It’s always fascinating to apply data/results like from this paper to help evaluate the hypothesis that machine learning/AI is mostly just a rough “lookup table” or memorization.
However real machine learning tries to approximate functions in n-dimensions and that is really, really, really hard to do. Currently no one really has a lookup table. There are some inputs where the error level is acceptably low, and others where the model just isn't optimized enough and the errors are ridiculous. The only question that remains to be answered, is whether any of these high-dimensional functions can actually be found by machine learning, or if we are just stuck with these endless approximations. Also I suppose you could ask if any such functions actually exist; maybe certain phenomena are just pure chaos.
So even if it all is mathematically equivalent to approximate lookup and approximate memorization, that doesn’t mean it’s “just” that.
“We show, however, that deep networks learned by the standard gradient descent algorithm are in fact mathematically approximately equivalent to kernel machines, a learning method that simply memorizes the data and uses it directly for prediction via a similarity function (the kernel)“