I think you're right, and the reason is probably that more complex concepts are hierarchies relying on the lower-level concepts to be fully correct before the h

I think you're right, and the reason is probably that more complex concepts are hierarchies relying on the lower-level concepts to be fully correct before the higher levels can function at all. This would create an inherent thresholding that could not be avoided by any choice of metric. To be fair though, the paper's discussion says they are not claiming that models cannot display any emergent abilities, just that some may be mirages.