The grammar in this makes it pretty hard to follow

Looks like the start of an interesting article. Needs development.

References:

https://github.com/WinVector/Examples/blob/main/Model_Homoto...

Yeah the GitHub link is the meat of the article. Funny stuff. I also would have assumed that the estimates wouldn't vary as much, naively.

Do you still see such dynamics in the coefficients if you have an order of magnitude more data or fewer dimensions? 100 points in 6D is not much even for linear regression, the model might just be too high variance to interpolate monotonically between the two populations.

The amount of data rapidly factors-out. One cat get the effect even for millions of points in 6d. It is the complexity of the model solution which is going to be degree D-1 polynomials over a shared degree D-1 denominator that drive the effect.

I may be misunderstanding, but wouldn't you see this effect any time you did a k fold cross validation?