论文标题
cnns组的通用近似定理
Universal Approximation Theorem for Equivariant Maps by Group CNNs
论文作者
论文摘要
组对称性是多种数据分布中固有的。保留对称性的数据处理被描述为一张模糊的地图，通常可以有效地实现高性能。卷积神经网络（CNN）已被称为具有均衡性的模型，并显示出某些特定组的近似地图。但是，CNN的通用近似定理已根据每个组和设置分别使用单个技术得出。本文提供了一种统一的方法，以在各种设置中获得CNN的均值图定理的通用近似定理。作为其重要优势，我们可以处理非紧凑型组的无限二维空间之间的非线性模糊图。
Group symmetry is inherent in a wide variety of data distributions. Data processing that preserves symmetry is described as an equivariant map and often effective in achieving high performance. Convolutional neural networks (CNNs) have been known as models with equivariance and shown to approximate equivariant maps for some specific groups. However, universal approximation theorems for CNNs have been separately derived with individual techniques according to each group and setting. This paper provides a unified method to obtain universal approximation theorems for equivariant maps by CNNs in various settings. As its significant advantage, we can handle non-linear equivariant maps between infinite-dimensional spaces for non-compact groups.
