LLMs can code in the same way they can use natural languages. But we know that programming languages have structure, we made them that way, from scratch, using Chomsky's theory no less.

Saying that because LLMs can learn programming languages using a different approach and therefore disprove the very theory they are built on is absurd.

Anyways, the paper is long and full of references, I didn't analyse it, does it include looks inside the model? For example, for LLMs to write code correctly, the structure of programming languages must be encoded somewhere in the weights of the model. A way to more convincingly disprove Chomsky's ideas would be to find which part of the network encodes structure in programming languages, and show that there is nothing similar for natural languages.