A new approach to neural networks using pseudo-differential operators

IF 0.9 3区 数学 Q2 MATHEMATICS
Hang Du, Shahla Molahajloo, Xiaogang Wang
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引用次数: 0

Abstract

In this paper, we initially concentrate on the concept of complex convolutional neural networks, constructing the essential frameworks required for managing complex-valued inputs. We subsequently introduce a novel neural network architecture that replaces the standard convolution operator with a more general operator known as pseudo-differential operators. This unique modification ensures the effective handling of an input’s frequency information through the application of appropriate filters. To validate this approach, we conducted empirical testing on one-dimensional and two-dimensional datasets. The results affirm the convergence and efficacy of this novel architecture, indicating a potential significant advancement in the field of complex neural network development.

Abstract Image

使用伪微分算子的神经网络新方法
在本文中,我们首先集中讨论了复杂卷积神经网络的概念,构建了管理复值输入所需的基本框架。随后,我们引入了一种新颖的神经网络架构,用一种更通用的算子(即伪差分算子)取代了标准卷积算子。这种独特的修改确保了通过应用适当的滤波器来有效处理输入的频率信息。为了验证这种方法,我们在一维和二维数据集上进行了实证测试。结果证实了这一新颖架构的收敛性和有效性,表明它有可能在复杂神经网络开发领域取得重大进展。
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来源期刊
CiteScore
2.20
自引率
9.10%
发文量
59
期刊介绍: The Journal of Pseudo-Differential Operators and Applications is a forum for high quality papers in the mathematics, applications and numerical analysis of pseudo-differential operators. Pseudo-differential operators are understood in a very broad sense embracing but not limited to harmonic analysis, functional analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and novel applications in engineering, geophysics and medical sciences.
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