Concentration of Measure and Global Optimization of Bayesian Multilayer Perceptron. Part I

IF 0.8 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI:10.1134/s1995080224600651

B. K. Temyanov, R. R. Nigmatullin

引用次数: 0

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.

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贝叶斯多层感知器的集中测量和全局优化。第一部分

摘要我们介绍了一个准球面坐标系，该坐标系被引入到具有 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，在这些坐标系中给出的回归损失函数就变成了取决于一组定义在球面和准径向坐标上的函数的总和。球面上的函数满足了度量集中的条件。当参数数趋于无穷大时，这些条件会导致损失函数向准径向对称函数集中。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Lobachevskii Journal of Mathematics MATHEMATICS-

CiteScore

1.50

自引率

42.90%

发文量

127

期刊介绍： Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.