What is the role of the word sampling in upsampling and downsampling?

Upsampling and downsampling are highly used in deep learning algorithms that involve convolutional neural networks.

Upsampling increases the size downsampling decreases the size of tensors.

What is the role of the word sampling in the words upsampling and downsampling?

Does it always have a connection with the sampling techniques that are generally used in statistics? Or is it true that sometimes it does not have any such connection and the only task of upsampling and downsampling is to increase and decrease respectively the size in any way?

• This is the type of question where providing a few examples of the usage of these words that you have found could be useful. Are you sure that "upsampling" and "downsampling" are widely used in deep learning? Pooling is sometimes called downsampling. So, I suppose that these words occurred in the context of convolutional neural networks, so you may want to use that tag for this post.
– nbro
Oct 5 at 17:08
• Having said that, pooling, indeed can be thought of a way of sampling, i.e. selecting one out of something, but often you do it deterministically (e.g. you take the maximum out of 4 numbers). So, I am not sure if it's really "sampling" if "sampling" implies that it's a stochastic selection, but maybe the definition of "sampling" does not imply that it's a stochastic process. Another thing to consider is if the word "sampling" should only be used when we are talking about the input and output data rather than other parts of the models.
– nbro
Oct 5 at 17:09

I think that this terminology originates from digital signal processing:

Given a signal at a given frequency, one would like to get an approximation of the signal, which would be obtained by sampling with a frequency $$n$$ times higher ($$n$$ times smaller) than for the original signal. The resulting signal should be close to the original in a certain sense - in the Fourier domain, for instance.