Did you read the article, or the actual research paper? They present a mathematical proof that any hypothetical method of training an AI that produces an algorithm that performs better than random chance could also be used to solve a known intractible problem, which is impossible with all known current methods. This means that any algorithm we can produce that works by training an AI would run in exponential time or worse.

The paper authors point out that this also has severe implications for current AI, too–since the current AI-by-learning method that underpins all LLMs is fundamentally NP-hard and can’t run in polynomial time, “the sample-and-time requirements grow non-polynomially (e.g. exponentially or worse) in n.” They present a thought experiment of an AI that handles a 15-minute conversation, assuming 60 words are spoken per minute (keep in mind the average is roughly 160). The resources this AI would require to process this would be 60*15 = 900. The authors then conclude:

“Now the AI needs to learn to respond appropriately to conversations of this size (and not just to short prompts). Since resource requirements for AI-by-Learning grow exponentially or worse, let us take a simple exponential function O(2n ) as our proxy of the order of magnitude of resources needed as a function of n. 2^900 ∼ 10^270 is already unimaginably larger than the number of atoms in the universe (∼10^81 ). Imagine us sampling this super-astronomical space of possible situations using so-called ‘Big Data’. Even if we grant that billions of trillions (10 21 ) of relevant data samples could be generated (or scraped) and stored, then this is still but a miniscule proportion of the order of magnitude of samples needed to solve the learning problem for even moderate size n.”

That’s why LLMs are a dead end.