@allison @cine @hakui I hope and pray that you are right.

I can see the headlines already:

The New York Post: Brainiac scientist proves that man is better than machine, wins million-dollar fortune. Read below [ad break]

American Scientist: 2035 Breakthrough Prize awarded for mathematical bound on the capabilities of neural architectures

Quanta Magazine: Renegade genius proves that neural architectures are arbitrarily well-approximated in polynomial time, declares "human insight is back on the table."

The actual arXiv preprint: In this paper, we approximate the output of a TWNNK (traditionally well-behaved neural network kernel) by an oracle that terminates in O(n^1384275904375081326409813407498674812650982174937509813745098630897019875108374985732049875943207987509183740918732409170) steps