4 ms·
> there are fewer local minima in a higher dimension Is it actually proven, or another hypothesis? What is the reason behind this?
by jxy 2y ago
> there are fewer local minima in a higher dimension
Is it actually proven, or another hypothesis? What is the reason behind this?
- jcrites 2y agoJust reasoning about this from first principles, but intuitively, the more dimensions you have, the more likely that you are to find a gradient in some dimension. In an N-dimensional space, a local minimum needs to be a minimum in all N dimensions, right? Otherwise the algorithm will keep exploring down the gradient. (Not an expert on this stuff.) The more dimensions there are, the more likely it seems to be that a gradient exists down to some greater minimum from any given point.