translation-equivariant

Definition

Shift the input and the output shifts by the same amount. Convolution has this property by construction, because the same kernel is applied at every position, which is why a CNN detects an object wherever it appears without needing to see it in every location during training. In practice the property is only approximate: padding, striding, and pooling break it at boundaries and across scales, and added positional encodings remove it deliberately.