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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Log-Sum-Exp Neural Networks and Posynomial Models for Convex and Log-Log-Convex Data
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Log-Sum-Exp Neural Networks and Posynomial Models for Convex and Log-Log-Convex Data

机译：Log-Sum-Exp神经网络和凸和对数-Log-Log-凸数据的多项式模型

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摘要

In this paper, we show that a one-layer feedforward neural network with exponential activation functions in the inner layer and logarithmic activation in the output neuron is a universal approximator of convex functions. Such a network represents a family of scaled log-sum exponential functions, here named log-sum-exp (LSET). Under a suitable exponential transformation, the class of LSET functions maps to a family of generalized posynomials GPOS(T), which we similarly show to be universal approximators for log-log-convex functions. A key feature of an LSET network is that, once it is trained on data, the resulting model is convex in the variables, which makes it readily amenable to efficient design based on convex optimization. Similarly, once a GPOS(T) model is trained on data, it yields a posynomial model that can be efficiently optimized with respect to its variables by using geometric programming (GP). The proposed methodology is illustrated by two numerical examples, in which, first, models are constructed from simulation data of the two physical processes (namely, the level of vibration in a vehicle suspension system, and the peak power generated by the combustion of propane), and then optimization-based design is performed on these models.
机译：在本文中，我们证明了具有内层指数激活函数和输出神经元对数激活的单层前馈神经网络是凸函数的通用逼近器。这样的网络代表了一系列对数和指数函数，在此称为对数和指数（LSET）。在适当的指数变换下，LSET函数的类映射到广义正定多项式GPOS（T）族，我们类似地将其显示为对数-对数-凸函数的通用逼近器。 LSET网络的一个关键特征是，一旦对它进行了数据训练，结果模型将在变量中凸出，这使得它易于适应基于凸优化的高效设计。同样，一旦在数据上训练了GPOS（T）模型，它就会产生一个多项式模型，该模型可以使用几何编程（GP）对其变量进行有效地优化。通过两个数值示例来说明所提出的方法，其中，首先，根据两个物理过程的模拟数据（即，车辆悬架系统中的振动水平以及丙烷燃烧产生的峰值功率）构建模型。 ，然后在这些模型上执行基于优化的设计。

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