Abstract

We present the description of a quasi-spherical coordinate system that is introduced in a space of parameters of a multilayer perceptron with ReLU and Leaky ReLU activation functions. In this instance, a regression loss function that is given in these coordinates becomes the sum of functions that depend on a set of functions defined on a sphere and a quasi-radial coordinate. Conditions for a concentration of measure are satisfied for the functions on the sphere. As a number of parameters tends to infinity, these criteria cause the loss function to concentrate toward a quasi-radially symmetric function.

中文翻译：

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贝叶斯多层感知器的测量集中和全局优化。第一部分

 抽象的

我们提出了准球坐标系的描述，该坐标系被引入具有 ReLU 和 Leaky ReLU 激活函数的多层感知器的参数空间中。在这种情况下，这些坐标中给出的回归损失函数成为依赖于球体和准径向坐标上定义的一组函数的函数之和。球上的函数满足测度集中的条件。由于许多参数趋于无穷大，这些标准导致损失函数集中于准径向对称函数。