I didn’t think much about the mathematical problem, but I think that the conjecture is at least wrong in spirit, and that LLMs are good counterexample for the spirit. An LLM by its own is not very good at being an assistant, but you need pretty small amounts of optimization to steer the existing capabilities toward being a good assistant. I think about it as “the assistant was already there, with very small but not negligible probability”, so in a sense “the optimization was already there”, but not in a sense that is easy to capture mathematically.
I didn’t think much about the mathematical problem, but I think that the conjecture is at least wrong in spirit, and that LLMs are good counterexample for the spirit. An LLM by its own is not very good at being an assistant, but you need pretty small amounts of optimization to steer the existing capabilities toward being a good assistant. I think about it as “the assistant was already there, with very small but not negligible probability”, so in a sense “the optimization was already there”, but not in a sense that is easy to capture mathematically.