论文标题
pac-bayesian的概括为e夫网络绑定
A PAC-Bayesian Generalization Bound for Equivariant Networks
论文作者
论文摘要
模棱两可的网络通过将这些对称性构建到模型中来捕获有关学习任务的对称性的感应偏见。在本文中，我们研究了模棱两可如何利用PAC Bayesian分析对等效网络的概括错误，其中特征空间的转换定律由组表示确定。通过使用每一层中傅立叶域中的模棱两可网络的扰动分析，我们得出了基于标准的PAC-bayesian泛化边界。边界表征了群体大小的影响，以及不可还能表示对概括误差的影响，从而为选择它们提供了指南。通常，边界表明，在模型中使用较大的组大小会改善广泛的数值实验证实的概括误差。
Equivariant networks capture the inductive bias about the symmetry of the learning task by building those symmetries into the model. In this paper, we study how equivariance relates to generalization error utilizing PAC Bayesian analysis for equivariant networks, where the transformation laws of feature spaces are determined by group representations. By using perturbation analysis of equivariant networks in Fourier domain for each layer, we derive norm-based PAC-Bayesian generalization bounds. The bound characterizes the impact of group size, and multiplicity and degree of irreducible representations on the generalization error and thereby provide a guideline for selecting them. In general, the bound indicates that using larger group size in the model improves the generalization error substantiated by extensive numerical experiments.
