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One underestimated approach to making superintelligence: designing the right prompt chain. If a smart person can come up with a genius idea/breakthrough through the right obsessive thought process, so too should a smart LLM be able to come up with a genius idea/breakthrough through the right obsessive prompt chain.
In this frame, the "self-improvement" which is often discussed as part of the path toward superintelligence would look like the LLM prompt chain improving the prompt chain, rather than rewiring the internal LLM neural nets themselves.