Lotka–Volterra model with mutations and generative adversarial networks

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-02-27 DOI:10.1134/s0040577924020077

S. V. Kozyrev

引用次数: 0

Abstract

A model of population genetics of the Lotka–Volterra type with mutations on a statistical manifold is introduced. Mutations in the model are described by diffusion on a statistical manifold with a generator in the form of a Laplace–Beltrami operator with a Fisher–Rao metric, that is, the model combines population genetics and information geometry. This model describes a generalization of the model of machine learning theory, the model of generative adversarial network (GAN), to the case of populations of generative adversarial networks. The introduced model describes the control of overfitting for generating adversarial networks.

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带有突变和生成式对抗网络的洛特卡-沃尔特拉模型

摘要介绍了一个统计流形上突变的 Lotka-Volterra 型群体遗传学模型。该模型中的突变是通过统计流形上的扩散来描述的，其发生器的形式是带有费雪-拉奥度量的拉普拉斯-贝尔特拉米算子，也就是说，该模型结合了种群遗传学和信息几何学。该模型描述了机器学习理论模型--生成式对抗网络（GAN）模型--在生成式对抗网络种群情况下的一般化。引入的模型描述了生成对抗网络的过拟合控制。

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

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.