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I remembered your phase transition idea, because it's very appealing to signify emergent capabilities.

GPT-4's ability to self-reflect (something 3.5 can't do) might be such phase transition:

https://www.youtube.com/watch?v=5SgJKZLBrmg

I'm writing a post about the Singularity, arguing that the tools for the self-improvement loops are all here already, self-reflection alone might be enough.

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Full argument, and GPT-4 agrees that it's a viable strategy for self-improving AI:

https://www.magyar.blog/p/singularity-we-have-all-the-loops

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