标题： 卷积神经网络的泛化界限 显示英文标题

标题： Generalization Bounds for Convolutional Neural Networks

摘要： 卷积神经网络（CNNs）在包括图像分类、语义分割和目标检测在内的广泛应用中取得了突破性性能。 以往关于表征神经网络泛化能力的研究主要集中在全连接神经网络（FNNs）上，将CNNs视为FNNs的一种特殊情况，而没有考虑卷积层的特殊结构。 在本工作中，我们通过利用其权重矩阵的稀疏性和排列结构，为CNNs提出了一个更紧的泛化界。 由于泛化界依赖于权重矩阵的谱范数，我们进一步研究了三种常用的卷积操作的谱范数，包括标准卷积、深度卷积和点卷积。 理论和实验结果都表明，我们对CNNs的界限比现有的界限更紧。 显示英文摘要

摘要： Convolutional neural networks (CNNs) have achieved breakthrough performances in a wide range of applications including image classification, semantic segmentation, and object detection. Previous research on characterizing the generalization ability of neural networks mostly focuses on fully connected neural networks (FNNs), regarding CNNs as a special case of FNNs without taking into account the special structure of convolutional layers. In this work, we propose a tighter generalization bound for CNNs by exploiting the sparse and permutation structure of its weight matrices. As the generalization bound relies on the spectral norm of weight matrices, we further study spectral norms of three commonly used convolution operations including standard convolution, depthwise convolution, and pointwise convolution. Theoretical and experimental results both demonstrate that our bounds for CNNs are tighter than existing bounds.