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Abstract <p>The problem of approximating nonlinear vector transformations using neural network algorithms is considered. In addition to approximation, one of the reasons for algorithms reaching local minima rather than global minima of the loss function during optimization is identified: the “switching off” or “death” of a significant number of neurons during training. A multidimensional neural mapping algorithm is proposed, programmatically implemented, and numerically investigated to drastically reduce the influence of this factor on approximation accuracy. The theory and results of numerical experiments on approximation using neural mapping are presented.</p>

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Deep Mapping Algorithm for More Effective Neural Network Training

  • 期刊论文

  • 发表日期：

    2025年12月19日

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  • H. Shen,
  • V. S. Smolin

摘要

Abstract

The problem of approximating nonlinear vector transformations using neural network algorithms is considered. In addition to approximation, one of the reasons for algorithms reaching local minima rather than global minima of the loss function during optimization is identified: the “switching off” or “death” of a significant number of neurons during training. A multidimensional neural mapping algorithm is proposed, programmatically implemented, and numerically investigated to drastically reduce the influence of this factor on approximation accuracy. The theory and results of numerical experiments on approximation using neural mapping are presented.