Regarding your empirical findings which may run counter to the question
Is manifold dimensionality actually a good predictor of which solution will be found?
I wonder if there’s a connection to asymptotic equipartitioning—it may be that the ‘modal’ (most ‘voluminous’ few) solution basins are indeed higher-rank, but that they are in practice so comparatively few as to contribute negligible overall volume?
This is a fuzzy tentative connection made mostly on the basis of aesthetics rather than a deep technical connection I’m aware of.
Yeah, this seems roughly correct, and similar to what I was thinking. There is probably even a direct connection to the “asymptotic equipartitioning” math, via manifold counts containing terms like “A choose B” from permutations of neurons.
Regarding your empirical findings which may run counter to the question
I wonder if there’s a connection to asymptotic equipartitioning—it may be that the ‘modal’ (most ‘voluminous’ few) solution basins are indeed higher-rank, but that they are in practice so comparatively few as to contribute negligible overall volume?
This is a fuzzy tentative connection made mostly on the basis of aesthetics rather than a deep technical connection I’m aware of.
Yeah, this seems roughly correct, and similar to what I was thinking. There is probably even a direct connection to the “asymptotic equipartitioning” math, via manifold counts containing terms like “A choose B” from permutations of neurons.