  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.
