Things that do not change over time or space is called statistical invariance. For example in image recognition, the presence of the image in the left side or the right side or any position is not relevant. Similarly in a text the position of the text “kitten”  in any part of the passage does not matter. Kitten is a kitten wherever it is placed in a text.

Such examples are the cases of the statistical invariance.

But how do we tell our deep learning networks that the image can be anywhere. It would be awesome if we could do so and the algorithm could know it and deal accordingly ?

The answer is the  translation variance. And this lead to the development of the convolutional networks. And in the convolutional network, they share the parameters across the weight.