Hmm, the inherent 1d nature of the visualization kinda makes it difficult to check for selection effects. I’m not convinced that’s actually what’s going on here. 1725 is special because the ridges of the splotch function are exactly orthogonal to x0. The odds of this happening probably go down exponentially with dimensionality. Furthermore, with more dakka, one sees that the optimization rate drops dramatically after ~15000 time steps, and may or may not do so again later. So I don’t think this proves selection effects are in play. An alternative hypothesis is simply that the process gets snagged by the first non-orthogonal ridge it encounters, without any serous selection effects coming into play.
Hmm, the inherent 1d nature of the visualization kinda makes it difficult to check for selection effects. I’m not convinced that’s actually what’s going on here. 1725 is special because the ridges of the splotch function are exactly orthogonal to x0. The odds of this happening probably go down exponentially with dimensionality. Furthermore, with more dakka, one sees that the optimization rate drops dramatically after ~15000 time steps, and may or may not do so again later. So I don’t think this proves selection effects are in play. An alternative hypothesis is simply that the process gets snagged by the first non-orthogonal ridge it encounters, without any serous selection effects coming into play.