Completely agree. Every model/dimensionality-reduction is in some sense compression, isn't it? We are taking a problem space with more parameters and detail a

Completely agree. Every model/dimensionality-reduction is in some sense compression, isn't it? We are taking a problem space with more parameters and detail and reducing it to a solution space with fewer parameters and possibly less detail (depending on whether the solution is exact or not which maps onto the compression being lossy or not). If I take the set of all points that are equidistant from a given point and line, that is an infinite set. But I can compress it down to three real numbers if I know that set can be represented y = ax^2 + bx +c, and noone goes "quadratic equations are just compression". A lot of people try to generate milage out of the idea of the compression being _lossy_ also. That's an intellectual dead end in the same way. Lots of useful models are a lossy compression.