Wouldn't this also mean that there's an inherent limit to that sort of model?

Not strictly speaking? A universal subspace can be identified without necessarily being finite.

As a really stupid example: the sets of integers less than 2, 8, 5, and 30 can all be embedded in the set of integers less than 50, but that doesn’t require that the set of integer is finite. You can always get a bigger one that embeds the smaller.

On the contrary, I think it demonstrates an inherent limit to the kind of tasks / datasets that human beings care about.

It's known that large neural networks can even memorize random data. The number of random datasets is unfathomably large, and the weight space of neural networks trained on random data would probably not live in a low dimensional subspace.

It's only the interesting-to-human datasets, as far as I know, that drive the neural network weights to a low dimensional subspace.

> Wouldn't this also mean that there's an inherent limit to that sort of model?

If all need just 16 dimensions if we ever make one that needs 17 we know we are making progress instead of running in circles.