Abstract

The article discusses the search for a global extremum in the training of artificial neural networks using a correlation indicator. A method based on a mathematical model of an artificial neural network presented as an information transmission system is proposed. Drawing attention to the fact that in information transmission systems widely used methods that allow effective analysis and recovery of useful signal against the background of various interferences: Gaussian, concentrated, pulsed, etc., it is possible to make an assumption about the effectiveness of the mathematical model of artificial neural network, presented as a system of information transmission. The article analyzes the convergence of training and experimentally obtained sequences based on a correlation indicator for fully-connected neural network. The possibility of estimating the convergence of the training and experimentally obtained sequences based on the joint correlation function as a measure of their energy similarity (difference) is confirmed. To evaluate the proposed method, a comparative analysis is made with the currently used indicators. The potential sources of errors in the least-squares method and the possibilities of the proposed indicator to overcome them are investigated. Simulation of the learning process of an artificial neural network has shown that the use of the joint correlation function together with the Adadelta optimizer allows us to get again in learning speed 2-3 times compared to CrossEntropyLoss.

中文翻译：

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使用神经网络监督学习的相关指标搜索全局极值

摘要

本文讨论了使用相关指标在人工神经网络训练中寻找全局极值的问题。提出了一种基于人工神经网络数学模型的信息传输系统方法。提请注意以下事实：在信息传输系统中，被广泛使用的方法可以在各种干扰（高斯，集中，脉冲等）干扰的背景下有效分析和恢复有用信号，因此可以对信号的有效性做出假设。人工神经网络的数学模型，表示为信息传输系统。本文基于全连接神经网络的相关指标，分析了训练序列和实验获得的序列的收敛性。证实了基于联合相关函数来估计训练序列和实验获得的序列的收敛性的可能性，以此作为它们的能量相似性（差异）的量度。为了评估所提出的方法，对当前使用的指标进行了比较分析。研究了最小二乘法中潜在的误差源以及提出的指标克服这些误差的可能性。人工神经网络学习过程的仿真表明，联合相关函数与Adadelta优化器的结合使用使我们的学习速度比CrossEntropyLoss还要高2-3倍。