卷积层对离散移位等变，但不对连续平移等变
Convolutional layers are equivariant to discrete shifts but not continuous translations
AI总结：
本文澄清CNN卷积层仅对离散像素移位等变、不对连续平移等变，并建议规范术语以避免混淆。
摘要：
这篇简短而朴素的札记旨在澄清关于卷积神经网络（CNN）的一个常见误解。CNN由卷积层组成，由于权重共享，卷积层具有移位等变性。然而，即使忽略边界效应，并且不存在池化和下采样，卷积层也不具有平移等变性。这是因为移位等变性是一种离散对称性，而平移等变性是一种连续对称性。这一事实在等变机器学习研究者中广为人知，但通常被非专家忽视。为尽量减少混淆，我们建议使用“shift equivariance（移位等变性）”一词指代像素中的离散移位，而用“translation equivariance（平移等变性）”指代连续平移。
英文摘要：
The purpose of this short and simple note is to clarify a common misconception about convolutional neural networks (CNNs). CNNs are made up of convolutional layers which are shift equivariant due to weight sharing. However, convolutional layers are not translation equivariant, even when boundary effects are ignored and when pooling and subsampling are absent. This is because shift equivariance is a discrete symmetry while translation equivariance is a continuous symmetry. This fact is well known among researchers in equivariant machine learning, but is usually overlooked among non-experts. To minimize confusion, we suggest using the term `shift equivariance' to refer to discrete shifts in pixels and `translation equivariance' to refer to continuous translations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
