I would have thought a triangular grid works better than a grid of squares. You get ~3n links vs ~2n for the square grid. Curious what the AI came up with.

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comboy 20 days ago | parent | next [-]

Yes, not providing visualization of the solution seems criminal.

	▲	red_admiral 20 days ago \| parent \| next [-]
		Unless it's a non-constructive proof.
	▲	kmeisthax 20 days ago \| parent \| prev [-]
		Knowing OpenAI, the solution's probably being withheld as a trade secret, lest it fall victim to distillation attacks (i.e. exactly the same shit they did to the open Internet).

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bustermellotron 20 days ago | parent | prev | next [-]

The grid of squares actually gets > Cn for any C. (More in fact… C can grow like n^a/loglog(n).) The AI proved > n^{1 + b} for some small b > 0, which a human (Will Sawin) has now proved can be about b = 0.014. The grid can be rescaled so the edges are not necessarily length 1, but other pairs will have length 1; that is necessary to get more than 2n unit distances.

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kilotaras 20 days ago | parent | prev [-]

Both 3n and 2n are linear, the broken conjecture is that you can't do better than linear.