Abstract functions are fully representable by function approximations in the limit n->inf; ie., sampling from a circle becomes a circle as samples -> infinity.

This makes all "studies" whose aim is to approximate a fully representable abstract mathematical domain irrelevant to the question.

This is just more evidence of the naivety, mendacity, and pseudoscientific basis of ML and its research.

As you sample all pixels from all photos on a mountain, the pixels don't become the mountain.

The structure of a mountain is not a pattern of pixels. So there is no function for a statistical alg to approximate, no n->infinity which makes the approximation exact.

By sampling from historical pixel patterns in previous images you can generate images in a pixel order that makes sense to a person already acquainted with what they represent. Eg., having seen a mountain (, having perspective, colour vision, depth, counterfactual simulation, imagination, ...).

In all these disagreeably dumb research papers that come out showing "world models" and the like you have the bad mathematicians and bad programmers called "AI researchers" giving a function approximation alg an abstract mathematical domain to approximate.

ie., if the goal is to "learn a circle" and you sample points from a circle, your approximation becomes exact in n->inf, because the target is *ABSTRACT*.

It's so dumb its kinda incomprehensible. It shows what a profound lack of understanding of science is rampent across the discipline.

MNIST, Games, Chess, Circles, Rulesets, etc. are all mathematical objects (shapes, rules). It is trivial to find a mathematical approximation to a mathematical object.

The world is not made out of pixels. Models of pixel patterns are not their targets.

This result is an argument for the conclusion you are reading it as arguing against.

That's because you don't understand what you're reading.