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For me, this question of the relevant scale(s) is the main point of introducing this work. d/w is one example of a cutoff, and one associated with the data distribution is another, but more work needs to be done to understand how to relate potentially different theoretical descriptions (for example, how these two cutoffs work together). We also mention the 'lattice as regulator' as a natural cut-off for physical systems, and hope to find similarly natural scales in real-world AI systems.
here
For example: https://www.lesswrong.com/posts/EhTMM77iKBTBxBKRe/the-laws-of-large-numbers
Thanks for the comment! I do hope that the thoughts expressed here can inspire some action, but I'm not sure I understand your questions. Do you mean 'centralized', or are you thinking about the conditions necessary for many small scale trading zones?
In this way, I guess the emergence of big science could be seen as a phase transition from decentralization -> centralization.
Thanks for your comment! It got me thinking a bit more about big science in general, and led to this post. I'd be curious to hear your thoughts.