方向。

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The primordial power spectrum informs the possible inflationary histories of our universe. Given a power spectrum, the ensuing cosmic microwave background is calculated and compared to the observed one. Thus, one focus of modern cosmology is building well-motivated inflationary models that predict the primordial power spectrum observables. The common practice uses analytic terms for the scalar spectral index $n_s$ and the index running $\alpha$, forgoing the effort required to evaluate the model numerically. However, the validity of these terms has never been rigorously probed and relies on perturbative methods, which may lose their efficacy for large perturbations. The requirement for more accurate theoretical predictions becomes crucial with the advent of highly sensitive measuring instruments. This paper probes the limits of the perturbative treatment that connects inflationary potential parameters to primordial power spectrum observables. We show that the validity of analytic approximations of the scalar index roughly respects the large-field/small-field dichotomy. We supply an easily calculated measure for relative perturbation amplitude and show that, for large field models, the validity of analytical terms extends to $\sim 3\%$ perturbation relative to a power-law inflation model. Conversely, the analytical treatment loses its validity for small-field models with as little as $0.1\%$ perturbation relative to the small-field test-case. By employing the most general artificial neural networks and multinomial functions up to the twentieth degree and demonstrating their shortcomings, we show that no reasonable analytic expressions correlating small field models to the observables the yield exists. Finally, we discuss the possible implications of this work and supply the validity heuristic for large and small field models.

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